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The use of structural durability analysis technology can effectively improve the economic efficiency of aircraft structures while ensuring their reliability. This paper utilizes the structural durability analysis technique to study the initial fatigue quality (IFQ) of a typical fatigue structure of 7B04-T651 high-strength aluminum alloy under the action of flight load spectrum of a certain type of aircraft. Firstly, the maximum likelihood estimation method is applied to the parameter estimation problem of crack initiation time distribution based on three-parameter Weibull distribution. The Monte Carlo method is used to verify the correctness of this approach. Secondly, fatigue tests under three different stress levels are carried out on the flight load spectrum. The logarithmic sample moment approach is proposed to process the equivalent initial flaw size distribution to obtain its general model. In addition, the initial fatigue quality model describing the typical structure is established, which verifies that the equivalent initial flaw size (EIFS) is less than the allowable 0.125 mm. By analyzing the initial fatigue quality of the typical structure, the correctness and practicability of the generalization method is demonstrated, and the life estimation model of this typical structure is built under different stress zones, different specified crack sizes and different reliability levels. [ABSTRACT FROM AUTHOR]

Dealing with competing risks is an important problem in reliability analysis and attracts much attention from scholars. It is more practical to consider competing risks with dependent failure causes in reality. In this article, statistical inference of the Marshall–Olkin bivariate Burr-XII distribution under adaptive type-II progressive hybrid censoring is discussed to show the procedure of dependent competing risks analysis in the complex data structure. The maximum likelihood estimation and lognormal approximation confidence intervals of parameters are computed. The existence and uniqueness of solutions are proved with Cauchy-Schwarz inequality. The Bayesian method with Gamma-Dirichlet prior and Metropolis-Hastings algorithm are further considered to find satisfied estimation of parameters. In addition, dynamic cumulative residual entropy is derived to quantify the information uncertainty of data. We finally compare the performance of various methods by conducting a simulation study and real data analysis. [ABSTRACT FROM AUTHOR]

In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and Ψ 2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao's score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's information criterion (DIC), sample size adjusted BIC (SABIC), relative entropy, the integrated classification likelihood criterion (ICL-BIC), the adjusted Lo–Mendell–Rubin (LMR), and Vuong-Lo–Mendell–Rubin (VLMR). The accuracy of the fit indices was assessed for correct detection of the number of latent classes for different simulation conditions including sample size (2,500 and 5,000), test length (15, 30, and 45), mixture proportions (equal and unequal), number of latent classes (2, 3, and 4), and latent class separation (no-separation and small separation). Simulation study results indicated that as the number of examinees or number of items increased, correct identification rates also increased for most of the indices. Correct identification rates by the different fit indices, however, decreased as the number of estimated latent classes or parameters (i.e., model complexity) increased. Results were good for BIC, CAIC, DIC, SABIC, ICL-BIC, LMR, and VLMR, and the relative entropy index tended to select correct models most of the time. Consistent with previous studies, AIC and AICc showed poor performance. Most of these indices had limited utility for three-class and four-class mixture 3PL model conditions. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications. [ABSTRACT FROM AUTHOR]

We derive and evaluate a novel estimation approach for the von Mises regression model based on a modified score function whose solution ensures an estimator with a smaller asymptotic bias than the original maximum likelihood estimator. We consider Monte Carlo simulation experiments to show that the new estimation approach yields nearly unbiased estimates. An application to real data is also considered for illustrative purposes. • Circular data. • Circular von Mises regression. • Modified score functions. • Novel estimation approach for the von Mises regression. [ABSTRACT FROM AUTHOR]

This article introduces a generalized method for estimating parameters of an alphastable distribution based on the characteristic function. We propose a novel approach that extends existing techniques. As an application, we compare our proposed method with the maximum likelihood method. Our results demonstrate the efficacy of the proposed method in accurately estimating the parameters of alpha-stable distributions. Additionally, we highlight the advantages of the proposed method ver maximum likelihood method in capturing the tails and skewness of the distribution. This research contributes to the advancement of statistical methods for modeling heavy-tailed and skewed distributed data, with applications in finance, risk management, and other fields. [ABSTRACT FROM AUTHOR]

