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The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology. [ABSTRACT FROM AUTHOR]

Summary: Binary data subject to one type of misclassification exist in various fields. It is collected in a double‐sampling scheme that includes a gold standard test and a fallible test. The main parameter of interest for this type of data is the positive probability p$$ p $$ of the gold standard test. Existing intervals are unreliable because the given nominal level 1−α$$ 1-\alpha $$ is not achieved. In this paper, we construct an exact interval by inverting the E+M score tests and improve it by the general h$$ h $$‐function method. We find that the total length of the improved interval is shorter than the exact intervals that are also the improved intervals when we apply the h$$ h $$‐function to several existing approximate intervals, including the score and Bayesian intervals. Therefore, it is recommended for practice. We are also interested in two other parameters: p∗$$ {p}^{\ast } $$—the difference between the two positive rates for the fallible and gold standard tests—and ξ$$ \xi $$—the false positive rate for the fallible test. To the best of our knowledge, the research on these two parameters is limited. For p∗$$ {p}^{\ast } $$, we find that any interval for p$$ p $$ can be converted to an interval for p∗$$ {p}^{\ast } $$. So, the interval converted from the aforementioned recommended interval for p$$ p $$ is recommended for inferring p∗$$ {p}^{\ast } $$. For ξ$$ \xi $$, the improved interval by the h$$ h $$‐function method over the E+M score interval is derived. We use an example to illustrate how the intervals are computed and provide a real data analysis. [ABSTRACT FROM AUTHOR]

The Lorenz curve portrays income distribution inequality. In this article, we develop three modified empirical likelihood (EL) approaches, including adjusted empirical likelihood, transformed empirical likelihood, and transformed adjusted empirical likelihood, to construct confidence intervals for the generalized Lorenz ordinate. We demonstrate that the limiting distribution of the modified EL ratio statistics for the generalized Lorenz ordinate follows scaled Chi-Squared distributions with one degree of freedom. We compare the coverage probabilities and mean lengths of confidence intervals of the proposed methods with the traditional EL method through simulations under various scenarios. Finally, we illustrate the proposed methods using real data to construct confidence intervals. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we propose confidence intervals for the population coefficient of variation based on some robust estimators such as trimmed mean, winsorized mean, Hodges-Lehmann estimator and trimean. The proposed confidence intervals and their bootstrap versions were compared with the existing confidence intervals for the population coefficient of variation. The performances of the proposed confidence intervals were evaluated via a Monte-Carlo simulation study by considering the coverage probability, average width, standard deviation of widths, and coefficient of variation of widths as comparison criteria. The proposed confidence intervals performed well in terms of coverage probability on symmetrical distributions. In the case of skewed distributions, they were closer to the nominal confidence level and had narrower widths than the others. As a result, we proposed to use confidence intervals based on the Hodges-Lehmann estimator and winsorized mean for small sample sizes ([Formula: see text]) and larger sample sizes for skewed distributions, respectively. The real-life datasets were analyzed to support the simulation results and confirm the practical applications of the proposed confidence intervals.

Non-Orthogonal Multiple Access (NOMA) and Fractional Frequency Reuse (FFR) were touted as two key techniques of the millimetre wave cellular system to derive spectrum efficiency and user performance improvement. By combining the NOMA and FFR techniques, this paper proposes a system to improve the performance of the NOMA user that utilises the NOMA-power domain technique to reuse an occupied Resource Block (RB). Besides following the power allocation policy of the NOMA technique, the resource allocation algorithm for the NOMA user is based on the FFR technique. Particularly, if the downlink Signal-to-Interference-plus-Noise ratio (SINR) of the NOMA user is greater than the threshold, it is allocated the Cell-Edge RB with a high interference level. Otherwise, it is served on the Cell-Center RB with a low interference level. The analytical and simulation results state that the proposed system can increase the coverage probability of the NOMA user up to 250%. [ABSTRACT FROM AUTHOR]

In R16, 3GPP proposed that user devices could utilize the 4G/5G cellular networks to report the received signal strength indicator (RSSI) of Wi-Fi signal based on the existing minimization of drive test (MDT) technology, making it possible to measure the coverage probability of indoor Wi-Fi networks. However, existing measurement methods of network coverage probability based on the MDT require the spatial coordinates provided by the GPS. As GPS has poor indoor localization accuracy, it is not able to be applied to indoor Wi-Fi networks. A measurement method for network coverage probability based on clustering without spatial coordinates was proposed. The proposed method could distinguish RSSI measurement reported on different locations, with the fact that their statistics were similar at similar locations. The coverage probability was accurately measured by utilizing the clustering results without knowing the spatial coordinates. Experimental results show that the coverage probability measured by the proposed method is very close to the probability measured by the known spatial coordinates, and the accuracy is much higher than existing methods.

