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Audit samples are selected by businesses, institutions, government agencies, and other organizations to check the accuracy of financial reports and assess the quality of services provided among other reasons. A standard design used in auditing is stratified simple random sampling. Point estimates and confidence intervals for population values are usual products of an audit. Cochran's sample size rule and its extension by Sugden, Smith, and Jones provided minimum sample size formulas for a simple random sample to ensure effective normal approximation and adequate coverage for nominal 95% confidence intervals of a standardized or Studentized sample mean. The purpose of this paper is to extend Cochran's rule and establish a formula for the minimum sample size for the normal approximation and the use of traditional one-sided or two-sided confidence intervals to be acceptable for mean estimation in stratified simple random samples. We concentrate on variables that are at least partially continuous. Simulations are used to examine the performance of our sample size formula with a variety of skewed populations based on ones encountered in auditing. [ABSTRACT FROM AUTHOR]

AbstractConstruction of confidence intervals (CIs) for the difference between means and for the ratio of means of two Maxwell distributions is considered. CIs based on the fiducial approach and parametric bootstrap method are proposed and compared with respect to coverage probability and precision. These methods are also extended to find CIs for a difference between percentiles and for a ratio of percentiles of two Maxwell distributions. In particular, CIs for the ratio of the 5th percentiles and for the ratio of the medians are developed and evaluated for accuracy in terms of coverage probability and compared in terms of precision. The methods are illustrated using two examples with real life data. [ABSTRACT FROM AUTHOR]

The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized pivotal quantity which is useful technique to deal with problem of nuisance parameters for finding interval estimator. This research provides the probability distribution and the properties of the statistics to lead the constructing of the confidence interval. The authors also prove the construction of the fiducial generalized pivotal quantity through iteratively reweighted least squares. The performance comparison for the new proposed method with other competing methods in the literature is studied through a simulation study. The results of the simulation study demonstrate that the proposed method is very satisfactory in terms of both the coverage probability and the average width of the confidence interval. Furthermore, the analysis of real data for patients of sickle cell disease also illustrates that the proposed method gives the smallest average width of the confidence interval. All these results confirm that the iteratively reweighted least squares fiducial generalized pivotal quantity confidence interval is recommended. [ABSTRACT FROM AUTHOR]

Abstract The process capability (PC) indices are considered numerical measures for process performance. Hence, they are widely adopted in manufacturing industry in Japan. This paper introduces a new generalized PC index, denoted as $$C_{pyk}$$ , for discrete processes, to determine the generalized $$C_{pyk}$$ index for discrete distributions-an area not previously explored in the literature. Some estimation methods are employed to estimate the discrete generalized PC index, $$C_{pyk}$$ , for the discrete Lindley distribution. The performance of these methods is also explored using simulation results. Additionally, non-parametric bootstrap methods, such as standard, percentile, student, and bias-corrected percentile, are used for interval estimation that provide more information than point estimates. In the simulation study, the coverage probabilities and average widths are examined for the bootstrap methods. The simulation results demonstrate that the maximum likelihood and bias-corrected percentile bootstrap methods outperform other estimation techniques. Two real-world applications are used to validate the theoretical findings.

In beyond 5G (B5G), the higher directivity and attenuation make millimeter-wave (mmWave) very vulnerable to blockages that degrades the system performance. However, reconfigurable intelligent surface (RIS) is considered as a key enabler for B5G applications to avoid the blockages effect. In this paper, to accurately model real-world behavior, we investigate a new analytical framework model for a RIS-aided wireless communication system with a random user deployment over Nakagami-$m$ fading channel where the user's position distributes according to random waypoint (RWP) model, to characterize the performance of the system, considering direct and indirect links. As a result, new expressions for end-to-end signal-to-noise ratio (SNR), coverage probability, and ergodic capacity (EC) are derived. The impact of different metrics such as: blockages density ($\lambda _{b}$), number of RIS reflecting elements ($N$), fading parameter at the indirect link ($m_{R}$), and path loss parameter ($\alpha$) has been studied to evaluate the system performance. The results provide valuable insights into the performance of the system under these metrics. The coverage probability is degraded by increasing the blockage density and path loss parameter as they hinder the signal propagation and limit the signal strength at the MU. For example, at $-10$ dB, the coverage probability is degrading from $8\times 10^{-2}$ for blockage density $\lambda _{b}=3$ Blockes/$km^{2}$ to $5\times 10^{-5}$ at $\lambda _{b}=11$ Blockes/$km^{2}$. On the other hand, increasing the number of RIS reflecting elements ($N$) and fading parameter ($m_{R}$) at the indirect link, improves the coverage probability by enhancing the signal strength, reducing the effects of fading, and compensating for environmental challenges such as blockages. For example, the coverage probability, at $-10$ dB, increases from $3\times 10^{-1}$ at number of reflecting elements $N = 15$ to $8\times 10^{-1}$ at $N=40$. As well, the increasing of $N$ and $m_{R}$ can significantly boost the EC as the system can direct the signal more effectively, which improves the overall signal quality and system capacity. The accuracy of the analysis is validated using the Monte Carlo simulations, which shows excellent agreement with the derived expressions.

The performance analysis for the reconfigurable intelligent surface (RIS)-aided large-scale heterogeneous networks (HetNets) with spatial repulsion among base stations (BSs) in real networks has yet to be fully explored. To fill the gap, the user performance in the RIS-aided two-tier HetNet with repulsion is analyzed in this paper. Specifically, the approximate closed-form expressions of the coverage probability (CP) of the typical user (TU) for the RIS-assisted two-tier HetNet, in which the spatial locations of the macrocell BSs are modeled as Beta Ginibre Point Process ( $\beta $ -GPP), under different operation models of RIS are derived. Moreover, for some special situations, simple formulas can be derived from these closed-form expressions, which numerically reveal the effectiveness of RIS on enhancing the CP in HetNet over the case without RIS. In addition, the extension of our analysis to the case where RISs are randomly scattered in the HetNets is discussed in this paper. Finally, we find that the CP of the TU in the real RIS-aided HetNet can be well predicted with high accuracy by our analysis in the numerical results, in which the performance comparison under different cases for different operation models of RIS is also conducted to provide a guidance for the effective utilization of RIS in practical HetNet.

In 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]

Forecasting future observations is one of the main goals of time series modeling. Point forecasts are the most common type of prediction, but interval predictions are more informative, usually obtained as prediction intervals (PIs). The conventional Box-Jenkins PIs perform well when the underlying distributional assumptions hold. To circumvent such adherence, resampling methods such as residual based Bootstrap were one of the approaches for constructing PIs, but these are only suitable when the order of the process is known. Sieve Bootstrap method has the advantage of requiring no such prior knowledge. In this work, two new Sieve Bootstrap methods have been proposed. The performance of the proposed methods for constructing PIs have been compared with the existing Bootstrap methods. One of the proposed methods, namely, predictive residual based rescaled Sieve Bootstrap (PRSB) has been found to outperform the other proposed predictive residual based Sieve Bootstrap (PSB) and also the existing methods considered. PSB method has been found to be superior to Box-Jenkins and existing Sieve Bootstrap methods. The proposed methods are not only an improvement over the existing predictive residual based Bootstrap methods in AR(p) set up but also have been extended to be applicable in ARMA(p, q) situations as well. [ABSTRACT FROM AUTHOR]

Pointwise tolerance intervals for linear regression models are well established in the literature, however, there is no gold standard for a procedure to construct simultaneous tolerance intervals for linear regression models. The existing methods vary considerably with respect to their finite sample performance in terms of coverage probabilities. Moreover, the numerical investigations into their coverage performance have only been conducted under very limited settings. In this work, we investigate the coverage performance for the major procedures available for the construction of simultaneous tolerance intervals for linear regression models, with increasing complexity in the structure of the models considered. We further show that an adjustment made to the confidence level for a product-set-based method provides coverages close to nominal for the majority of models considered, and this adjusted method is nearly always better than each of the other existing methods. Simultaneous tolerance intervals are then constructed and interpreted for a chemical oxygen demand regression model and two models for the strength of polymer-modified cement mortar. [ABSTRACT FROM AUTHOR]

AbstractWe study interval estimation of the sample size parameter of the binomial and hypergeometric distributions and of the count parameter of the negative binomial distribution. We compare the performance of the analogs of some of the most notable confidence procedures in the literature, adapting these procedures to our setting. We consider only methods that maintain a coverage probability at or above the nominal confidence level, and in all cases analyzed we identify the procedure(s) attaining the shortest confidence interval length, as judged by cumulative average length and expected length. A link to a Shiny web app is provided for computing the recommended confidence intervals in practice. [ABSTRACT FROM AUTHOR]

In 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 ( n = 10 and 15) 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. [ABSTRACT FROM AUTHOR]

Portnoy (The American Statistician, 73:1, 10–15, 2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X ∼ N (μ , σ 2) . Here we extend this result to obtaining 1-sample confidence intervals for σ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (The American Statistician, 73:1, 10–15, 2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

The performance of energy harvesting (EH)-enabled long-range (LoRa) networks is analyzed in this work. Specifically, we employ deep learning (DL) to estimate the coverage probability (Pcov) of the considered networks. Our study incorporates a general fading distribution, specifically the Nakagami-m distribution, and utilizes tools from stochastic geometry (SG) to model the spatial distributions of all nodes and end-devices (EDs) with EH capability. The DL approach is employed to overcome the limitations of model-based methods that can only evaluate the Pcov under simplified network conditions. Therefore, we propose a deep neural network (DNN) that estimates the Pcov with high accuracy compared to the ground truth values. Additionally, we demonstrate that DL significantly outperforms the Monte Carlo simulation approach in terms of resource consumption, including time and memory.

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.

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.

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]

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]

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.

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.

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.

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.

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]

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]

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.

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]

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]