India is dependent on rainfall for agriculture, food security and economic advancements. Spatial and temporal variability of rainfall is well reported, as well as the recent upsurge of extremes due to climate change. In Maharashtra, rainfall intensity varies widely from very high (coasts) to low (west-interior). Extreme value analysis (EVA) of heavy annual rainfall for the various districts of Maharashtra was conducted to ascertain the following for each district: suitable extreme value distribution; extreme (high) annual rainfall; efficacy of gap-filling for missing annual record/s. The suitability of various statistical distributions for representing high annual rainfall values was evaluated using Anderson–Darling test (quantitative), quantile and probability plots (qualitative). The gap-filling exercise resulted in minor variations (<10%) in the estimated extremes, positive as well as negative, for different cases. Therefore, the results of EVA on the actual records are advocated. The suitable distributions for 35 districts are presented in maps and Frechet distribution was adjudged suitable for almost 60% of districts. The estimated extremes for all districts are listed for different return periods for ready reference. These values would be useful for the planning and construction of hydraulic structures, water resources and reservoir management, design and planning of irrigation. Research highlights: Suitable probability distribution functions for modelling the extremes of annual rainfall in each district of Maharashtra have been identified and the parameters have been provided. Extreme values of annual rainfall for each district in Maharashtra for selected return periods have been presented. Evaluation was performed on whether the gaps in the annual rainfall records would affect EVA of the annual rainfall in the districts of Maharashtra. [ABSTRACT FROM AUTHOR]

The prior plays a central role in Bayesian inference but specifying a prior is often difficult and a prior considered appropriate by a modeler may be significantly biased. We propose multi-pass Bayesian estimation (MBE), a robust Bayesian method capable of adjusting the prior's influence on the inference result based on the prior's quality. MBE adjusts the relative importance of the prior and the data by iteratively performing approximate Bayesian updates on the given data, with the number of updates determined using a cross-validation method. The repeated use of the data resembles the data cloning method, but data cloning performs maximum likelihood estimation (MLE), while MBE interpolates between standard Bayesian inference and MLE; there are also algorithmic differences in how MBE and data cloning make repeated use of the data. Alternatively, MBE can be considered a method for constructing a new prior from the given initial prior and the data. We additionally provide a new non-asymptotic bound on the convergence of data cloning, and provide an MBE-like iterative heuristic approach which achieves faster convergence speed by boosting posterior variance. In numerical simulations on several simulated and real-world datasets, MBE provides robust inference results as compared to standard Bayesian inference and MLE. [ABSTRACT FROM AUTHOR]

This study delves into the computation and evaluation of the expected Fisher information matrix within the context of the Poisson-type I half logistic (PHL) distribution. Leveraging confidence intervals and their associated coverage probabilities, our investigation aimed to study the performance of information matrix by the maximum likelihood method in estimating parameters. Our results unveiled a consistent trend: as the sample size expanded, a reduction in the length of the confidence interval was observed, and the 95% asymptotic confidence interval's coverage probability aligned within the expected nominal size. This serves as a testament to the accuracy and robustness of the information matrix's performance within the PHL distribution framework. Also, tested using some real data set. [ABSTRACT FROM AUTHOR]

In this article, we propose a new length-biased weighted form of Wilson Hilferty distribution named as Length-Biased Weighted Wilson Hilferty Distribution. The various Statistical properties of the proposed distribution like, reliability function, hazard rate function, reverse hazard rate function, moment generating function, quantile function, the coefficient of variation etc. are considered to understand its nature. Furthermore, we have used the method of maximum likelihood for estimation of the parameters of proposed distribution. Also, we obtain the Shannon's entropy, stochastic ordering, Lorenz and Bonferroni curves. The performance of the proposed distribution is compared with competitive distributions using two real data sets. [ABSTRACT FROM AUTHOR]

