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As one of the largest frequency regulation markets, the Pennsylvania-New Jersey-Maryland Interconnection (PJM) market allows extensive access of Battery Energy Storage Systems (BESSs). The designed signal regulation D (RegD) is friendly for use with BESSs with a fast ramp rate but limited energy. Designing operating strategies and optimizing the sizing of BESSs in this market are significantly influenced by the regulation signal. To represent the inherent randomness of the RegD signal and reduce the computational burden, typical frequency regulation scenarios with lower resolution are often generated. However, due to the rapid changes and energy neutrality of the RegD signal, generating accurate and representative scenarios presents challenges for the methods based on shape similarity. This paper proposes a novel probability-based method for generating typical regulation scenarios. The method relies on the joint probability distribution of two features with a 15-min resolution, extracted from the RegD signal with a 2 s resolution. The two features can effectively portray the characteristic of RegD signal and its influence on BESS operation. Multiple regulation scenarios are generated based on the joint probability distributions of these features at first, with the final typical scenarios chosen based on their probability distribution similarity to the actual distribution. Utilizing regulation data from the PJM market in 2020, this paper validates and analyzes the performance of the generated typical scenarios in comparison to existing methods, specifically K-means clustering and the forward scenarios reduction method. [ABSTRACT FROM AUTHOR]

Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian‐like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian‐like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability. I examine empirical work that sheds light on the idea that animals can make decisions in a Bayesian‐like manner. I show evidence that animals are sensitive to variation in reward options and can make probabilistic inferences, two foundations of Bayesian‐like estimation. I also show that Bayesian models often predict the behavior of individuals in different environmental contexts. [ABSTRACT FROM AUTHOR]

Multivariate time series anomaly detection is a crucial data mining technique with a wide range of applications in areas such as IT applications. Currently, the majority of anomaly detection methods for time series data rely on unsupervised approaches due to the rarity of anomaly labels. However, in real-world scenarios, obtaining a limited number of anomaly labels is feasible and affordable. Effective usage of these labels can offer valuable insights into the temporal characteristics of anomalies and play a pivotal role in guiding anomaly detection efforts. To improve the performance of multivariate time series anomaly detection, we proposed a novel deep learning model named EDD (Encoder-Decoder-Discriminator) that leverages limited anomaly samples. The EDD model innovatively integrates a graph attention network with long short term memory (LSTM) to extract spatial and temporal features from multivariate time series data. This integrated approach enables the model to capture complex patterns and dependencies within the data. Additionally, the model skillfully maps series data into a latent space, utilizing a carefully crafted loss function to cluster normal data tightly in the latent space while dispersing abnormal data randomly. This innovative design results in distinct probability distributions for normal and abnormal data in the latent space, enabling precise identification of anomalous data. To evaluate the performance of our EDD model, we conducted extensive experimental validation across three diverse datasets. The results demonstrate the significant superiority of our model in multivariate time series anomaly detection. Specifically, the average F1-Score of our model outperformed the second-best method by 2.7% and 73.4% in both evaluation approaches, respectively, highlighting its superior detection capabilities. These findings validate the effectiveness of our proposed EDD model in leveraging limited anomaly samples for accurate and robust anomaly detection in multivariate time series data. [ABSTRACT FROM AUTHOR]

Given the constraints on the invariant distribution in chaotic systems, flexibly setting the probability distribution of chaotic signals poses a significant challenge. To tackle this issue, this paper proposes a strategy that transforms the task into solving and modifying the probability density function of the chaotic intrinsic signal. Initially, kernel density estimation algorithms are employed to address the issue of obtaining smooth probability density functions for high-dimensional chaotic signals. Any chaotic signal can serve as the intrinsic signal source, with its probability density function and distribution function being solvable using this algorithm. Subsequently, a graph-based transformation algorithm is introduced for the flexible adjustment of chaotic signal probability distribution. This algorithm can convert the intrinsic signal into a chaotic signal with the desired distribution type based on the characteristics of the target distribution, providing an analytical expression for the transformation relationship. Finally, the effectiveness of this strategy is validated by generating uniform distribution chaotic signals using a Chua chaotic signal as the intrinsic source. The outstanding performance of this signal in suppressing common-mode conducted electromagnetic interference in high-frequency converters is highlighted. The experimental results demonstrate this strategy's ability to flexibly configure probability distribution types of chaotic signals. Additionally, chaotic signals with a uniform distribution can achieve uniform power spectrum shaping, with a suppression effect on maximum common-mode conducted electromagnetic interference reaching 16.56 dB. [ABSTRACT FROM AUTHOR]

We introduce a new unified extension of the integral form of Euler's beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer's confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function. [ABSTRACT FROM AUTHOR]

