Showing papers on "Coverage probability published in 2022"

Unified Analysis of Coordinated Multipoint Transmissions in mmWave Cellular Networks

Abstract: This article performs a unified analysis of three coordinated multipoint (CoMP) transmission strategies in the downlink of mmWave cellular networks, including the fixed-number base station (BS) cooperation (FNC), the fixed-region BS cooperation (FRC), and the interference-aware BS cooperation (IAC). We first develop a comprehensive framework for CoMP operation in cellular networks, and investigate the network performance under a Poisson point process (PPP) model together with mmWave spectrum. To show what fraction of users in the network achieve target reliability for a given signal to interference-plus-noise ratio (SINR)/signal-to-interference ratio (SIR), we derive the SINR/SIR meta distributions, and further obtain the coverage probability as well as mean local delay for the three cooperation strategies. A pivotal intermediate step to compute the performance metrics is the derivation of joint distributions of distances between a typical user and cooperative BSs. Our analysis demonstrates that parameters of blockage have a significant influence on the network performance for the three CoMP schemes. We find that the FRC scheme makes more users achieve the given link reliability for the scenario with a low density of BSs, while the IAC scheme provides better performance for the network with a high density of BSs. Moreover, the optimal CoMP scheme can be approximately selected by considering the nearest distance from the serving BS to user and the radius of the approximate line-of-sight (LoS) region in the cellular networks.

Interval prediction of short-term traffic speed with limited data input: Application of fuzzy-grey combined prediction model

Abstract: Short-term traffic speed prediction, including level and interval prediction, is a key component of proactive traffic control in the intelligent transportation systems (ITS). In particular, predicting intervals may provide traffic managers with more useful information for making reasonable decisions than predicting traffic levels. In this study, a combined model (FIG-GARM) of fuzzy information granulation (FIG) and grey autoregressive model (GARM) is proposed for the prediction interval (PI) of traffic speed. In order to investigate the performance of the FIG-GARM model, using real-world traffic speed data collected from an urban freeway in Edmonton, Canada, and the proposed FIG-GARM model is compared with the interval-grey model first order single variable (GM (1,1)), FIG-GM (1,1), and interval-GARM for PI of traffic speed. The results show that the FIG-GARM model can generate workable PI of the traffic speed, proving the validity of the proposed model. In addition, the PI of traffic speed obtained by FIG-GARM model has higher prediction interval coverage probability (PICP), narrower width interval (WI), and higher index P, which can provide decision support for the robust and accurate prediction of intelligent transportation systems.

Stochastic Geometry Analysis of IRS-Assisted Downlink Cellular Networks

Abstract: Using stochastic geometry tools, we develop a comprehensive framework to analyze the downlink performance of various types of users (e.g., users served by direct base station (BS) transmissions and indirect intelligent reflecting surface (IRS)-assisted transmissions) in a cellular network with multiple BSs and IRSs. For the proposed users, we provide the approximate expressions for the performance in terms of coverage probability, ergodic capacity, and energy efficiency (EE). The proposed stochastic geometry framework can capture the impact of channel fading, locations of BSs and IRSs, arbitrary phase-shifts and interference experienced by a typical user supported by direct transmission and/or IRS-assisted transmission. For IRS-assisted transmissions, we first model approximate the desired signal power from the nearest IRS as a sum of scaled generalized gamma (GG) random variables whose parameters are functions of the IRS phase shifts. Then, we derive the Laplace Transform (LT) of the received signal power in a closed form. Also, we approximate the aggregate interference from multiple IRSs as the sum of normal random variables. Then, we derive the LT of the aggregate interference from all IRSs and BSs. The derived LT expressions are used to calculate coverage probability, ergodic capacity, and EE for users served by direct BS transmissions as well as users served by IRS-assisted transmissions. Finally, we derive the overall network coverage probability, ergodic capacity, and EE based on the fraction of direct and IRS-assisted users, which is defined as a function of the deployment density of IRSs, as well as blockage probability of direct transmission links. Numerical results validate the derived analytical expressions and extract useful insights related to the number of IRS elements, large-scale deployment of IRSs and BSs, and the impact of IRS interference on direct transmissions.