Natural catastrophes have a tremendous influence on the environment and our economy, which has raised significant concerns and spurred scientific research. Several studies have been done to model the economic losses brought on by natural disasters. In this article, we primarily concentrate on examining the distributions of economic losses resulting from big catastrophes including wildfires, earthquakes, droughts, volcanic eruptions, and harsh weather. We recommend utilizing five well-known statistical distributions, including the Weibull, Log-logistics, Gamma, Generalized Pareto, and Lognormal distributions since we observe the skewed forms of the empirical distributions. We employ the maximum likelihood technique for each distribution for the available data sets in order to estimate the distributions. The parameter estimations are numerically computed using the PSO method. We select the distribution that best fits the economic losses using the Akaike Information Criterion and Kolmogorov-Smirnov statistics. We discovered that the Log-logistic distribution is the distribution that fits the total economic losses caused by all-natural disasters the best. [ABSTRACT FROM AUTHOR]

This article introduces an innovative extension of the Juchez distribution, referred to as the length-biased Juchez distribution. This distribution, a specific instance of the broader weighted distribution, is thoroughly explored in terms of mathematical and statistical properties. Parameter estimation is accomplished through the application of maximum likelihood estimation techniques. To highlight the practical significance of this new distribution, a comprehensive analysis is conducted using two real-life lifetime datasets. The findings underscore the relevance and applicability of the proposed distribution in modeling and analyzing diverse datasets. [ABSTRACT FROM AUTHOR]

This paper pictures the importance and the generalization of a new family of distribution developed on Triangle distribution. The new family provides some useful expansions, properties and a suitable alternative to some of existing models with same and higher number of parameters. Exponential distribution (one parameter) and Inverse Weibull distribution (Two parameter) play the role of sub-models. This new family distribution is used as a statistical model to estimate the parameters using the maximum likelihood estimation method. A complete study of Percentage points has been tabled. Two real-world data sets are investigated, demonstrating the suggested model's capacity to fit a variety of data sets along with some other models. [ABSTRACT FROM AUTHOR]

Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing. [ABSTRACT FROM AUTHOR]

This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information available is in the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function links equal importance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Nanchang University (Engineering & Technology) is the property of Nanchang University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Nanchang University (Engineering & Technology) is the property of Nanchang University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we attempted to expand the Frechet distribution by employing the T-X family of distributions and named the newly formulated model Extended odd Frechet-exponential distribution (EOFED). Several structural properties, reliability measurements and characteristics were estimated and discussed. The study presents graphs which depict the behaviour of the probability density function, cumulative distribution function and the hazard rate function. The adaptability and flexibility of this novel distribution were achieved through the application of real-world data sets. A simulation study was performed to evaluate and compare the output efficacy of the estimators. [ABSTRACT FROM AUTHOR]

For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall's notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity ρ , is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of ρ . This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that ρ is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms. [ABSTRACT FROM AUTHOR]

The management of Agri-food supply chains is a complex task, given the unique product characteristics, perishability, uncertain demand, and specific storage requirements. This research introduces an innovative approach to optimizing product allocation among producers, brokers, wholesalers, and retailers, focusing on minimizing transportation costs and network delivery time through multi-objective programming. To address uncertainties, supply and demand constraints are modelled using a gamma distribution, and the maximum likelihood estimation method determines their parameters with specified probabilities. The study conducts a case analysis to showcase the model's practical effectiveness, and a numerical comparison with alternative approaches is included. The primary goal of this study is to enhance the efficiency of agri-food supply chain management practices, providing valuable insights for practitioners in the field, with a focus on cost reduction and improved delivery time. [ABSTRACT FROM AUTHOR]

Determination of rock mass deformation modulus (Erm) is an important but very challenging task in rock mechanics and rock engineering. Direct measurements of Erm by in-situ tests are expensive, time-consuming, and sometimes even impossible. Since the nondestructive and easy geophysical method is commonly used to measure the P-wave velocity (Vp) in the field, the study has developed an empirical correlation between Erm and Vp based on 834 collected datasets by considering both inherent and transformation uncertainties. The information criteria are employed to select the best model for deriving a general empirical correlation. The maximum likelihood estimation (MLE) method and computational intelligence techniques like particle swarm optimisation (PSO), artificial bee colony (ABC), and differential evolution (DE) algorithms are used to specify the incorporated parameters of each candidate model. Based on the derived general empirical equation, a Bayesian equivalent sample approach using Markov Chain Monte Carlo (MCMC) simulation is applied to conduct probabilistic characterisation of Erm by combining prior knowledge and project-specific observed Vp data. Comparative studies of the results from theory and in-situ measured Erm values suggest that the proposed method is effective and validate the applicability of the derived general empirical correlation. [ABSTRACT FROM AUTHOR]

Statistical data analysis is of great interest in every field of management, business, engineering, medicine, etc. At the time of classification and analysis, errors may arise, like a classification of observation in the other class instead of the actual class. All fields of science and economics have substantial problems due to misclassification errors in the observed data. Due to a misclassification error in the data, the sampling process may not suggest an appropriate probability distribution, and in that case, inference is impaired. When these types of errors are identified in variables, it is expected to consider the problem's solution regarding classification errors. This paper presents the situation where specific counts are reported erroneously as belonging to other counts in the context of size biased Uniform Poisson distribution, the so-called misclassified size biased Uniform Poisson distribution. Further, we have estimated the parameters of misclassified size biased Uniform Poisson distribution by applying the method of moments, maximum likelihood method, and approximate Bayes estimation method. A simulation study is carried out to assess the performance of estimation methods. A real dataset is discussed to demonstrate the suitability and applicability of the proposed distribution in the modeling count dataset. A Monte Carlo simulation study is presented to compare the estimators. The simulation results show that the ML estimates perform better than their corresponding moment estimates and approximate Bayes estimates. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parametric accelerated failure time (AFT) hazard-based regression model with the extended alpha-power exponential (EAPE) baseline distribution. The proposed model is called the extended alpha-power exponential-AFT (EAPE-AFT) regression model. We show that the EAPE distribution is closed under the AFT model. The parameters of the proposed EAPE-AFT model have been estimated by using the method of maximum likelihood estimation. An extensive simulation study was also conducted to examine the performance of the estimates under several scenarios based on the shapes of the baseline hazard function. Finally, real-life censored survival data has been used to illustrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

This research aims to compare the ability and item parameter estimations of Item Response Theory according to Maximum likelihood and Bayesian approaches in different Monte Carlo simulation conditions. For this purpose, depending on the changes in the priori distribution type, sample size, test length, and logistics model, the ability and item parameters estimated according to the maximum likelihood and Bayesian method and the differences in the RMSE of these parameters were examined. The priori distribution (normal, left-skewed, right-skewed, leptokurtic, and platykurtic), test length (10, 20, 40), sample size (100, 500, 1000), logistics model (2PL, 3PL). The simulation conditions were performed with 100 replications. Mixed model ANOVA was performed to determine RMSE differentiations. The prior distribution type, test length, and estimation method in the differentiation of ability parameter and RMSE were estimated in 2PL models; the priori distribution type and test length were significant in the differences in the ability parameter and RMSE estimated in the 3PL model. While prior distribution type, sample size, and estimation method created a significant difference in the RMSE of the item discrimination parameter estimated in the 2PL model, none of the conditions created a significant difference in the RMSE of the item difficulty parameter. The priori distribution type, sample size, and estimation method in the item discrimination RMSE were estimated in the 3PL model; the a priori distribution and estimation method created significant differentiation in the RMSE of the lower asymptote parameter. However, none of the conditions significantly changed the RMSE of item difficulty parameters. [ABSTRACT FROM AUTHOR]

Zero-and-one-inflated geometric distribution model was investigated, the conditional distribution of latent variables were constructed, and a sampling algorithm was designed. On the basis of data expansion, the maximum likelihood estimation, expectation maximization (EM) algorithm and Bayesian method were employed to estimate the model parameters. Different sample sizes and parameter true values were setted, and the performance of these methods were evaluated through numerical simulations. Finally, the Detroit traffic accident deaths dataset in 1994 of United States were analyzed, the results indicate that zero-and-one-inflated geometric distribution model can fit the dataset better. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunications Science is the property of Beijing Xintong Media Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, a new Modi-Exponential distribution is considered under Type-I and Type-II censoring. Some statistical and reliability characteristics of the distribution are specified. Statistical inferences of the Modi-Exponential parameters based on Type-I and Type-II censored data are discussed. The maximum likelihood estimation method is used for estimation of unknown parameters along with reliability characteristics. Asymptotic confidence intervals are also obtained for interval estimation. Monte-Carlo Simulation study is performed to study the performances of estimators. Further, two real data sets are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper presents a particle swarm optimization-guided maximum likelihood estimation enabled (MLE) adaptive extended Kalman filter (EKF) with unknown inputs algorithm for estimating the dynamic nonlinear thermal states for an indoor heating ventilation and air conditioning system. The concept of MLE has been introduced to enhance the speed of convergence of the filtering parameters in adaptive EKF. The nonlinear indoor environment has been modelled employing equivalent RC network taking relative humidity into account. At the outset, an EKF-based method accommodating the unknown inputs and an adaptive estimator-based variant of it are developed for estimating the temperature of the walls of a laboratory-scale realistic environment. Subsequently the proposed scheme comes into play to deal with the scenarios associated with undesirable divergence and poor initialization utilizing the metaheuristically adapted optimal regularizer. The proposed technique outperforms the other contemporary state-of-the-art counterparts in terms of mean squared error. [ABSTRACT FROM AUTHOR]

We consider the statistical analysis of heterogeneous data for prediction, in situations where the observations include functions, typically time series. We extend the modeling with mixtures-of-experts (ME), as a framework of choice in modeling heterogeneity in data for prediction with vectorial observations, to this functional data analysis context. We first present a new family of ME models, named functional ME (FME), in which the predictors are potentially noisy observations, from entire functions. Furthermore, the data generating process of the predictor and the real response, is governed by a hidden discrete variable representing an unknown partition. Second, by imposing sparsity on derivatives of the underlying functional parameters via Lasso-like regularizations, we provide sparse and interpretable functional representations of the FME models called iFME. We develop dedicated expectation–maximization algorithms for Lasso-like regularized maximum-likelihood parameter estimation strategies to fit the models. The proposed models and algorithms are studied in simulated scenarios and in applications to two real data sets, and the obtained results demonstrate their performance in accurately capturing complex nonlinear relationships and in clustering the heterogeneous regression data. [ABSTRACT FROM AUTHOR]

Considering the testing process of the software system as a stochastic process is a primary approach to the software reliability modeling technique. Besides some popular distributions, the Poisson distribution has been considered the best based on its advantage when modeling the times at which arrivals enter a system. In the non-homogeneous Poisson process group of models, the S-shaped function is a value curve with many good results. This paper proposes a new imperfect debugging software reliability model based on (1) an Imperfect debugging assumption (the testing process could cause new faults); and (2) the Fault detection rate can be controlled more effectively by the appearance of a growth-rate-controller. The real data from industrial projects verify the application of this model based on good popular criteria values. [ABSTRACT FROM AUTHOR]

In this study, the Topp-Leone family of distribution approach was used to modify the Burr Hatke Exponential distribution to provide adequate fits for some engineering and health data which previous existing distributions in the family of Burr Hatke Exponential have failed to do. The new distribution improves the robustness of Burr Hatke Exponential distribution by making it capable of modeling emerging new world complex data with varying features, possesses greater capacity and flexibility to model lifetime data, has better goodness of fit. Some mathematical properties of the derived distribution such as quantile function, moments, order statistics, entropies, etc were obtained and discussed. Some non-Bayesian estimation approaches like maximum likelihood estimation (ML), maximum Product spacing estimation (MPSE), Least squares estimation (LS), weighted least squares estimation (WLS), Cramer-von-Mises estimation (CVM), Anderson-Darling estimation (AD), and right-tailed Anderson Darling estimation (RTAD), as well as Bayesian method under independent gamma priors were adopted to estimate the parameters of the model and the various methods proved efficient. From the simulation results, the bias and root mean squared error for the parameters are relatively small and the become smaller as the sample size becomes larger. This shows convenience and improved estimation accuracy. We further constructed a regression model using the proposed distribution. Extensive simulation studies were used to determine the efficiency of the method in both the estimation of its parameters and that of the regression model. The TL-BHE regression was fitted on censored CD4 count data of HIV/AIDs patients. The competitiveness, applicability, and usefulness of the model were demonstrated using datasets and the results validate the theoretical findings. The results indicate that the TL-BHE distribution achieved better results than the baseline distribution and other variants of the classical distributions.

Electricity price forecasting (EPF) is a complex task due to market volatility and nonlinearity, which cause rapid and unpredictable fluctuations and introduce heteroscedasticity in forecasting. These factors result in varying prediction errors over time, making it difficult for models to capture stable patterns and leading to poor performance. This study introduces the Heteroscedastic Temporal Convolutional Network (HeTCN), a novel Encoder-Decoder framework designed for day-ahead EPF. HeTCN utilizes a Temporal Convolutional Network (TCN) to capture long-term dependencies and cyclical patterns in electricity prices. A key innovation is the heteroscedastic output layer, which directly represents variable uncertainty, enhancing performance under fluctuating market conditions. Additionally, a multi-view feature selection algorithm identifies crucial factors for specific periods, improving forecast precision. The framework employs an improved loss function based on maximum likelihood estimation (MLE), which adjusts for the heteroscedastic nature of electricity prices by predicting both the mean and variance of the price distribution. This approach mitigates the impact of extreme price spikes and reduces overfitting, resulting in robust and reliable predictions. Comprehensive evaluations demonstrate HeTCN’s superiority over existing solutions such as DeepAR and the Temporal Fusion Transformer (TFT), with average improvements of 25.3%, 24.9%, and 17.4% in the mean absolute error (MAE), symmetric mean absolute percentage error (sMAPE), and the root of mean squared error (RMSE) compared to DeepAR, and 17.6%, 14.4%, and 13.6% relative to TFT across five distinct electricity markets. These results underscore HeTCN’s effectiveness in managing volatility and heteroscedasticity, marking a significant advancement in electricity price forecasting.

In contemporary data analysis, the need for flexible and adaptable probabilistic models capable of capturing complex dependencies and tail behaviors in real-life datasets has become increasingly apparent. In light of this demand, A new trigonometric generalized family of distribution, the "Transmuted Cosine Topp-Leone G Family" is proposed in this study. Established on the foundations of, this family combines the adaptability of the Topp-Leone distribution with the periodicity of the cosine function and transmutation theory to produce a flexible framework that may be used to represent a wide range of real-life phenomena. We derive some of the statistical properties of the introduced family such as; survival and hazard functions, and moment and moment-generating functions. Moreover, the model parameters are estimated using the Maximum Likelihood method, and a Monte Carlo simulation was performed to ascertain the behavior and the consistency of the estimates. We investigate the shape of the distribution parameters which results in distributions with left-skew, right-skew, increasing, and decreasing shapes. Lastly, through empirical demonstrations, we showcase the efficacy of the family TrCTLG models in fitting lifetime datasets.

In recent decades, many research studies have been conducted for the development of some new modifications of different baseline distributions to cope with real-world problems. This paper proposes a novel generalization of probability distributions, called modified type- II half-logistic distribution. We have derived the new family of probability distributions using T-X family with input as a type II variant of the half-logistic distribution. For the purpose of demonstration, the Weibull distribution is considered as a sub-model. Various algebraic properties of the suggested distribution have been discussed. For efficient parameter estimation, we have used the maximum likelihood principle. Additionally, two real-world data sets from the literature have been considered to illustrate the practical usefulness and significance of the suggested model.

Abstract The aim of this article is to define a new flexible statistical model to examine the COVID‐19 data sets that cannot be modeled by the inverse exponential distribution. A novel extended distribution with one scale and three shape parameters is proposed using the generalized alpha power family of distributions to derive the generalized alpha power exponentiated inverse exponential distribution. Some important statistical properties of the new distribution such as the survival function, hazard function, quantile function, rth moment, Rényi entropy, and order statistics are all derived. The method of maximum likelihood estimation is used to estimate the parameters of the new distribution. The performance of the estimators are assessed through Monte Carlo simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to COVID‐19 data sets in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels and other well‐known distributions.