Summary: An evaluation of various transmit precoding schemes is proposed in this thesis on basis of spectral efficiency (SE) of massive MIMO (m‐MIMO) system in 2 GHz spectrum. The present generation of wireless networks must be rethought due to the rapidly rising user base, huge volume data transfer, wide coverage requirement, and exponential rise in data rate. 5G mobile network includes a multi‐fold increase in network capacity, energy conservation, decreased latency, higher coverage probability, and a seamless connection. m‐MIMO has provided good solution for enhancing the data rate with the coverage, overcoming the effects of multipath fading and has also increased diversity of the system. Massiveness of MIMO system along with 5G network is the key technology to address the issue of SE, throughput, improvement of QoS (quality of service), coverage probability, power delay profile, diversity simulation, energy efficiency, and improvement in bit error rate. Parameters such as SE, throughput, and coverage probability are important for any communication system, and their improvement can increase overall capacity of cellular network system and could meet the requirement of upcoming demand for mobile network. The research paper is focused on performance analysis of m‐MIMO with reference to the SE of various transmit precoding schemes. Simulation results show that SE provided by M‐MMSE (multi‐cell minimum mean‐squared error) technique of precoding ranks highest for the same number of antennas and pilot reuse factor as compared to other schemes. [ABSTRACT FROM AUTHOR]

This article presents the problem of interval estimation of the mean, difference and ratio of means for zero-adjusted inverse Gaussian distributions. Confidence intervals of the mean are derived using signed log-likelihood, method of variance estimate recovery (MOVER), generalized variable, and Bayesian approaches. For two populations, we derive MOVER, generalized variable-based interval, and Bayesian intervals for the difference and ratio of means. We perform intensive simulations to compare the proposed confidence intervals of the function of parameters. Finally, illustrative examples are given using real data sets from different fields. [ABSTRACT FROM AUTHOR]

The Birnbaum–Saunders distribution is of particular interest for statistical inference. This distribution represents the failure time distribution in engineering. In addition, the Birnbaum–Saunders distribution is commonly used in different areas of science and engineering. Percentiles are a frequently employed statistical concept. Percentiles help ascertain the position of an observation concerning the percentage of data points below it. These percentiles serve as indicators of both the central tendency and the dispersion of data. While comparing two data distributions, the mean is typically the most dependable parameter for describing the population. However, in situations where the distribution exhibits significant skewness, percentiles may sometimes offer a more reliable representation. Herein, the confidence intervals for the difference between percentiles of Birnbaum–Saunders distributions were constructed by the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach. A Monte Carlo simulation was conducted to evaluate the performance of the confidence intervals. The performance was considered via coverage probability and average width. The findings suggest that utilizing the GCI approach is advisable for estimating confidence intervals for the disparity between two percentiles. Ultimately, the outcomes of the simulation investigation, coupled with an application in the field of environmental sciences, were outlined. [ABSTRACT FROM AUTHOR]

AbstractIn epidemiological cohort studies, the relative risk is a key measure to gauge the connection between two treatments or exposures. It quantifies the proportional change in the risk of disease due to the application of a specific treatment. However, the conventional methods for calculating relative risk, available in widely-used software, might yield inaccurate results when applied to correlated binary data from studies conducted over time or in clusters. Recently, various techniques have been proposed to estimate the risk ratio for correlated binary data. However, some methods exhibit a tradeoff between maintaining accurate coverage probability (CP) and ensuring an appropriate interval width or location. This paper introduces a new approach to confidently estimating the risk ratio using a hybrid method. This hybrid method combines two distinct confidence intervals (CIs) derived from single risk rates to establish a unified confidence interval for their ratio. Furthermore, we present a methodology to construct a confidence interval for the risk ratio, which builds upon established methods for correlated binary data. This extension incorporates principles such as the design effect and adequate sample sizes commonly used in representative sample surveys. An extensive simulation study is conducted to evaluate the effectiveness of these proposed methods. The performance of the methods is thoroughly examined in various scenarios. Additionally, the practicality of the proposed methods is showcased through three real-life examples. These examples involve comparing the side effects of low-dose tricyclic antidepressants with a placebo, assessing the efficacy of a treatment group in a teratological experiment, and evaluating the efficiency of active drugs in curing infections during clinical trials. [ABSTRACT FROM AUTHOR]

This paper investigates the symbol error rate (SER) and coverage probability of single reconfigurable intelligent surface (S-RIS) and double reconfigurable intelligent surface (D-RIS) systems operating over Weibull fading channels. In the S-RIS system, the RIS is positioned between the base station and user link, while in the D-RIS system, RIS-1 and RIS-2 are placed near the base station and user respectively. By leveraging the central limit theorem, we derive the statistical parameters of the received signal-to-noise ratio (SNR) and subsequently closed-form expressions for SER and coverage probability of both systems using the moment-generating function. Also, we determine the optimal location of the RISs in D-RIS system from the simulations of SER. Comparative analysis reveals that the D-RIS system exhibits superior error performance and provides better coverage than the S-RIS system, despite having an equal number of reflecting elements. In addition, we provide an energy consumption gain analysis of the D-RIS system. [ABSTRACT FROM AUTHOR]