Performance Analysis of Cascaded Reconfigurable Intelligent Surface Networks

Abstract: Reconfigurable intelligent surfaces (RIS) have been presented as a solution to realize the concept of smart radio environments, wherein uninterrupted coverage and extremely high quality of service can be ensured. In this letter, assuming that multiple RIS are deployed in the propagation environment, the performance of a cascaded RIS network affected by imperfect phase estimation is evaluated. Specifically, we derive closed-form expressions for the outage probability, the ergodic capacity and the average symbol error probability that can be utilized to evaluate the coverage of the proposed network, as well as the average capacity and the data transmission accuracy. Finally, we validate the derived expressions through simulations and show that by choosing the number of the participating RIS correctly, a cascaded RIS network can outperform a single RIS-aided system and extend the network’s coverage efficiently.

Coverage Analysis for UAV-Assisted mmWave Cellular Networks Using Poisson Hole Process

Abstract: To reduce strong mutual interference between unmanned aerial vehicles (UAVs) and ground base stations (GBSs) and to balance the quality of service (QoS) of cell-center and cell-edge users, in UAV-assisted millimeter wave (mmWave) cellular networks we let the UAVs serving as aerial base stations (ABSs) keep a certain distance from the GBSs. It is assumed that GBSs are distributed by a Poisson point process (PPP) on the ground, and the location of UAVs is modeled as a Poisson hole process (PHP) at a certain altitude. Based on the preserving neighbor hole approximation method, the nearest distance distribution functions are derived. With the strongest average received power association policy, we provide the distribution functions of serving distances and the user association probabilities. Then, the coverage probability of the considered network is derived. The coverage performance of two special cases, the mmWave terrestrial cellular network and the UAV-assisted mmWave cellular network with PPP model, are also derived. In addition, the analysis framework is extended into the scenario where UAVs have different altitudes. Through simulations, optimal key ABS parameters maximizing the coverage probability are demonstrated. It also unveils that the proposed UAV-assisted mmWave cellular network can enhance the coverage probability via carefully designing of system parameters.

Bayesian Confidence Interval for Ratio of the Coefficients of Variation of Normal Distributions: A Practical Approach in Civil Engineering

Abstract: The coefficient of variation (CV) is a useful statistical tool for measuring the relative variability between multiple populations, while the ratio of CVs can be used to compare the dispersion. In statistics, the Bayesian approach is fundamentally different from the classical approach. For the Bayesian approach, the parameter is a quantity whose variation is described by a probability distribution. The probability distribution is called the prior distribution, which is based on the experimenter’s belief. The prior distribution is updated with sample information. This updating is done with the use of Bayes’ rule. For the classical approach, the parameter is quantity and an unknown value, but the parameter is fixed. Moreover, the parameter is based on the observed values in the sample. Herein, we develop a Bayesian approach to construct the confidence interval for the ratio of CVs of two normal distributions. Moreover, the efficacy of the Bayesian approach is compared with two existing classical approaches: the generalised confidence interval (GCI) and the method of variance estimates recovery (MOVER) approaches. A Monte Carlo simulation was used to compute the coverage probability (CP) and average length (AL) of three confidence intervals. The results of a simulation study indicate that the Bayesian approach performed better in terms of the CP and AL. Finally, the Bayesian and two classical approaches were applied to analyse real data to illustrate their efficacy. In this study, the application of these approaches for use in classical civil engineering topics is targeted. Two real data, which are used in the present study, are the compressive strength data for the investigated mixes at 7 and 28 days, as well as the PM2.5 air quality data of two stations in Chiang Mai province, Thailand. The Bayesian confidence intervals are better than the other confidence intervals for the ratio of CVs of normal distributions. Doi: 10.28991/CEJ-SP2021-07-010 Full Text: PDF

Mobility-Aware Performance in Hybrid RF and Terahertz Wireless Networks

Abstract: Using tools from stochastic geometry, this paper develops a tractable framework to analyze the performance of a mobile user in a two-tier wireless network operating on sub-6GHz and terahertz (THz) transmission frequencies. Specifically, using an equivalence distance approach, we characterize the overall handoff (HO) probability in terms of the horizontal and vertical HO and mobility-aware coverage probability. In addition, we characterize novel coverage probability expressions for THz network in the presence of molecular absorption noise and highlight its significant impact on the users’ performance. Specifically, we derive a novel closed-form expression for the Laplace Transform of the cumulative molecular noise and interference observed by a mobile user in a hybrid RF-THz network. Furthermore, we provide a novel approximation to derive the conditional distance distributions of a typical user in a hybrid RF-THz network. Finally, using the overall HO probability and coverage probability expressions, the mobility-aware probability of coverage has been derived in a hybrid RF-THz network. Our mathematical results validate the correctness of the derived expressions using Monte-Carlo simulations. The results offer insights into the adverse impact of users’ mobility and molecular noise in THz transmissions on the probability of coverage of mobile users. Our results demonstrate that a small increase in the intensity of terahertz base-stations (TBSs) (about 5 times) can increase the HO probability much more compared to the case when the intensity of RF BSs (RBSs) is increased by 100 times. Furthermore, we note that high molecular absorption can be beneficial (in terms of minimizing interference and molecular noise) for specific deployment intensity of TBSs and the benefits can outweigh the drawbacks of signal degradation due to molecular absorption.