Evidence suggests that the critical rainfall thresholds are among the most important factors for flash flood early warnings. In this article, Mingshan River of Ya'an is taken as an example for the contrastive analysis of four rainfall thresholds quantitative approaches, three data-driven statistical inductive approaches, and a hydrologic-dynamic approach are employed in this article to analyze the rainfall threshold of flash flood disaster of various rainfall duration(1, 3, 6, 12, 24 h). The results indicate that the single gauge thresholds approach applies to the scenarios with even-distributed and dense rain gauges. The regional thresholds approach employs areal precipitation instead of single gauge, is applicable to the scenarios with an inadequate amount of gauges, and the thresholds given by this approach are relatively low. The common frequency approach quantifies rainfall thresholds takes a long series of historic gauge data as the sample, and uses probability density functions to obtain the rainfall thresholds linked to the specific frequencies of local flash floods. The results given by the common frequency approach suggest that the fitting curve given by generalized extreme value distribution is optimal, while logarithmic normal distribution and Gumbel distribution are suboptimal. The simple data requirements are the distinctive advantage of this approach and could be applied in scenarios with inadequate flash flood records and rain gauges, but the shortcoming is that the quantified thresholds tend to be artificially high while the frequencies of flash floods are underestimated. Practically, this shortcoming could be reduced by bringing in appropriate attenuation coefficients. The hydrologic-dynamic approach, namely Flood Area hydro-model, applies to the refined simulation of the flash flood life cycle process of the small-sized montane basin. The shortcoming of this approach is that the calculated lowest early warning threshold tends to be overestimated and flash floods are triggered by higher precipitations. In general, thresholds given by data-driven statistical inductive approaches tend to be overestimated, while thresholds given by hydrologic-dynamic approach tend to be underestimated, and multi-methods examinations and modifications are imperative in practice. [ABSTRACT FROM AUTHOR]

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained. [ABSTRACT FROM AUTHOR]

We studied the earthquake detection capacity of DONET (Dense Oceanfloor Network system for Earthquakes and Tsunamis) operating in the Nankai Trough, a target region monitored for future megathrust earthquakes. The focus of this paper was to evaluate the impact on this capacity from the malfunction of parts of the network. For this purpose, the completeness magnitude, above which all earthquakes are considered to be detected by a seismic network, was used. Then, a catalog that includes events observed by DONET was used. We found spatiotemporal variability of completeness magnitude, ranging from values below 1 in one of the areas where stations are densely deployed to values above 2 at the periphery and outside of the DONET area. We conducted a simulation computation for cases of malfunction of densely distributed stations. The results showed that completeness estimates in the area near the malfunctioning stations were about 1 magnitude larger. This implies that malfunction repair and/or replacement with new stations would be desirable because they pronouncedly affect earthquake monitoring. We then demonstrated an example of how to use the information of completeness magnitude as prior knowledge to compute the b value of the Gutenberg-Richter distribution. The result indicates the b value as a proxy that can help to image stress heterogeneity when there is a magnitude-6 class slow slip event on the Nankai Trough plate boundary. [ABSTRACT FROM AUTHOR]

Silver iodide is a prototype compound of superionic conductors that allows ions to flow through its structure. It exhibits a first-order phase transition at 420 K, characterized by an abrupt change in its ionic conductivity behavior, and above this temperature, its ionic conductivity increases by more than three orders of magnitude. Introducing small concentrations of carbon into the silver iodide structure produces a new material with a mixed conductivity (ionic and electronic) that increases with increasing temperature. In this work, we report the experimental results of the ionic conductivity as a function of the reciprocal temperature for the (AgI)x − C(1−x) mixture at low carbon concentrations (x = 0.99, 0.98, and 0.97). The ionic conductivity behavior as a function of reciprocal temperature was well fitted using a phenomenological model based on a random variable theory with a probability distribution function for the carriers. The experimental data show a proximity effect between the C and AgI phases. As a consequence of this proximity behavior, carbon concentration or temperature can control the conductivity of the (AgI)x − C(1−x) mixture. [ABSTRACT FROM AUTHOR]

In the regional flood frequency analysis, the selection of important site characteristics and a suitable number of clusters have a significant role in finding homogeneous regions. Generally, it is difficult to determine the exceedance threshold value or the number of average peaks per year (λ) in Partial Duration Series (PDS), and this difficulty is intensified in the context of regional frequency analysis, though, there are only limited studies to report this difficulty. In the present study, the Mahanadi basin is divided into homogeneous regions by using fifteen effective variables by applying different clustering techniques. Factor analysis has been introduced in finding suitable site variables. Out of fifteen variables, nine variables are selected based on factor analysis loadings. Two hard clustering techniques i.e. Hierarchical (HC), K-Means Clustering (KM) along with the Fuzzy C-Mean Clustering (FCM) techniques are used for finding out the possible number of clusters. To validate the results we used cluster validation indices to locate the optimal number of clusters. Results of the homogeneous region found from the FCM and KM hard clustering approach are more accurate and more robust than HC. The suitability of many frequency distributions to be used in the regional frequency is inspected. The results confirmed that the Generalized Pareto (GP) best described the PDS in the study area and also, show that the best PDS/GP performance is found in almost all the values of λ (2, 2.5, and 3). To test the homogeneity and to identify the best-fit frequency distribution, a regional L-moment algorithm is used. A unique regional flood frequency equation is developed which estimates the flood quantiles of ungauged catchments for each region of the basin and an index flood is also specified concerning catchment characteristics by using the multiple linear regression approach for designing small and medium hydraulic structures in the basin. The results are compared with the previous studies of flood frequency in this basin. [ABSTRACT FROM AUTHOR]