We consider the problems of point, and interval estimation of the p th quantile of the first population when progressive type-II censored samples are available from several exponential populations with a common location, and different scale parameters. First, in the case of point estimation, we derive the maximum likelihood estimator, a modification to it and the uniformly minimum variance unbiased estimator (UMVUE) of the quantile. An estimator dominating the UMVUE is derived. Further, a class of affine equivariant estimators is derived, and an inadmissibility result is proved. Consequently, improved estimators dominating the UMVUE are derived. In the case of interval estimation, several confidence intervals, such as generalized confidence interval, bootstrap confidence interval, and the highest posterior density confidence interval, are obtained for the quantile. The point estimators are compared through the risk values, whereas the interval estimators are compared through coverage probability and average length using a simulation study numerically. The conclusions regarding their performances have been made based on our simulation study. Finally, a real-life data set has been considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

The average transmit power and coverage probability (Pcov) of uplink energy harvesting-enabled long-range networks are investigated in the present paper. Particularly, we model the end-device (EDs) according to the homogeneous Poisson point process while the power beacon is randomly distributed on the circle in the middle of the network. All EDs rely on the harvested energy to perform their operations and transmissions. Under this context, the upper bound of the average transmit power of an end-device is derived in the closed-form expression. The signal-to-noise-ratio condition of the coverage probability is given in the closed-form expression as well. Simulation results are provided to corroborate the accuracy of the derived mathematical framework as well as to feature the impact of some key parameters on the considered metrics. Our findings unveil that increasing either the number of power beacons or their transmit power will monotonically ameliorate the Pcov. Nevertheless, rising the average number of EDs will significantly decline the Pcov's performance. [ABSTRACT FROM AUTHOR]

ABSTRACTThe average transmit power and coverage probability (Pcov) of uplink energy harvesting-enabled long-range networks are investigated in the present paper. Particularly, we model the end-device (EDs) according to the homogeneous Poisson point process while the power beacon is randomly distributed on the circle in the middle of the network. All EDs rely on the harvested energy to perform their operations and transmissions. Under this context, the upper bound of the average transmit power of an end-device is derived in the closed-form expression. The signal-to-noise-ratio condition of the coverage probability is given in the closed-form expression as well. Simulation results are provided to corroborate the accuracy of the derived mathematical framework as well as to feature the impact of some key parameters on the considered metrics. Our findings unveil that increasing either the number of power beacons or their transmit power will monotonically ameliorate the Pcov. Nevertheless, rising the average number of EDs will significantly decline the Pcov's performance.

Assessing heterogeneity between studies is a critical step in determining whether studies can be combined and whether the synthesized results are reliable. The I 2 statistic has been a popular measure for quantifying heterogeneity, but its usage has been challenged from various perspectives in recent years. In particular, it should not be considered an absolute measure of heterogeneity, and it could be subject to large uncertainties. As such, when using I 2 to interpret the extent of heterogeneity, it is essential to account for its interval estimate. Various point and interval estimators exist for I 2 . This article summarizes these estimators. In addition, we performed a simulation study under different scenarios to investigate preferable point and interval estimates of I 2 . We found that the Sidik–Jonkman method gave precise point estimates for I 2 when the between-study variance was large, while in other cases, the DerSimonian–Laird method was suggested to estimate I 2 . When the effect measure was the mean difference or the standardized mean difference, the Q -profile method, the Biggerstaff–Jackson method, or the Jackson method was suggested to calculate the interval estimate for I 2 due to reasonable interval length and more reliable coverage probabilities than various alternatives. For the same reason, the Kulinskaya–Dollinger method was recommended to calculate the interval estimate for I 2 when the effect measure was the log odds ratio. [ABSTRACT FROM AUTHOR]

While the transition to 6G network technology has introduced significant advancements in mobile communications, it has also presented challenges to achieving optimal signalinterference-noise-ratio (SINR), especially in urban and suburban environments. This study focuses on SINR distributions within the lower-value spectrum characteristic of 6G environments, with the goal of refining coverage probability models. Through advanced simulations, the study enhanced existing models by considering factors such as antenna heights and signal frequencies. The findings showed a sharp initial increase in coverage probability in urban areas with additional base stations, contrasting with a more linear improvement in suburban areas. Specifically, urban coverage probability improved from 0.60 to 0.77, while suburban coverage saw a gradual increase from 0.50 to 0.63 with increased base station density. The study highlighted the need for tailored 6G deployment strategies to effectively address the unique challenges of urban versus suburban settings. The findings offer valuable insights for network planners and operators in optimizing 6G networks, emphasizing the significance of SINR optimization in achieving high-quality network coverage across different geographical landscapes. [ABSTRACT FROM AUTHOR]