Coverage Probability of Double-IRS Assisted Communication Systems

Abstract: In this letter, we focus on the coverage probability of a double-intelligent reflecting surface (IRS) assisted wireless network and study the impact of multiplicative beamforming gain and correlated Rayleigh fading. In particular, we obtain a novel closed-form expression of the coverage probability of a single-input single-output (SISO) system assisted by two large IRSs while being dependent on the corresponding arbitrary reflecting beamforming matrices (RBMs) and large-scale statistics in terms of correlation matrices. Taking advantage of the large-scale statistics, i.e., statistical channel state information (CSI), we perform optimization of the RBMs of both IRSs once per several coherence intervals rather than at each interval. Hence, we achieve a reduction of the computational complexity, otherwise increased in multi-IRS-assisted networks during their RBM optimization. Numerical results validate the analytical expressions even for small IRSs, confirm enhanced performance over the conventional single-IRS counterpart, and reveal insightful properties.

Performance of dense wireless networks in 5G and beyond using stochastic geometry

Abstract: Device density in cellular networks is expected to increase considerably in the near future. Accordingly, the access point (AP) will be equipped with massive multiple-input multiple-output (mMIMO) antennas, using collimated millimeter-wave (mmW) and sub-THz communications, and increasing the bandwidth to accommodate the growing data rate demands. In this scenario, interference plays a critical role and, if not characterized and mitigated properly, might limit the performances of the network. In this context, this paper derives the statistical properties of the aggregated interference power for a cellular network equipping a mMIMO cylindrical array. The proposed statistical model considers the link blockage and other network parameters such as antenna configuration and device density. The findings show that the characteristic function (CF) of the aggregated interference power can be regarded as a weighted mixture of two alpha-stable distributions. Furthermore, by analyzing the service probability, it is found that there is an optimal configuration of the array depending on the AP height and device density. The proposed statistical model can be part of the design of dense networks providing valuable insights for optimal network deployment and resource management and scheduling.

OUP accepted manuscript

Abstract: Abstract It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval’s performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately $50\%$ probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations.

Coverage Analysis of mmWave and THz-Enabled Aerial and Terrestrial Heterogeneous Networks

Abstract: Heterogeneous networks (HetNets) are becoming a promising solution for future wireless systems to satisfy the high data rate requirements. This paper introduces a stochastic geometry framework for the analysis of the downlink coverage probability in a multi-tier HetNet consisting of a macro-base station (MBS) operating at sub-6 GHz, millimeter wave (mmWave)-enabled unmanned aerial vehicles (UAVs) operating at 28 GHz, and small BSs operating both at mmWave and THz frequencies. The analytical expressions for the coverage probability for each tier have been derived in the paper. Monte Carlo simulations are then performed to validate the analytical expressions. The effectiveness of the HetNet is analyzed on various performance metrics including association and coverage probabilities for different network parameters. We show that the mmWave and THz-enabled cells provide significant improvement in the achievable data rates because of their high available bandwidths, however, they have a degrading effect on the coverage probability due to their high propagation losses.

Outage Probability of Intelligent Reflecting Surface Assisted Full Duplex Two-Way Communications

Abstract: In this letter, we study the outage probability (OP) of intelligent reflecting surface (IRS) assisted full duplex two-way (TW) communication systems, which characterizes the performance of overcoming the transmitted data loss caused by long deep fades. To this end, we first derive the probability distribution of the cascaded end-to-end equivalent channel with an arbitrarily given IRS beamformer. Our analysis shows that deriving such probability distribution in the considered case is more challenging than the case with the phase-matched IRS beamformer. Then, with the derived probability distribution of the equivalent channel, we obtain the closed-form expression of the OP. It theoretically shows that the number of reflecting elements has a conspicuous effect on the improvement of the system reliability. Extensive numerical results verify the correctness of the derived results and confirm the superiority of the considered IRS assisted TW communication system comparing to the one-way counterpart.