To study the distribution of corrosion depth along the longitudinal direction of tensile steel bars embedded in recycled aggregate concrete (RAC) beams under static loads, a total of 12 RAC beams were designed for accelerated corrosion testing by considering three types of recycled coarse aggregate (RCA) replacement ratios (i.e. 0%, 50% and 100%) and four kinds of static load levels (i.e. 0, 0.2, 0.4 and 0.6). The results demonstrated that the corrosion depth of tensile reinforcement showed an increasing trend with the increase of static load level. The maximum corrosion depth had a good quadratic polynomial relationship with the average corrosion depth of tensile reinforcement and increased with the average corrosion depth. For beams with the same RCA replacement ratio, there was a good linear relationship between the overall uneven corrosion coefficient and average mass loss of tensile reinforcement. The probability distribution type of corrosion depth along the longitudinal direction of tensile reinforcement was mainly a lognormal distribution. An increase in both RCA replacement ratio and static load level could make the probability distribution curve of corrosion depth move to the right, as well as increase the dispersion of corrosion depth around its mean value. [ABSTRACT FROM AUTHOR]

A strategy to obtain the DNA base-pair sequence is proposed from the information of the time series data of the size fluctuations (breathing) of local denaturation zones (bubbles). In one of the previous publication of the author,1 it was shown how the DNA stability parameters were evaluated from an equilibrium distribution profile of bubble opening for a known sequence of heteropolymeric DNA. This paper attempts to know whether the reverse could be done, i.e., by knowing the stability parameters and the distribution profile for an unknown DNA sequence, whether the proper base-pair sequence can be evaluated or not. To get the DNA sequence, a non-trivial search process has been used. The problem has been cast as one of optimization problem and stochastic optimizer Genetic Algorithm has been used to optimize the DNA sequence in order to reach the correct or objective equilibrium distribution profile. We have tested the strategy for three DNA sequences, L33B9, L42B18 and the promoter sequence of the T7 bacteriophage. The DNA base pair sequence could be obtained from the information of the time series data of the size fluctuations (breathing) of local denaturation zones (bubbles). The problem has been cast as one of optimization problem and stochastic optimizer Genetic Algorithm. [ABSTRACT FROM AUTHOR]

Free Space Optical Quantum Communication (FSOQC) is a new wireless approach that allows users to communicate in a secure and faster manner. The working mode of quantum communication is based on quantum physics and is somewhat probabilistic in nature. In order to carry quantum signal in a scattered environment, it is needed to derive the probability distribution of transmittance for a specified region at a desired communication link distance. To understand the performance of FSOQC under adverse weather condition, the effects of various atmospheric parameters such as fog, rain, and turbulence need to be analyzed. In the present study, an attempt is made to predict transmittance for a tropical location, Kolkata, India in real-time conditions, and Keyrate is estimated based on the predicted transmittance. The diurnal, monthly and yearly variation of transmittance is analyzed which is required for effective implementation of a quantum communication system. Two alternative situations, with and without sunlight are considered for Keyrate computation. A combination of two techniques, Difference Frequency Generation and Spontaneous Parametric Down Conversion has been applied to increase Keyrate under adverse weather condition. The operating wavelength is 800 nm, and combined technique is developed around that wavelength. [ABSTRACT FROM AUTHOR]

The scoring habits of experts are embodied in expert evaluation scale (EES). We show that many inaccurate consensus and ranking results can occur in group decision making (GDM) problems without considering EES. To remove the impacts of EESs, we propose the definition of EES and the uniform EES (UEES) strategy. Then, we prove the influence of the selection of UEES strategy on two consistency measures and two aggregation operators. In real-world GDM problems, a decision maker (DM) usually hopes that the final scores of alternatives are subject to his/her desired distribution. Therefore, a novel ranking method by UEES strategy is proposed to obtain DM's desired final scores. Finally, a numerical example is used to clarify the effectiveness of the proposed method, and a simulation experiment shows that the proposed method is more suitable for large sample cases but the accuracy is still at a high level under small sample cases. [ABSTRACT FROM AUTHOR]

Heavy rainfall has consistently acted as the primary catalyst for floods, resulting in numerous casualties and significant economic losses globally. Rainfall forecasting is accomplished by analysing existing rainfall data, which is then used to analyse the hydraulic system's features. Gaining an understanding of rainfall requirements is a crucial challenge for every location, particularly in the case of India, given its diverse geographical area, population, and other influencing factors that impact various demands. This study evaluated the rainfall data for a span of 1990-2021 in six districts of Kerala State, India. To match the rainfall data from all districts, we utilized both Kaumarasamy-distribution and Dagum-distributions. Various Probabilistic tests, were employed to comparing these distributions. The results revealed that, in Kasargod, the Kumarasamy distribution demonstrates superior goodness-of-fit with the lowest Kolmogorov-Smirnov statistic (0.0597) and Anderson-darling statistic (2.271). However, in Wayanad, Malappuram, Palakkad, Idukki, and Trivandrum, the Dagum distribution consistently exhibits the most accurate fit, evident from its lowest Kolmogorov-Smirnov statistics (0.07447, 0.05435, 0.0556, 0.03636, 0.04291) and favourable Chi-Squared statistics (19.471, 8.4907, 19.239, 5.7318, 7.5297). These results emphasize the regional variation in precipitation data and the suitability of specific distribution models for accurate representation across different locations. [ABSTRACT FROM AUTHOR]