Frequentist confidence intervals that include some element of data-based model selection or model averaging is an active area of research. Assessments of the performance, in terms of coverage and expected length, of such intervals yield few positive results. Efron, JASA 2014, proposed a confidence interval centred on a bootstrap smoothed estimator, with width proportional to an estimator of Efron's delta method approximation to the standard deviation of this estimator. Recently, Kabaila and Wijethunga assessed the performance of this confidence interval using a testbed consisting of two nested linear regression models, with error variance assumed known. This interval was shown to have far better coverage properties than the corresponding post-model-selection confidence interval. However, its expected length properties were not as good as had been hoped for. For this testbed, we ask the following question. Does there exist a formula for the data-based width of a confidence interval centred on the bootstrap smoothed estimator so that it has good performance in terms of both coverage and expected length? Using a decision-theoretic performance bound we answer this question in the negative. [ABSTRACT FROM AUTHOR]

In case-control studies, odds ratios (OR) are calculated from 2 × 2 tables and in some instances, we observe small cell counts or zero counts in one of the cells. The corrections to calculate the ORs in the presence of empty cells are available in literature. Some of these include Yates continuity correction and Agresti and Coull correction. However, the available methods provided different corrections and the situations where each could be applied are not very apparent. Therefore, the current research proposes an iterative algorithm of estimating an exact (optimum) correction factor for the respective sample size. This was evaluated by simulating data with varying proportions and sample sizes. The estimated correction factor was considered after obtaining the bias, standard error of odds ratio, root mean square error and the coverage probability. Also, we have presented a linear function to identify the exact correction factor using sample size and proportion. [ABSTRACT FROM AUTHOR]

The weighted sum of binomial proportions and the interaction effect are two important cases of the linear combination of binomial proportions. Existing confidence intervals for these two parameters are approximate. We apply the h -function method to a given approximate interval and obtain an exact interval. The process is repeated multiple times until the final-improved interval (exact) cannot be shortened. In particular, for the weighted sum of two proportions, we derive two final-improved intervals based on the (approximate) adjusted score and fiducial intervals. After comparing several currently used intervals, we recommend these two final-improved intervals for practice. For the weighted sum of three proportions and the interaction effect, the final-improved interval based on the adjusted score interval should be used. Three real datasets are used to detail how the approximate intervals are improved. [ABSTRACT FROM AUTHOR]

Purpose: A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS. Design/methodology/approach: In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques. Findings: The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study. Originality/value: The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature. [ABSTRACT FROM AUTHOR]

With the deployment of satellite constellations, Internet-of-Things (IoT) devices in remote areas have gained access to low-cost network connectivity. In this paper, we investigate the performance of IoT devices connecting in up-link through low Earth orbit (LEO) satellites to geosynchronous equatorial orbit (GEO) links. We model the dynamic LEO satellite constellation using the stochastic geometry method and provide an analysis of end-to-end availability with low-complexity and coverage performance estimates for the mentioned link. Based on the analytical expressions derived in this research, we make a sound investigation on the impact of constellation configuration, transmission power, and the relative positions of IoT devices and GEO satellites on end-to-end performance.

Communicating in a non-terrestrial network (NTN) has recently emerged as a promising technology to provide global seamless connectivity. Although low earth orbit (LEO) satellites in an NTN have been employed for providing ubiquitous coverage and high data rates for ground users, especially in emergent outdoor scenarios, NTN has not been integrated into the design of multi-connectivity for users in a terrestrial network (TN). Inspired by the 3rd Generation Partnership Program (3GPP) suggestion, this paper investigates TN-NTN-combined multi-connectivity downlink multiple-input multiple-output (MIMO) communication system, where each user may simultaneously connect to a base station (BS) in a TN and an LEO satellite in an NTN. Specifically, each user may have four different downlink access modes: served by both an LEO satellite and a BS, served by a BS, served by an LEO satellite, and not scheduled. Zero-forcing beamforming is employed at each LEO satellite to reduce the mutual interference among the satellite’s served users, and maximum ratio transmission beamforming is used at each terrestrial BS to enhance the downlink signal strength. By deriving the probability of each access mode and modeling the interference in such a TN-NTN-combined multi-connectivity MIMO system, we obtain a typical user’s downlink coverage probability and average achievable data rate. Extensive Monte Carlo simulations are conducted to validate our analytical derivations. Simulation results demonstrate that the user’s coverage probability and average achievable data rate can be significantly improved by realizing multi-connectivity with both TN and NTN compared to pure TN or NTN.