OUP accepted manuscript

Abstract: Inverse probability weighting (IPW) and targeted maximum likelihood estimation (TMLE) are methodologies that can adjust for confounding and selection bias and are often used for causal inference. Both estimators rely on the positivity assumption that within strata of confounders there is a positive probability of receiving treatment at all levels under consideration. Practical applications of IPW require finite inverse probability (IP) weights. TMLE requires that propensity scores (PS) be bounded away from 0 and 1. Although truncation can improve variance and finite sample bias, this artificial distortion of the IP weights and PS distribution introduces asymptotic bias. As sample size grows, truncation-induced bias eventually swamps variance, rendering nominal confidence interval coverage and hypothesis tests invalid. We present a simple truncation strategy based on the sample size, n, that sets the upper bound on IP weights at $\sqrt{\textit{n}}$ ln n/5. For TMLE, the lower bound on the PS should be set to 5/($\sqrt{\textit{n}}$ ln n/5). Our strategy was designed to optimize the mean squared error of the parameter estimate. It naturally extends to data structures with missing outcomes. Simulation studies and a data analysis demonstrate our strategy's ability to minimize both bias and mean squared error in comparison with other common strategies, including the popular but flawed quantile-based heuristic.

On the Deployment of Small Cells in 3D HetNets With Multi-Antenna Base Stations

Abstract: With the dense deployment of small cells, the impact of height difference between base stations (BSs) and user equipment (UE) on the performance of heterogeneous networks (HetNets) becomes significant. The traditional two-dimensional models are no longer sufficient to capture the three-dimensional (3D) features of dense HetNets. On the other hand, deploying multiple antennas on BSs is a promising approach to improve network capacity. In this paper, we propose a 3D model for a $K$ -tier HetNet with multi-antenna BSs, where different tiers share the same frequency band but may differ in BS height, BS density, number of antennas per BS, BS transmit power, association bias, and path loss exponent. We analytically derive the per-tier association probability under both the strongest received signal and the closest BS cell-association strategies. Based on that, we derive the expressions for the downlink ergodic rate, area spectral efficiency (ASE) and energy efficiency. The numerical results reveal that in the presence of macrocell BSs, for low to medium small-cell BS (SBS) densities, the closest BS cell-association strategy leads to low ergodic rate, ASE and energy efficiency regardless of the SBS height; while at very high SBS densities, under both cell-association strategies, SBSs should be deployed at the same height as UE to achieve high ergodic rate, ASE and energy efficiency. Moreover, we find that for a given SBS height, there exists an optimal combination of SBS density and number of antennas per SBS that maximizes the system energy efficiency.

Data-Adaptive Selection of the Propensity Score Truncation Level for Inverse Probability Weighted and Targeted Maximum Likelihood Estimators of Marginal Point Treatment Effects.

Abstract: Inverse probability weighting (IPW) and targeted maximum likelihood estimation (TMLE) are methodologies that can adjust for confounding and selection bias that are often used for causal inference. Both estimators rely on the positivity assumption that within strata of confounders there is a positive probability of receiving treatment at all levels under consideration. Practical applications of IPW require finite IP weights. TMLE requires propensity scores (PS) be bounded away from zero and one. Although truncation can improve variance and finite sample bias, this artificial distortion of the IP weights and PS distribution introduces asymptotic bias. As sample size grows, truncation-induced bias eventually swamps variance, rendering nominal confidence interval coverage and hypothesis tests invalid. We present a simple truncation strategy based on the sample size, $n$, that sets the upper bound on IP weights at $\sqrt{n}\ln n/5$. For TMLE, the lower bound on the PS should be set to $5/\left(\sqrt{n}\ln n\right)$). Our strategy was designed to optimize mean squared error (MSE) of the parameter estimate. It naturally extends to data structures with missing outcomes. Simulation studies and a data analysis demonstrate our strategy's ability to minimize both bias and MSE compared to other common strategies, including the popular, but flawed, quantile-based heuristic.