It has recently been remarked that the argument for physicalism from the causal closure of the physical is incomplete. It is only effective against mental causation manifested in the action of putative mental forces that lead to acceleration of particles in the nervous system. Based on consideration of anomalous, physically unaccounted-for correlations of neural events, I argue that irreducible mental causation whose nature is at least prima facie probabilistic is conceivable. The manifestation of such causation should be accompanied by a local violation of the Second Law of thermodynamics. I claim that mental causation can be viewed as the disposition of mental states to alter the state probability distribution within the nervous system, with no violation of the conservation laws. If confirmed by neurophysical research, it would indicate a kind of causal homogeneity of the world. Causation would manifest probabilistically in both quantum mechanical and psychophysical systems, and the dynamics of both would be determined by the temporal evolution of the corresponding system state function. Finally, I contend that a probabilistic account of mental causation can consistently explain the character of selectional states that ensure the uniformity of causal patterns, as well as the fact that different physical realizers of a mental property cause the same physical effects in different contexts. [ABSTRACT FROM AUTHOR]

Diameter at breast height (DBH) is a unique attribute used to characterize forest growth and development for forest management planning and to understand forest ecology. Forest managers require an array of DBHs of forest stands, which can be reconstructed using selected probability distribution functions (PDFs). However, there is a lack of practices that fit PDFs of sub-dominating species grown in natural mixed forests. This study aimed to fit PDFs and develop predictive models for PDF parameters, so that the predicted distribution would represent dynamic forest structures and compositions in mixed forest stands. We fitted three of the simplest forms of PDFs, log-normal, gamma, and Weibull, for the DBH of eight tree species, namely balsam fir (Abies balsamea [L.] Mill.), eastern white pine (Pinus strobus L.), paper birch (Betula papyrifera Marshall), red maple (Acer rubrum L.), red pine (Pinus resinosa Aiton), sugar maple (Acer saccharum Marshall), trembling aspen (Populus tremuloides Michx), and white spruce (Picea glauca [Moench] Voss), all grown in natural-origin mixed forests in Ontario province, Canada. We estimated the parameters of the PDFs as a function of DBH mean and standard deviation for these species. Our results showed that log-normal fit the best among the three PDFs. We demonstrated that the predictive model could estimate the recovered parameters unbiasedly for all species, which can be used to reconstruct the DBH distributions of these tree species. In addition to prediction, the cross-validated R2 for the DBH mean ranged between 0.76 for red maple and 0.92 for red pine. However, the R2 for the regression of the standard deviation ranged between 0.00 for red pine and 0.69 for sugar maple, although it produced unbiased predictions and a small mean absolute bias. As these mean and standard deviations are regressed with dynamic covariates (such as stem density and stand basal area), in addition to climate and static geographic variables, the predicted DBH distribution can reflect change over time in response to management or any type of disturbance in the regime of the given geography. The predictive model-based DBH distributions can be applied to the design of appropriate silviculture systems for forest management planning. [ABSTRACT FROM AUTHOR]

Abstract We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.

Probability-based methodologies have gained widespread recognition for their pivotal role in steering decision-making in contexts marked by uncertainty or vagueness. In order to guarantee that decisions made in these circumstances are both significant and impactful, various methodologies focused on probability have been devised and utilized. This study seeks to significantly enrich the existing literature by proposing a new probability model termed the weighted sine exponentiated Weibull distribution. Certain characteristics are obtained for the suggested model. Additionally, the parameter estimation method and simulation studies related to the suggested model are also provided. Two distinct data sets, acquired from the disciplines of physical education and reliability, were effectively implemented using the proposed model, resulting in a successful outcome. Through the utilization of the p-value and various tests, it becomes apparent that the weighted sine exponentiated Weibull model consistently surpasses its competitor distributions in terms of statistical significance. The proposed model’s practical illustration highlights its effectiveness and potential for extensive use in both physical education and reliability research and practice.

Yager (2014) proposed a transformation for negating the happening of an uncertain event which opposes the occurrence of any uncertain event by redistributing its probability equally among the other outcomes. Yager's negation applied repeatedly on any probability distribution converges to the uniform distribution (all events having identical probability of occurrence). In most cases, uniform distribution is the maximum entropy probability distribution (MEPD) as it has maximum uncertainty inherent in it. However, if some information is available regarding the occurrence of events associated with a random experiment, then MEPD may or may not be a uniform distribution. In this work, we have first explored some new properties of Yager's negation and then investigated Yager's negation when we have some additional information about the probability distribution other than the natural constraints. The MEPD in the presence of this additional information is determined using the negation of probabilities. It is shown that the existence of MEPD (and as a result the maximum entropy) largely depends on the parameters of the additional constraints. Some numerical examples have been considered for comparing the MEPD with and without additional constraints. [ABSTRACT FROM AUTHOR]

In this article, we present a novel approach to fatigue life prediction based on a Jenkin–Masing model. The Jenkin–Masing model describes the mechanical response of a material through a large number of parallel microelements, which are taken to be elastic-perfectly plastic with different yield strengths. Even below the macroscopic yield of the material, plastic strain is accumulated in the weaker microelements during cyclic loading. These microelements are taken to fail when a critical level of plastic strain is accumulated in them. We study the monotonic response, cyclic behavior and fatigue life of this model. In particular, the model shows how different realizations of distributions of microelement strengths may show similar monotonic behavior but very different fatigue behavior. This model provides insight into the origin of the large scatter in fatigue life widely observed in experimental results. [ABSTRACT FROM AUTHOR]

This study explores a new family of distributions to enhance the analysis capabilities of COVID-19 events, providing valuable insights for informed decision-making and effective public health management. Accurate understanding and prediction of COVID-19 transmission patterns and their impacts are crucial in reducing the mortality rate, especially in proactive control and mitigation efforts. The proposed approach focuses on a best-fit probabilistic model that incorporates a comprehensive assessment of various statistical measures. Additionally, seven well-recognized classical point estimation methods are employed to identify the most suitable approach for assisting epidemiologists in their analysis. The study analyzes COVID-19 data from multiple countries, including the Netherlands, Mexico, the United Kingdom, China, Canada, Saudi Arabia, and Italy, considering different aspects such as mortality rates and the number of deaths. By evaluating the performance of the new alpha generated family of distributions in modeling COVID-19 events. This research contributes to the advancement of our understanding of the disease's probabilistic nature. The findings have practical implications, guiding the development of public health policies, resource allocation strategies, and intervention plans, ultimately facilitating more effective control and mitigation of COVID-19 outbreaks.

Aiming at the problem of uncertainty and complexity of battlefield situation, which leads to the poor accuracy of risk prediction in the process of research and judgment, it is proposed to build a situation-risk model and construct the risk possibility distribution in order to realize the accurate prediction of risk. Firstly, the risk prediction index system is established from the enemy situation, our situation and the battlefield environment situation research and judgment content; secondly, the role of situation information on the risk is analyzed, and the risk model such as exponential, Z-type, tangent and so on is constructed and the risk value interval is calculated; then, based on the fuzzy function constructing method in the possibility theory, and relying on the weighting difference and uncertainty measurement, the risk possibility distribution is constructed within the risk value interval. Finally, an example of a defense mission is used to verify the feasibility and reasonableness of the proposed method by combining the expert system and cloud modeling methods in an experiment. The results show that the proposed method can fully take into account the uncertainty of situational information in risk prediction, which provides an important basis for subsequent planning decision-making.

This paper examines the distribution of eigenvalues for a 2 × 2 random confusion matrix used in machine learning evaluation. We also analyze the distributions of the matrix's trace and the difference between the traces of random confusion matrices. Furthermore, we demonstrate how these distributions can be applied to calculate the superiority probability of machine learning models. By way of example, we use the superiority probability to compare the accuracy of four disease outcomes machine learning prediction tasks. [ABSTRACT FROM AUTHOR]

Based on the daily rainfall data and interpolation data of 53 meteorological stations in and around the Yongding River Basin in the past 60 years, the evolution characteristics of precipitation in the Yongding River Basin from 1960 to 2019 were analyzed by various variation diagnosis methods. The results show that a) the annual rainfall in the Yongding River Basin has a downward trend. On the seasonal scale, the summer rainfall has a significant downward trend, and the spring, autumn and winter rainfalls have an upward trend. b) In terms of spatial distribution, the annual precipitation shows an insignificant downward trend in most areas, a significant downward trend in a small area below the Guanting Reservoir, and an insignificant upward trend in spring, autumn and winter, only an insignificant downward trend in some areas. On the contrary, the summer precipitation shows a downward trend in most areas of the basin. c) After the abrupt change of precipitation, the distribution function of annual precipitation increases at the minimum value and decreases at the maximum value, and the distribution function of precipitation in July and August decreases as a whole. [ABSTRACT FROM AUTHOR]

The beetle antennae search algorithm (BAS) is inspired by the search behavior of long-horned beetles and is widely used in optimization problems. However, in the typical BAS algorithm, there are problems such as the insufficient optimization ability of beetle individuals and the lack of consideration of historical dynamic information in the algorithm search process, resulting in sufferings from local optimum, low diversity, and imbalanced utilization, etc. To solve these problems, an improved beetle swarm antennae search algorithm based on multiple operators, dubbed MO-BSAS, is proposed. First, the elite opposition-based learning is used to initialize the beetle population, which improves the population diversity and optimization ability of the algorithm; then, the Lévy Flight strategy is used to improve the traditional beetle moving operator. In addition, a multi-operator search strategy determined by the damped sinusoidal probability factor is designed to balance the exploitation and exploration capabilities of the algorithm and speed up its convergence. The MO-BSAS algorithm is compared with BSA and 8 popular or state-of-the-art smart algorithms under 14 different benchmark functions, and the experimental results show that the MO-BSAS algorithm has a shorter convergence time and better convergence accuracy than the algorithms compared, which verifies the effectiveness of the improved algorithm. [ABSTRACT FROM AUTHOR]