We hereby present a novel interference mitigation strategy specifically designed to enhance the quality of service that a typical terrestrial user equipment (UE) would experience after the occurrence of a calamity. In particular, we devise a novel stochastic geometry framework where the functioning ground base stations are modeled as an inhomogeneous Poisson point process, and promote proper silencing as an effective solution to improve both coverage and reliability (which is usually overlooked in emergency scenarios); in particular, the latter is evaluated by means of the signal-to-interference-plus-noise ratio (SINR) meta distribution performance metric. The derived downlink performances assume Rayleigh fading conditions for all wireless links. The numerical results show insightful trends in terms of both average coverage probability (which is optimized by choosing the best area for applying the silencing strategy) and SINR meta distribution, depending on: distance of the UE from the disaster epicenter (henceforth intended as the center of the area where the BS can be damaged), disaster radius (also referring to the latter area), and quality of resilience of the terrestrial network. The aim of this paper is therefore to prove the effectiveness of proper silencing in emergency scenarios, at least from the coverage and reliability perspectives.

AbstractIn meta-analysis, heterogeneity between independent studies is one of the important reference indicators for comprehensive analyses. It is usually described in terms of the variance between groups of the random-effect model. The existing methods are used to construct their confidence intervals based on the assumption of the normal distribution, but in reality, this assumption is often violated, especially in rare binary events. Recently, the method of the jackknife empirical likelihood was proposed to build confidence intervals; however, it tends to perform not as good as the parametric methods when the number of studies involved is small. Therefore, we propose to use the adjusted jackknife empirical likelihood, transformed jackknife empirical likelihood, and transformed adjusted jackknife empirical likelihood to construct confidence intervals for heterogeneity of the rare binary event. We investigate the performance of the proposed methods through the simulations based on different distributions, especially for skewed distributions and the small sample sizes. Applications to real data with the proposed methods are also provided. [ABSTRACT FROM AUTHOR]

We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased estimator, this CI has higher coverage probability for confidence levels above 91. 7%, even if the biased and unbiased estimators have equal mean squared error. The second CI trades some of this "excess" coverage for shorter length. The third CI is centered at a convex combination of the two estimators to further reduce length. Practically, these CIs apply broadly and are simple to compute. [ABSTRACT FROM AUTHOR]

The paper investigates the impact of sample points on SINR-based m-coverage probability in the context of 6G networks, considering the evolving landscape of mobile network architecture. Signal-Interference-Noise Ratio (SINR) is a critical metric for assessing cellular network performance. Conventionally, it is believed that increasing sample points significantly improves SINR coverage probability, especially within the range of 2^6 to 2^10. To explore this assertion, advanced simulations are conducted in both single-tier and multi-tier networking scenarios, employing the Poisson point process to spatially distribute nodes. The evaluation focuses on SINR values less than 1, using five distinct sample points. Surprisingly, the results reveal a remarkable finding: beyond an increment value of 2^2, increasing sample points has minimal impact on SINR-based m-coverage probability for both single-tier and multi-tier networks. This intriguing observation challenges the traditional understanding of the relationship between sample points and SINR coverage probability. The study's insights have significant implications for designing and optimizing 6G networks, guiding network planners in making informed decisions regarding resource allocation and computational tradeoffs. As 6G technology ushers in a transformative era of interconnectedness, understanding the saturation point of SINR coverage probability becomes pivotal for unleashing its full potential, fostering global connectivity and enabling innovative applications. [ABSTRACT FROM AUTHOR]

We present a numeric search algorithm to determine confidence intervals for the parameters of the negative binomial distribution that are substantially more precise (shorter) than those of any existing method. We derive confidence intervals for the mean μ for any specified number of successes k by means of a conditional minimal cardinality approach that efficiently accommodates the relationship of the variability of the negative binomial distribution to its mean. Confidence intervals for the success parameter p are easily obtained from the inverse relationship between μ and p. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are commonly used to test the performance of estimators and models from rival methods, under a range of data-generating processes. This tool improves our understanding of the relative merits of rival methods in different contexts, such as varying sample sizes and violations of assumptions. When used, it is common to report the bias or the root mean squared error of the different methods. It is far less common to report the standard deviation, overconfidence, coverage probability, or power. Each of these six performance statistics provides important, and often differing, information regarding a method's performance. Here, we present a structured way to think about Monte Carlo performance statistics. In replications of three prominent papers, we demonstrate the utility of our approach and provide new substantive results about the performance of rival methods. [ABSTRACT FROM AUTHOR]

Because of the increased mobility of vehicle users, it might be difficult to keep communication services in vehicle networks effective and dependable. Huge hurdles have been presented to vehicular networks as a result of the meteoric rise in the amount of data, which comes with the needs of high dependability and low latency. The deployment of access point servers at geographic locations that are closer to the vehicles in order to provide real-time service to applications that are based on the vehicles is one possible option. However, there is a limited amount of cache store space, and there is also a lack of a tractable access mode allocation method. As a result of these factors, it is very difficult to strike a compromise between the network transmission performance and fronthaul savings. Because the signal-to-interference-ratio (SIR) can be enhanced with switching mode in vehicular infrastructure, it may be possible to achieve higher levels of dependability. To serve all of the vehicles, the conventional allocation in vehicular network may not be sufficient on its own for two reasons: (1) the number of vehicles exceeds the number of paths, and (2) a vehicle may be located outside of the coverage path. Therefore, the implementation of switching mode allocation in vehicular communication is very necessary in order to increase the number of vehicles that can be supplied. In this paper, allocation using V2I, V2V, and V2X modes have been analyzed to provide dependable coverage for vehicles. These methods are used for communicating with other vehicles. In this paper, the numerical analysis has been performed such that SIR is optimized. In switching mode allocation, it has been shown that establishing a variable SIR threshold is helpful in achieving a path coverage that can be relied upon. It has been shown beyond a reasonable doubt that the coverage probability is likewise directly dependent on SIR thresholds. The theoretical analysis is verified, and it is confirmed that the suggested method is capable of achieving significant performance improvement in terms of coverage probability and data rate. [ABSTRACT FROM AUTHOR]

Summary: The performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek & Fletcher (2012, Computational Statistics & Data Analysis, 56, 2809–2815), depends greatly on the data‐based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh & Abeysekera (2016, Scandinavian Journal of Statistics, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data‐based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life 'Cholesterol' data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval. [ABSTRACT FROM AUTHOR]

This work introduces a family of theta power-transformed exponentiated distributions. A sub-model, the theta power transformed exponentiated Weibull (TPTEW), is considered in detail. It is of particular interest because the density function assumes a variety of symmetrical and asymmetrical shapes. The new model's parameters have been estimated using four different approaches, including maximum likelihood, least squares, weighted least squares, and Cramer-von Mises. A simulation study has been conducted to assess the effectiveness of the same. Estimates of the TPTEW parameters derived from all four estimation techniques are efficient and very near to the true values, with negligible mean square error and biases for different combinations of parameters. Moreover, the model's usefulness is investigated using three data sets. Based on comparison with the existing most popular distributions in the literature, the results demonstrate that the proposed model provides a better fit to the data. [ABSTRACT FROM AUTHOR]

In combination with the expected traffic avalanche foreseen for the next decade, solutions supporting energy-efficient, scalable and flexible network operations are essential. Considering the myriad of user case requirements, THz and mmW bands will play key roles in 6G networks. While mmW is known for short-rate LOS connections, THz transmission is subjected to even severe propagation losses, resulting in very short-range connections. In this context, we evaluate a dynamic multi-band user association algorithm to optimize connectivity in coexisting RF/mmW/THz networks. The algorithm periodically calculates association scores for each user–base station pair based on real-time channel conditions across bands, accounting for factors like signal strength, link blockage risk and noise. It then reassociates users in batches to balance loads while considering user priorities and network conditions. We simulate the algorithm's performance within a realistic propagation model, where high path loss, molecular absorption, blockage, and narrow beam widths contribute to lower coverage at higher frequencies. Results demonstrate the algorithm's ability to efficiently utilize network resources across diverse operating environments. In addition, our results show that the choice of frequency band depends on the specific requirements of the application, the environment, and the trade-offs between coverage distance, capacity, and interference conditions. [ABSTRACT FROM AUTHOR]

Abstract Because of the increased mobility of vehicle users, it might be difficult to keep communication services in vehicle networks effective and dependable. Huge hurdles have been presented to vehicular networks as a result of the meteoric rise in the amount of data, which comes with the needs of high dependability and low latency. The deployment of access point servers at geographic locations that are closer to the vehicles in order to provide real-time service to applications that are based on the vehicles is one possible option. However, there is a limited amount of cache store space, and there is also a lack of a tractable access mode allocation method. As a result of these factors, it is very difficult to strike a compromise between the network transmission performance and fronthaul savings. Because the signal-to-interference-ratio (SIR) can be enhanced with switching mode in vehicular infrastructure, it may be possible to achieve higher levels of dependability. To serve all of the vehicles, the conventional allocation in vehicular network may not be sufficient on its own for two reasons: (1) the number of vehicles exceeds the number of paths, and (2) a vehicle may be located outside of the coverage path. Therefore, the implementation of switching mode allocation in vehicular communication is very necessary in order to increase the number of vehicles that can be supplied. In this paper, allocation using V2I, V2V, and V2X modes have been analyzed to provide dependable coverage for vehicles. These methods are used for communicating with other vehicles. In this paper, the numerical analysis has been performed such that SIR is optimized. In switching mode allocation, it has been shown that establishing a variable SIR threshold is helpful in achieving a path coverage that can be relied upon. It has been shown beyond a reasonable doubt that the coverage probability is likewise directly dependent on SIR thresholds. The theoretical analysis is verified, and it is confirmed that the suggested method is capable of achieving significant performance improvement in terms of coverage probability and data rate.

Constructing a confidence interval for the ratio of bivariate normal means is a classical problem in statistics. Several methods have been proposed in the literature. The Fieller method is known as an exact method, but can produce an unbounded confidence interval if the denominator of the ratio is not significantly deviated from 0; while the delta and some numeric methods are all bounded, they are only first-order correct. Motivated by a real-world problem, we propose the penalized Fieller method, which employs the same principle as the Fieller method, but adopts a penalized likelihood approach to estimate the denominator. The proposed method has a simple closed form, and can always produce a bounded confidence interval by selecting a suitable penalty parameter. Moreover, the new method is shown to be second-order correct under the bivariate normality assumption, that is, its coverage probability will converge to the nominal level faster than other bounded methods. Simulation results show that our proposed method generally outperforms the existing methods in terms of controlling the coverage probability and the confidence width and is particularly useful when the denominator does not have adequate power to reject being 0. Finally, we apply the proposed approach to the interval estimation of the median response dose in pharmacology studies to show its practical usefulness.

Confidence intervals are valuable tools in statistical practice for estimating binomial proportions, with the most well-known being the Wald and Clopper-Pearson intervals. However, it is known that these intervals perform poorly in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals in the literature, although these may also have deficiencies. In this work, we investigate the performance of several of these confidence intervals using the parametric family p^c=X+cn+2c{\widehat{p}}_{c}=\frac{X+c}{n+2c} with c≥0c\ge 0 to estimate the parameter pp. Rather than using the confidence intervals approach, this analysis is done from the hypothesis tests approach. Our primary goal with this work is to identify values of cc that result in better-performing tests and to establish an optimal procedure.

Recent cellular systems are moving towards heterogeneous cellular networks (HCNs) that consist of a mixture of miniature cells and legacy macro-cells to meet the requirements of wireless data traffic, owing to the immense amount of multi-purpose mobile applications. The inclusion of small cells is a cost-effective solution for enhancing the size and coverage of the existing macro-cellular network. This article assumes a heterogeneous cellular network consisting of two tiers of base stations (BSs): large-scale (macro) and small-scale (pico) BSs. The users are evenly distributed, and each tier of BSs and users create a uniform Poisson point process (PPP). Practical third-generation partnership project (3GPP) models for path loss are considered, and three camping/association criteria are utilized to relate user equipment (UEs) to large or small-scale BSs, including coupled and decoupled camping criteria to study coverage. The impact of several system design parameters on coverage is investigated using the aforementioned heterogeneous cellular network, association criteria, and 3GPP path loss models. Our simulation results provide insights into the effect of infrastructure sharing between macro and pico-cells and user density on coverage. We also explore the impact of fractional power control (FPC) and signaling limits on coverage under all considered association strategies. Finally, we investigate the effect of open-loop UE transmission power, pico-density, and biasing on coverage. Specifically, we thoroughly explore the effect of empty BSs on coverage under all system design parameters.

Abstract Inferring the difference between means of two independent normal distributions with unknown variances, which is called the Behrens–Fisher problem, is common in statistical studies. The performance of classical methods for the Behrens–Fisher problem is a little liberal or conservative for small sample sizes. Moreover, classical methods are not easy to understand for students. In this article, we present a simple approximation method for the Behrens–Fisher problem, which is suitable for small sample sizes. The proposed method demonstrated shortened expected widths (EWs) while maintaining the coverage probabilities (CPs). The proposed method is a competitive alternative methods for small sample sizes. All methods were illustrated using three real examples. We recommended several methods for use in practice according to their performance in both CPs and EWs. [ABSTRACT FROM AUTHOR]

The dependency structure between hydrological variables is of critical importance to hydrological modelling and forecasting. When a copula capturing that dependence is fitted to a sample, information on the uncertainty of the fit is needed for subsequent hydrological calculations and reasoning. A new method is proposed to report inferential uncertainty in a copula parameter. The method is based on confidence curves constructed with the use of a pseudo maximum likelihood estimator for the copula parameter. The method was tested on synthetic data and then used as a tool in two hydrological examples. The first examines the probability of major floods in two locations on the Rhine River and its tributaries in the same calendar year. In the second example, rainfall-runoff from a karst region in Tunisia was analysed to determine a confidence interval for the delay between precipitation and runoff. [ABSTRACT FROM AUTHOR]

When teaching we usually not only demonstrate/discuss how a certain method works, but, not less important, why it works. In contrast, the Wald confidence interval for a binomial p constitutes an excellent example of a case where we might be interested in why a method does not work. It has been in use for many years and, sadly enough, it is still to be found in many textbooks in mathematical statistics/statistics. The reasons for not using this interval are plentiful and this fact gives us a good opportunity to discuss all of its deficiencies and draw conclusions which are of more general interest. We will mostly use already known results and bring them together in a manner appropriate to the teaching situation. The main purpose of this article is to show how to stimulate students to take a more critical view of simplifications and approximations. We primarily aim for master's students who previously have been confronted with the Wilson (score) interval, but parts of the presentation may as well be suitable for bachelor's students. [ABSTRACT FROM AUTHOR]

It is well known that the variances of the least squares estimates are large and they can be far away from their true values in the case of multicollinearity. Therefore, the ridge regression method can be used as an alternative to the least squares method. However, the ridge estimator has a disadvantage that its distribution is unknown, so only asymptotic confidence intervals are obtained. The purpose of this paper is to study the impact of several ridge regularization parameters on the mean interval lengths of the confidence intervals and coverage probabilities constructed by the ridge estimator. A bootstrap method for the selection of ridge regularization parameter is used as well as the parametric methods. In order to compare the confidence intervals, standard normal approximation, student-t approximation and bootstrap methods are used and comparison is illustrated via real data and simulation study. The simulation study shows that the bootstrap choice of ridge regularization parameter yields narrower standard normal approximated confidence intervals than the PRESS choice of ridge regularization parameter but wider standard normal approximated, student-t approximated and bootstrap confidence intervals than the GCV choice of ridge regularization parameter. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is emerging as a promising technology to achieve coverage enhancement. This paper develops a tractable analytical framework based on stochastic geometry for performance analysis of RIS-assisted millimeter wave networks. Based on the framework, a two-step cell association criterion is proposed, and the analytical expressions of the user association probability and the coverage probability in general scenarios are derived. In addition, the closed-form expressions of the two performance metrics in special cases are also provided. The simulation results verify the accuracy of the theoretically derived analytical expressions, and reveal the superiority of deploying RISs in millimeter wave networks and the effectiveness of the proposed cell association scheme to improve coverage. Furthermore, the effects of the RIS parameters and the BS density on coverage performance are also investigated. [ABSTRACT FROM AUTHOR]

Due to the discrete nature and parameter constraints, the interval estimation of a Poisson parameter with background has been a challenging problem in statistics. Among the existing good methods, the FC interval, RW interval, G interval, MS interval, and EB interval have conservative coverage probability in our simulation study. In this paper, we propose a randomized confidence interval (CI) for a constrained Poisson parameter based on the inferential model (IM) and suggest the practical use of its nonrandomized approximation. The randomized IM CI is proven to guarantee the exact coverage probability, and our nonrandomized approximation has coverage closer to the confidence coefficient than the existing CIs in most cases. Moreover, our nonrandomized interval always has the shortest expected length among the six CIs. Finally, a real example is used to demonstrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

Measurement errors affect the properties of obtained optimal estimators. Further, they affect the accuracy of estimation, although the size of the measurement error required to invalidate an estimation method remains unknown. In this study, we described the effects of measurement errors on estimation and the derived asymptotic covariance matrix by using the properties of unbiased estimating equations. We evaluated different estimation methodologies using various combinations of sample sizes and average reliability ratios. Simulation studies have compared estimators in terms of simulated bias, mean squared error, and coverage probability for the slope parameter. By comparing estimation approaches in terms of bias, mean squared error, and coverage probability, we found that the average reliability ratio of 0.65 and a sample size of 20 yielded estimator stability, with only slight differences in these three attributes. If the sample size was increased, the cutoff point for the average reliability ratio could be relaxed. This process has been in this study illustrated using real datasets. [ABSTRACT FROM AUTHOR]

In this article, we have proposed a new confidence interval for the product of standardized generalized variance for k-multivariate normal populations. The results are reported in terms of coverage probabilities and average lengths by designing a simulation study. The performance of the proposed confidence interval is evaluated by comparing it to those provided by Najarzadeh. The results are acceptable. In order to exploit the usefulness of the proposed confidence interval, real life data applications are discussed. [ABSTRACT FROM AUTHOR]

The authors considered the problem of testing equality of two multivariate normal mean vectors when the covariance matrices are unknown and arbitrary. Given auxiliary variables with known means, the authors proposed a pivotal quantity which is similar to the Hotelling T2 statistic and obtained a satisfying approximation to its distribution. The authors also outlined hypothesis testing and confidence estimation based on the approximate distribution. The merits of the test were studied using Monte Carlo simulation. Monte Carlo studies indicated that the test is very satisfactory even for moderately small samples. At last, the authors illustrated the proposed methods by an example. [ABSTRACT FROM AUTHOR]