Interval Prediction Method for Solar Radiation Based on Kernel Density Estimation and Machine Learning

Abstract: Precise global solar radiation (GSR) data are indispensable to the design, planning, operation, and management of solar radiation utilization equipment. Some examples prove that the uncertainty of the prediction of solar radiation provides more value than deterministic ones in the management of power systems. This study appraises the potential of random forest (RF), V-support vector regression (V-SVR), and a resilient backpropagation artificial neural network (Rprop-ANN) for daily global solar radiation (DGSR) point prediction from average relative humidity (RHU), daily average temperature (AT), and daily sunshine duration (SD). To acquire more accurate predictions of DGSR and examine the influence of historical DGSR on the performance of point prediction models, two different model inputs are considered: (1) three meteorological variables and (2) the lags of DGSR and three meteorological variables. Then, two interval prediction methods are developed by introducing the KDE to out-of-bag (OOB), introducing kernel density estimation (KDE) to split conformal (SC) based on the three machine learning models. The two methods for interval prediction are denoted as OOB-KDE and SC-KDE. The mean absolute error (MAE), mean relative error (MRE), and Kendall rank correlation (Kendall) are used to assess the point prediction models. The performance of interval prediction methods is evaluated by the prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width criteria (CWC). The following conclusions are drawn from this study. First, the V-SVR model performs best with the lowest mean absolute error (MAE) of 0.016 and mean relative error (MRE) of 0.001. Second, the lags of DGSR improve the prediction accuracy by about 30%. Third, the OOB-KDE and SC-KDE methods improved the quality of the prediction interval (PI). OOB-KDE improved CWC by 81%, and SC-KDE improved CWC by 99.99%. Fourth, the best interval prediction result is obtained using the SC-KDE method using the V-SVR model. The average difference between its PICP and prediction interval nominal coverage (PINC) is only 3% of the PINC, and its PINAW is less than 0.007.

Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier Sensing

Abstract: We propose using Carrier Sensing (CS) for distributed interference management in millimeter-wave (mmWave) cellular networks where spectrum is shared by multiple operators that do not coordinate among themselves. In addition, even the base station sites can be shared by the operators. We describe important challenges in using traditional CS in this setting and propose enhanced CS protocols to address these challenges. Using stochastic geometry, we develop a general framework for downlink coverage probability analysis of our shared mmWave network in the presence of CS and derive the downlink coverage probability expressions for several CS protocols. Our work is the first to investigate and analyze (using stochastic geometry) CS for mmWave networks with spectrum and BS sites shared among non-coordinating operators. We evaluate the downlink coverage probability of our shared mmWave network using simulations as well as numerical examples based on our analysis. Our evaluations show that our proposed approach leads to an improvement in coverage probability, compared to the coverage probability with no CS, for higher values of signal-to-interference and noise ratio (SINR). Interestingly, our evaluations also reveal that for lower values of SINR, not using any CS is the best strategy in terms of the downlink coverage probability.

Performance Modeling and Analysis of Base Station Cooperation for Cellular-Connected UAV Networks

Abstract: This paper studies the performance of base station (BS) cooperation for the downlink transmission of an unmanned aerial vehicle (UAV) in a cellular-connected UAV network. Performance models are derived for investigating the downlink transmission performance of a UAV with BS cooperation in terms of coverage probability and achievable throughput. In deriving the performance models, we consider two UAV distribution cases: general case and worst case, in which the locations of UAVs follow different distributions. Meanwhile, we introduce a line-of-sight (LoS) ball model to describe the LoS probability of the downlink channel between a BS and a UAV, and show that it has a good approximation to the ITU LoS model, and can largely simplify the derivation of the performance models. Monte Carlo simulation results are shown to validate the derived performance models. The impacts of major network parameters on the downlink transmission performance are investigated through numerical results. The performance models can be used to provide theoretical guidance for the design of a BS cooperation strategy.

Confidence intervals of mean residual life function in length-biased sampling based on modified empirical likelihood

Abstract: ABSTRACT The mean residual life (MRL) function is one of the basic parameters of interest in survival analysis. In this paper, we develop three procedures based on modified versions of empirical likelihood (EL) to construct confidence intervals of the MRL function with length-biased data. The asymptotic results corresponding to the procedures have been established. The proposed methods exhibit better finite sample performance over other existing procedures, especially in small sample sizes. Simulations are conducted to compare coverage probabilities and the mean lengths of confidence intervals under different scenarios for the proposed methods and some existing methods. Two real data applications are provided to illustrate the methods of constructing confidence intervals.