The seasonal cycle (SC) of surface air temperature is a substantial element in climatology. Some basic and important topics in climate change studies are based on accurate and reliable estimation of SCs, such as percentile‐based indices of extremes and probability density function (PDF) changes of daily temperatures. For both of them, most studies characterized SCs using averages of multi‐days windows, which is not smooth and accurate enough representing the extreme thresholds and climatological normal of SCs. It is necessary to construct smooth and reasonable SCs for more accurate estimation of temperature changes on extreme thresholds and PDFs. In this study, we propose a flexible method based on generalized additive models for location scale and shape and penalized b‐spline smoothing technique with respective distributions to construct smooth SCs and SC for extreme temperatures (SCETs). The accuracy of the constructed smooth SCETs is good with the estimation biases of percentiles tending to be zero. The constructed smooth SCET also exhibits good stability over time, such that the magnitude changes of temperatures on each calendar day are close to climatic changes of mean temperature when the concerned period shifts. Based on the constructed smooth SCs, climatic changes by seasons and PDFs between two periods, 1961–1990 and 1991–2020, are examined over China. The increase of thresholds for hot extremes in spring during the recent period is prominent, while the increase of thresholds for daytime cold extremes in summer over a part of central to southern China is also notable. The smooth SCs and SCETs based on our flexible statistical modelling framework can characterize daily extreme temperatures reasonably and accurately, and should be expected to have more applications for a better understanding of climate changes related to distributions and seasonal cycles. [ABSTRACT FROM AUTHOR]

The choice of the most suitable probability distribution for rainfall varies across different geographical regions due to varying spatial and temporal variability. Therefore, there is an ongoing need to conduct research aimed at determining the optimal distribution models for various locations. This study was specifically designed to investigate the variability in rainfall patterns and identify the most appropriate probability distribution models for total monthly rainfall in selected agricultural areas in Nigeria. To achieve this, a comprehensive analysis was conducted on 41 years rainfall data spanning from 1982 to 2022. Ten different probability distributions were applied to fit these data for each calendar month as well as for the overall dataset. Applicable parameters (shape, scale, location, rate, logarithmic mean, and logarithmic standard deviation) for each distribution were estimated using maximum likelihood estimates. The selection of the best-fit distribution model for each month was based on three criteria, including the Akaike information criteria (AIC), Bayesian information criteria (BIC), and corrected Akaike information criteria (CAIC). The results revealed that the Pearson III and loglogistic distributions provided the best-fit model for rainfall data during most months at selected locations. However, when considering the overall rainfall across most locations, the Gamma distribution exhibited superior performance compared to the other distributions. This research contributes to the enhancement of integrated water resources management and facilitates the accurate evaluation and planning of water resources in selected agricultural hubs in Nigeria, with the ultimate aim of improving agricultural productivity. [ABSTRACT FROM AUTHOR]

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce (Picea mariana (Mill) B.S.P.) and jack pine (Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH. [ABSTRACT FROM AUTHOR]

This study explores a new family of distributions to enhance the analysis capabilities of COVID-19 events, providing valuable insights for informed decision-making and effective public health management. Accurate understanding and prediction of COVID-19 transmission patterns and their impacts are crucial in reducing the mortality rate, especially in proactive control and mitigation efforts. The proposed approach focuses on a best-fit probabilistic model that incorporates a comprehensive assessment of various statistical measures. Additionally, seven well-recognized classical point estimation methods are employed to identify the most suitable approach for assisting epidemiologists in their analysis. The study analyzes COVID-19 data from multiple countries, including the Netherlands, Mexico, the United Kingdom, China, Canada, Saudi Arabia, and Italy, considering different aspects such as mortality rates and the number of deaths. By evaluating the performance of the new alpha generated family of distributions in modeling COVID-19 events. This research contributes to the advancement of our understanding of the disease's probabilistic nature. The findings have practical implications, guiding the development of public health policies, resource allocation strategies, and intervention plans, ultimately facilitating more effective control and mitigation of COVID-19 outbreaks. [ABSTRACT FROM AUTHOR]

This study investigates event-based rainfall characteristics in Sinai (Egypt) using hourly precipitation data from the Global Satellite Mapping of Precipitation (GSMaP). A hierarchical cluster analysis of a 19-year dataset (2003–2021) identified five regions in Sinai. Distinct storms were identified using a minimum inter-event time of 5 h. The analysis of storm characteristics revealed that rainfall events in Sinai last from 1.7 to 3.6 h, with a mean storm volume of 6.4 mm. Rainfall intensity ranges from 1.7 to 4 mm/h, and the average dry period duration is 34 days. The northern region has the highest frequency of storms (25 events/year). The Weibull distribution was found to fit the best for all rainfall characteristics except for intensity, which was best represented by the generalized extreme value distribution. This study provides valuable insights about rainfall events in Sinai that can be applied to improve flood mitigation strategies and water resources management. [ABSTRACT FROM AUTHOR]

In today’s data-rich era, there is a growing need for developing effective similarity and dissimilarity measures to compare vast datasets. It is desirable that these measures reflect the intrinsic structure of the domain of these measures. Recently, it was shown that the space of finite probability distributions has a symmetric structure generated by involutive negation mapping probability distributions into their “opposite” probability distributions and back, such that the correlation between opposite distributions equals –1. An important property of similarity and dissimilarity functions reflecting such symmetry of probability distribution space is the co-symmetry of these functions when the similarity between probability distributions is equal to the similarity between their opposite distributions. This article delves into the analysis of five well-known dissimilarity functions, used for creating new co-symmetric dissimilarity functions. To conduct this study, a random dataset of one thousand probability distributions is employed. From these distributions, dissimilarity matrices are generated that are used to determine correlations similarity between different dissimilarity functions. The hierarchical clustering is applied to better understand the relationships between the studied dissimilarity functions. This methodology aims to identify and assess the dissimilarity functions that best match the characteristics of the studied probability distribution space, enhancing our understanding of data relationships and patterns. The study of these new measures offers a valuable perspective for analyzing and interpreting complex data, with the potential to make a significant impact in various fields and applications. [ABSTRACT FROM AUTHOR]

Aiming at the problem of uncertainty and complexity of battlefield situation, which leads to the poor accuracy of risk prediction in the process of research and judgment, it is proposed to build a situation-risk model and construct the risk possibility distribution in order to realize the accurate prediction of risk. Firstly, the risk prediction index system is established from the enemy situation, our situation and the battlefield environment situation research and judgment content; secondly, the role of situation information on the risk is analyzed, and the risk model such as exponential, Z-type, tangent and so on is constructed and the risk value interval is calculated; then, based on the fuzzy function constructing method in the possibility theory, and relying on the weighting difference and uncertainty measurement, the risk possibility distribution is constructed within the risk value interval. Finally, an example of a defense mission is used to verify the feasibility and reasonableness of the proposed method by combining the expert system and cloud modeling methods in an experiment. The results show that the proposed method can fully take into account the uncertainty of situational information in risk prediction, which provides an important basis for subsequent planning decision-making. [ABSTRACT FROM AUTHOR]

Weather generators can serve as an important tool for estimating the probability distributions of hydrometeorological variables to determine extreme rainfall quantiles. It is really of great significance for flood disaster management in data-deficient areas. The annual maximum daily rainfall (MDR) dataset was expanded in this study using a multi-site weather generator model coupled with maximum entropy resampling (MWG-MER), resulting in a sizable resampled dataset of extreme variables. The MDR records from 14 weather stations in the Jing River Basin were chosen to confirm the MWG-MER model's applicability on the Chinese Loess Plateau. There, the best-fitting probability distributions were discovered using the L-moments approach, and the resampled data was utilized to determine the spatial pattern of the probability distribution of MDR. The findings demonstrate that the MWG-MER model implemented a limited extrapolation and offered a larger resampling dataset that only used the first principal component to preserve the primary statistical properties of the observed MDR data. The resampling data had good fitting performance compared to the measured data at all sites and revealed different best-fit probability distributions from the measured data at some sites, implying an improvement in the MWG-MER model's distribution fitting accuracy. With the aid of the resampling data, the spatial pattern of the MDR distribution in the Jing River Basin was discovered, and more logical partitions were provided. This information is crucial for scientifically determining the MDR probability distribution in data-deficient areas and for directing the management of flood disasters in the Loess Plateau and other similar regions. [ABSTRACT FROM AUTHOR]

The expansion of the application domains is greatly aided by the generalization of distributions. To achieve this, an extension of the two–parameter Kumaraswamy distribution to a three–parameter second order transmuted Kumaraswamy distribution has been presented in this study utilizing the cubic transmutation map. Along with the order statistics and parameter estimates, a number of statistical characteristics are shown. The performance of the estimated parameters has been demonstrated through simulation study. A few applications additionally serve to demonstrate the suggested distribution’s dominating applicability. [ABSTRACT FROM AUTHOR]

In this paper, a supervisory control concept for wind farms is proposed based on the neighboring wind turbines control functions in localized areas for power optimization considering wake effects. The flow control in wind farms to maximize power production is a challenging problem due to its time-varying nonlinear wake dynamics. Hence, we develop a method that authorizes coordination in a wind farm for a squarely payoff-based scenario where the turbines have access only to measurements from their neighbors via repeated interactions. Therefore, in order to maximize output power in a wind farm, an Adaptive Learning Game Theory (ALGT) method is introduced. This control scheme provides an interaction framework that constructs a series of common control functions. Here, in every iteration, each turbine chooses an independent decision according to a localized control law. The control objective of wind turbine i determines how each turbine adjusts a decision at each iteration by processing available information. [ABSTRACT FROM AUTHOR]

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rockfall blocks are often fragmented due to the preceding fall process. The in situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in situ block size distributions with many blocks within the whole range of block sizes. In the current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model synthetic rock masses on the basis of discrete fracture networks. They statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine in situ block size distributions. We wanted to know whether the in situ block size distributions derived from the synthetic rock mass models can be described by probability distribution functions, and if so, how well. We fitted various distribution functions to three determined in situ block size distributions of different lithologies. We compared their correlations using the Kolmogorov–Smirnov test and the mean-squared error method. We show that the generalized exponential distribution function best describes the in situ block size distributions across various lithologies compared to 78 other distribution functions. This could lead to more certain, accurate, verifiable, holistic, and objective results. Further investigations are required. [ABSTRACT FROM AUTHOR]

The Demand-Driven Material Resource Planning (DDMRP) method is one of the newer methods of inventory management in an enterprise. Its creation was initiated by a change in the business environment and the characteristics of today's supply chains. DDMRP brings a combined pull/push approach to inventory management based on creating strategic stacks in the supply chain and managing inventory at these strategic points based on customer orders. The DDMRP system provides a simple methodology that is easy to apply, even in smaller businesses, without the need for advanced information systems. However, a simple methodology also has its limitations because, in many cases, intuitive and subjective approaches are used to set inventory management parameters (variability factor, running time factor, seasonality factor, thresholds, etc.). Simplified parameter determination may, under certain conditions, lead to some storage tanks being too high or too low for certain periods of time. We know from classical inventory management, in the conditions of setting stack parameters in DDMRP, that the deficiency can be eliminated by the use of statistical–analytical approaches and optimisation techniques. This article deals with the issue of setting optimal values of storage tanks in DDMRP, while the correctness of the methodology is verified through simulation of the demand-driven planning process. The correctness and usability of the proposed approaches in sizing strategic reservoirs in DDMRP was confirmed through the results of stimulation experiments. [ABSTRACT FROM AUTHOR]

Various in silico approaches to predict activity and properties of chemical compounds constitute nowadays the basis of computer-aided drug design. While there is a general focus on the predictions of values, mathematically more appropriate is the prognosis of probability distributions, which offers additional possibilities, such as the evaluation of uncertainty, higher moments, and quantiles. In this study, we applied the Hierarchical Correlation Reconstruction approach to assess several ADMET properties of chemical compounds. It uses multiple linear regression to independently assess multiple moments, which are then finally combined into predicted probability distribution. The method enables inexpensive selection of compounds with properties nearly certain to fall into the particular range during virtual screening and automatic rejection of predictions characterized by high rate of uncertainty; however, unlike to the currently used virtual screening methods, it focuses on the prediction of the property distribution, not its actual value. Moreover, the presented protocol enables detection of structural features, which should be carefully considered when optimizing compounds towards particular property, as well as it provides deeper understanding of the examined compound representations. [ABSTRACT FROM AUTHOR]

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The record values data have received the attention of researchers in statistics for over seven decades. Through these decades the records have played a significant and widely utilized role for statistical inference in parameter estimation, predicting future values, hypothesis tests, as well as stressstrength tests, and characterizing distributions. In this paper, the types of record values, some distributional properties, and statistical inferences of record values and their applications are reviewed. The purpose of this paper is to shed light on the role of record values in statistical inference. Therefore, we will examine this issue from two perspectives, the first perspective being estimation and the second perspective being prediction. These are through some of the most important lifetime distributions are Exponential, Weibull, Gumbel, Geometric, Pareto, Generalized exponential, Rayleigh, Lomax, and Nadarajah-Haghighi distributions. I hope that the findings of this paper will be useful for researchers in various fields and lead to further enhancement of research in record values theory and its applications. [ABSTRACT FROM AUTHOR]

New parameters can be added to expand families of distribution for greater flexibility or to construct covariate models in several ways. In this study, a trigonometric-type distribution called Sine-Weibull distribution was developed by adopting the Weibull distribution as the baseline distribution and Sine-G Family as the generator to generate a flexible probability distribution without the need for extra parameters. The moment, moment generating function, entropy, and order statistics are some of the mathematical aspects of this distribution that were derived. The Maximum Likelihood approach was used to estimate the new distribution's parameters. Using actual datasets, the Sine-Weibull distribution's applicability was demonstrated. [ABSTRACT FROM AUTHOR]

A comprehensive understanding of velocity distribution is the fundamental information hydraulic engineers need to estimate an alluvial channel's discharge and stage characteristics. This study examines the Tsallis entropy approach for estimating streamwise velocity patterns in open channels. Entropy, which quantifies system uncertainty, has been applied in hydraulic research to account for variables such as shear strength, silt content, and flow velocities. However, its applicability to non-uniform channel sections remains unexplored. In the current work, the velocities estimation under various experimental conditions was calculated using the Tsallis entropy approach, wherein the random variable employed for constructing the velocity estimations was the time-averaged normalised velocity. This study considered two experimental conditions: (1) channels with attached spurs under seepage and non-seepage conditions and (2) channels with a 31-degree bank slope with and without an upstream pit. The velocity pattern obtained closely corresponds to the experimental data, exhibiting significant accuracy. However, it should be noted that the accuracy of the velocity pattern is slightly diminished in the region near the spur field when the y / D value is below 0.3. The difference can be caused by factors such as the area's non-uniform cross-section, sediment interaction along the bed, and secondary currents, which ultimately affect the velocity profile. [ABSTRACT FROM AUTHOR]