Measurements and Analysis of Large Scale LoRa Network Efficiency

Abstract: The LoRa networks allow building long-range and low power wireless networks using a star of stars topology, with multiple gateways serving low-cost devices. We present the measurements obtained in an urban environment from two independent real-life network topologies located in two Polish cities. These topologies consist of about 6400 and 4400 location points and included more than eight mln data points. We focus on the variability of RSSI (Received Signal Strength Index), SNR (Signal to Noise Ratio), probability of packet delivery, and these measures' dependence on distance. We also present an estimated path loss derived from the measurement data. The analysis shows significant variability of packet delivery probability and the RSSI. Approximately 65% of the population provides > 80% packet delivery probability in setup A, and 85% of the population provides > 80% packet delivery probability in setup B. The calculated path loss model is slightly more pessimistic than shown by most studies, as at longer distances, the measured SNR and RSSI are higher than the actual average since all transmissions with RSSI lower than gateway sensitivity (reception threshold) are not considered in the analysis as there is no data recorded. We also compare the measurements with simulated path loss, showing that commonly used simulation models may overestimate the path loss for larger distances.

Empirical likelihood inference for the mean past lifetime function

Abstract: In survival analysis and reliability theory, the mean past lifetime (MPL), arises in situations where the mean time elapsed since the failure of a component T, given that it has failed before time t, is of interest. For inference on the MPL function, some procedures have been proposed in the literature for the MPL function's estimator. In this paper, an empirical likelihood (EL) inference procedure of the MPL function is developed. In addition to that, we obtain the adjusted EL and mean EL confidence interval for the MPL function. The EL confidence intervals are compared through extensive simulation studies in terms of coverage probability and the average length of the confidence interval. The simulation studies showed that the proposed EL methods have better coverage probability and shorter average lengths than the normal approximation results. Finally, the proposed methods are illustrated by two real data analyses.

On the SIR Meta Distribution for Cache-Enabled Wireless Networks With Random Discontinuous Transmission: Analysis and Optimization

Abstract: A fine-grained analysis of the cache-enabled networks is crucial for system design. In this paper, we focus on the meta distribution of the signal-to-interference ratio for the cache-enabled networks where the locations of the base stations are modeled as a Poisson point process. With the application of the random caching and the random discontinuous transmission schemes, we derive the moments of the conditional successful transmission probability, the exact meta distribution and its beta approximation by utilizing stochastic geometry. The closed-form expressions of the mean and variance of the local delay (i.e., the jitter) are also derived. We then consider the maximization of the mean successful transmission probability and the minimization of the average system transmission delay by jointly optimizing the caching probability and the BS active probability. Finally, the numerical results demonstrate the superiority of the proposed optimization schemes over the existing caching strategies and reveal the impacts of the key network parameters on the cache-enabled networks in terms of successful transmission probability, successful transmission probability variance, meta distribution, mean local delay and jitter.

Empirical-likelihood-based confidence intervals for quantile regression models with longitudinal data

Abstract: In this paper, we present three empirical likelihood (EL)-based inference procedures to construct confidence intervals for quantile regression models with longitudinal data. The traditional EL-based method suffers from an under-coverage problem, especially in small sample sizes. The proposed modified EL-based non-parametric methods including adjusted empirical likelihood (AEL), the transformed empirical likelihood (TEL), and the transformed adjusted empirical likelihood (TAEL) exhibit good finite sample performance over other existing procedures. Simulations are conducted to compare the performances of the proposed methods with the other methods in terms of coverage probabilities and average lengths of confidence intervals under different scenarios.

Generalized interval estimation of process capability indices for the Birnbaum–Saunders distribution

Abstract: Since sampling variation would lead to the inaccurate assessment of process capability indices (PCIs), the interval estimation of PCIs has received considerable attention recently. The coverage probabilities (CPs) of the widely used bootstrap confidence intervals (BCIs) of PCIs are not sufficiently close to their nominal confidence level. Moreover, the bootstrap method is time‐consuming. This paper develops a procedure for constructing generalized confidence intervals (GCIs) of two widely used percentile‐based PCIs for the Birnbaum–Saunders (BS) distribution. A simulation study is conducted and the results indicate that the proposed GCI outperforms its bootstrap counterparts in terms of the CPs, the average widths (AWs) of the confidence intervals, and the variability of the interval widths. Finally, two real examples are used to illustrate the implementation of the proposed procedure.

Confidence Intervals for Common Coefficient of Variation of Several Birnbaum-Saunders Distributions

Abstract: The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand.