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In this study, constant-stress accelerated life testing has been investigated using type-II censoring of failure data from a truncated normal distribution. Various classical estimation approaches are discussed for estimating model parameters, hazard rates, and reliability functions. Among these methods are maximum likelihood estimation, the EM algorithm, and maximum product spacing estimation. Interval estimation is also introduced in the context of asymptomatic confidence intervals and bootstrap intervals. Furthermore, the missing information principle was employed to compute the observed Fisher information matrix. Three optimality criteria linked with the Fisher information matrix are considered to find out the optimal value of each stress level. To interpret the proposed techniques, Monte Carlo simulations are run in conjunction with real data analysis. [ABSTRACT FROM AUTHOR]

In this paper, Bayesian and non-Bayesian estimations of the shape parameter of the Inverted Topp-Leone distribution are studied under a progressive Type I censoring scheme. The maximum likelihood estimator (MLE) and Bayes estimator (BE) of the unknown parameter under the squared error loss (SEL) function are obtained. Three types of confidence intervals are discussed for the unknown parameter. A simulation study is performed to compare the performances of the proposed methods, and two numerical examples have been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) are often used to assess process performance. Higher PCIs do not mean lower rejection rates. Thus, loss-based PCIs are better for process capability measurement. This study introduces a new capability index, S pk ′ , based on a symmetric loss function for normal process, to include loss into capability analysis. We then estimate PCI S pk ′ employing six standard techniques of estimation and compare their mean squared errors (MSEs) through simulation analysis. For the index S pk ′ , asymptotic confidence intervals (ACI), generalized confidence intervals (GCI), and parametric bootstrap confidence intervals (BCIs) are used to construct confidence intervals. Monte Carlo simulation evaluates ACI, GCI, and BCIs average widths and coverage probabilities. Our experiments showed that MPSE produced the smallest width. B C p -boot outperformed its competitors. For most sample sizes and estimation methodologies, P -boot has a greater CP. Two electronic industry data sets are evaluated to demonstrate the accuracy of the suggested estimating methodologies, ACI, GCI, and BCIs. [ABSTRACT FROM AUTHOR]

Thailand is currently grappling with a severe problem of air pollution, especially from small particulate matter (PM), which poses considerable threats to public health. The speed of the wind is pivotal in spreading these harmful particles across the atmosphere. Given the inherently unpredictable wind speed behavior, our focus lies in establishing the confidence interval (CI) for the variance of wind speed data. To achieve this, we will employ the delta-Birnbaum-Saunders (delta-BirSau) distribution. This statistical model allows for analyzing wind speed data and offers valuable insights into its variability and potential implications for air quality. The intervals are derived from ten different methods: generalized confidence interval (GCI), bootstrap confidence interval (BCI), generalized fiducial confidence interval (GFCI), and normal approximation (NA). Specifically, we apply GCI, BCI, and GFCI while considering the estimation of the proportion of zeros using the variance stabilized transformation (VST), Wilson, and Hannig methods. To evaluate the performance of these methods, we conduct a simulation study using Monte Carlo simulations in the R statistical software. The study assesses the coverage probabilities and average widths of the proposed confidence intervals. The simulation results reveal that GFCI based on the Wilson method is optimal for small sample sizes, GFCI based on the Hannig method excels for medium sample sizes, and GFCI based on the VST method stands out for large sample sizes. To further validate the practical application of these methods, we employ daily wind speed data from an industrial area in Prachin Buri and Rayong provinces, Thailand.

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the Expectation-Maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane's method and Gibbs sampling procedure, using the gamma prior and the general entropy loss (GEL) function, have been obtained. Several confidence intervals are proposed, such as the asymptotic confidence intervals (ACIs), bootstrap confidence intervals, and the highest posterior density (HPD) credible intervals. The prediction for future observations has been considered under one and two-sample Bayesian prediction methods using the type-i hybrid censoring scheme. An extensive simulation study has been conducted to numerically evaluate all the estimators' performances. The point estimators are compared through their biases and mean squared errors (MSEs). The performances of confidence intervals are evaluated using coverage probability (CP), average length (AL), and probability coverage density (PCD). Two real-life datasets have been considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

Performance capability indices are valuable measures to evaluate the quality of a product. In this paper, we consider inference on a lifetime performance index when the product's lifetime follows a gamma distribution with unknown parameters. The bias and mean square error of the maximum likelihood estimator and other proposed estimators are compared. Also, an asymptotic confidence interval using the maximum likelihood estimator, thirteen bootstrap confidence intervals, and four generalized pivotal quantities are derived for the performance capability index. A Monte Carlo simulation is provided to investigate the accuracy of expected lengths and coverage probabilities of the confidence intervals. An actual data set is used to illustrate the estimators and confidence intervals. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process's performance under this ideal scheme. [ABSTRACT FROM AUTHOR]

This paper illustrated how nonparametric bootstrap methods for double-censored data can be used to conduct some hypothesis tests, such as quartiles' hypothesis tests. Through simulation studies, the smoothed bootstrap (SB) method performed better results than Efron's method in most scenarios, particularly for small datasets. The SB method provided smaller discrepancies between the actual and nominal error rates. [ABSTRACT FROM AUTHOR]

In this paper, we consider a compartmental model to fit the real data of confirmed active cases with COVID-19 in Portugal, from March 2, 2020 until September 10, 2021 in the Primary Care Cluster in Aveiro region, ACES BV, reported to the Public Health Unit. The model includes a deterministic component based on ordinary differential equations and a stochastic component based on bootstrap methods in regression. The main goal of this work is to take into account the variability underlying the data set and analyse the estimation accuracy of the model using a residual bootstrapped approach in order to compute confidence intervals for the prediction of COVID-19 confirmed active cases. All numerical simulations are performed in R environment (R version. 4.0.5). The proposed algorithm can be used, after a suitable adaptation, in other communicable diseases and outbreaks. [ABSTRACT FROM AUTHOR]

This paper illustrated how nonparametric bootstrap methods for double-censored data can be used to conduct some hypothesis tests, such as quartiles' hypothesis tests. Through simulation studies, the smoothed bootstrap (SB) method performed better results than Efron's method in most scenarios, particularly for small datasets. The SB method provided smaller discrepancies between the actual and nominal error rates.

In this paper, we consider a compartmental model to fit the real data of confirmed active cases with COVID-19 in Portugal, from March 2, 2020 until September 10, 2021 in the Primary Care Cluster in Aveiro region, ACES BV, reported to the Public Health Unit. The model includes a deterministic component based on ordinary differential equations and a stochastic component based on bootstrap methods in regression. The main goal of this work is to take into account the variability underlying the data set and analyse the estimation accuracy of the model using a residual bootstrapped approach in order to compute confidence intervals for the prediction of COVID-19 confirmed active cases. All numerical simulations are performed in R environment ( version. 4.0.5). The proposed algorithm can be used, after a suitable adaptation, in other communicable diseases and outbreaks.

In vitro dissolution profile has been shown to be correlated with the drug absorption and has often been considered as a metric for assessing in vitro bioequivalence between a test product and corresponding reference one. Various methods have been developed to assess the similarity between two dissolution profiles. In particular, similarity factor $${f_2}$$ f 2 has been reviewed and discussed extensively in many statistical articles. Although the $${f_2}$$ f 2 lacks inferential statistical properties, the estimation of $${f_2}$$ f 2 and its various modified versions were the most widely used metric for comparing dissolution profiles. In this paper, we investigated performances of the naive $${f_2}$$ f 2 estimate method, bootstrap $${f_2}$$ f 2 confidence interval method and bias corrected-accelerated (BCa) bootstrap $${f_2}$$ f 2 confidence interval method for comparing dissolution profiles. Our studies show that naive $${f_2}$$ f 2 estimate method and BCa bootstrap $${f_2}$$ f 2 confidence interval method are unable to control the type I error rate. The bootstrap $${f_2}$$ f 2 confidence interval method can control the type I error rate under a specific level. However, it will cause great conservatism on the power of the test. To solve the potential issues of the previous methods, we recommended a bootstrap bias corrected (BC) $${f_2}$$ f 2 confidence interval method in this paper. The type I error rate, power and sensitivity among different $${f_2}$$ f 2 methods were compared based on simulations. The recommended bootstrap BC $${f_2}$$ f 2 confidence interval method shows better control of type I error than the naive $${f_2}$$ f 2 estimate method and BCa bootstrap $${f_2}$$ f 2 confidence interval method. It also provides better power than the bootstrap $${f_2}$$ f 2 confidence interval method. [ABSTRACT FROM AUTHOR]

In vitro dissolution profile has been shown to be correlated with the drug absorption and has often been considered as a metric for assessing in vitro bioequivalence between a test product and corresponding reference one. Various methods have been developed to assess the similarity between two dissolution profiles. In particular, similarity factor $${f_2}$$ f 2 has been reviewed and discussed extensively in many statistical articles. Although the $${f_2}$$ f 2 lacks inferential statistical properties, the estimation of $${f_2}$$ f 2 and its various modified versions were the most widely used metric for comparing dissolution profiles. In this paper, we investigated performances of the naive $${f_2}$$ f 2 estimate method, bootstrap $${f_2}$$ f 2 confidence interval method and bias corrected-accelerated (BCa) bootstrap $${f_2}$$ f 2 confidence interval method for comparing dissolution profiles. Our studies show that naive $${f_2}$$ f 2 estimate method and BCa bootstrap $${f_2}$$ f 2 confidence interval method are unable to control the type I error rate. The bootstrap $${f_2}$$ f 2 confidence interval method can control the type I error rate under a specific level. However, it will cause great conservatism on the power of the test. To solve the potential issues of the previous methods, we recommended a bootstrap bias corrected (BC) $${f_2}$$ f 2 confidence interval method in this paper. The type I error rate, power and sensitivity among different $${f_2}$$ f 2 methods were compared based on simulations. The recommended bootstrap BC $${f_2}$$ f 2 confidence interval method shows better control of type I error than the naive $${f_2}$$ f 2 estimate method and BCa bootstrap $${f_2}$$ f 2 confidence interval method. It also provides better power than the bootstrap $${f_2}$$ f 2 confidence interval method. [ABSTRACT FROM AUTHOR]

In this article, we studied a generalization of the log-normal distribution called Zografos-Balakrishnan log-normal distribution and investigate its various important properties and functions including moments, quantile function, various reliability measures, Rényi entropy, and some inequality measures. The estimation of unknown parameters is discussed by the methods of maximum likelihood, and the Bayesian technique and their simulation studies are also carried out. The applicability of the distribution is illustrated utilizing a real dataset. A likelihood ratio test is utilized for testing the efficiency of the third parameter. The effectiveness of this model for the dataset is also established using the parametric bootstrap approach.

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique’s and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose.

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results. [ABSTRACT FROM AUTHOR]

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique's and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, the bivariate generalized Rayleigh distribution is introduced based on Clayton copula and denoted as (Clayton-BGR). The likelihood function for progressive Type-II censoring scheme with random removal is derived and applied on the Clayton-BGR distribution. Bayesian and non -Bayesian estimation methods based on progressive Type-II censoring have been discussed. Asymptotic confidence intervals and bootstrap confidence intervals for the unknown parameters are obtained. Also, a simulation study has been conducted to compare the performances between censoring schemes. Also, two real data sets are analyzed to investigate the models and useful results are obtained for illustrative purposes. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.

The problems of estimation and classification for two logistic populations with a common location and different scale parameters are considered. The MLEs of the associated parameters are derived by solving a system of non-linear equations numerically as they do not have closed-form expressions. The asymptotic confidence intervals and bootstrap confidence intervals are derived numerically. Bayes estimators for the associated parameters using Lindley's approximation method with respect to three types of priors, namely the vague prior, Jeffrey's prior and conjugate prior, are also derived numerically. Further, Bayes estimators using the Markov chain Monte Carlo (MCMC) method that uses the Metropolis-Hastings algorithm are also derived. Moreover, using these MCMC samples, the highest posterior density (HPD) credible confidence intervals are also derived for the associated parameters. The point estimators are compared through their bias and mean squared error, whereas the interval estimators are compared through coverage probabilities and expected lengths using the Monte-Carlo simulation method numerically. Based on these estimators, certain classification rules are derived to classify a new observation into one of the two logistic populations under the same model set-up. The expected probability of misclassification for each classification rule is computed numerically to evaluate their performances. Finally, two real-life examples are considered where the datasets have been satisfactorily modeled by using the logistic distribution with a common location, and the estimation and classification methodologies have been demonstrated. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the PCI Cpc which is based on the proportion of conformance and is applicable to normally as well as non-normally and continuous as well as discrete distributed processes. In order to estimate the PCI Cpc when the process follows exponentiated exponential distribution, we have used five classical methods of estimation. The performances of these classical estimators are compared with respect to their biases and mean squared errors (MSEs) of the index Cpc through simulation study. Also, the confidence intervals for the index Cpc are constructed using five bootstrap confidence interval (BCIs) methods. Monte Carlo simulation study has been carried out to compare the performances of these five BCIs in terms of their average width and coverage probabilities. Besides, net sensitivity (NS) analysis for the given PCI Cpc is considered. We use two data sets related to electronic and food industries and two failure time data sets to illustrate the performance of the proposed methods of estimation and BCIs. Additionally, we have developed PCI Cpc using aforementioned methods for generalized Rayleigh distribution. [ABSTRACT FROM AUTHOR]

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher's information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

We propose a generalized first progressive failure hybrid censoring scheme in this paper, which guarantees the time to complete the life test. We use classical and Bayesian methods to calculate the unknown parameter's point and interval estimator of Lindley distribution under the scheme. The maximum likelihood estimation is obtained by maximizing the log-likelihood function. we calculate the asymptotic confidence intervals and coverage probabilities of the parameter. Additionally, there are two bootstrap confidence intervals by bootstrap method. In Bayes theory, the Metropolis-Hastings algorithm is applied to obtain the Bayes estimator and highest posterior density credible intervals of the unknown parameter, which has a gamma prior. The waiting time data set is analysed by the mentioned method for illustration purposes, Monte Carlo simulations experiment are designed to compare the performance of the proposed point and interval estimate methods. [ABSTRACT FROM AUTHOR]

Based on the hybrid censored samples, this article deals with the problem of point and interval estimation of the stress-strength reliability R = P(Y < X) when X and Y both have independent generalized inverted exponential distributions with different shape and common scale parameters. The maximum likelihood estimation, Bayes estimation and parametric bootstrap methods are used for estimating R. Also, asymptotic confidence interval of R is derived based on the asymptotic distribution of R. Bayesian estimation procedure is carried out using Lindley approximation and Markov Chain Monte Carlo methods. Bayes estimate and the HPD credible interval of R are obtained using non-informative and gamma informative priors. A Monte Carlo simulation study is carried out for comparing the different proposed estimation methods. Finally, a pair of real data sets is analyzed for illustration purposes.

Thailand is currently grappling with a severe problem of air pollution, especially from small particulate matter (PM), which poses considerable threats to public health. The speed of the wind is pivotal in spreading these harmful particles across the atmosphere. Given the inherently unpredictable wind speed behavior, our focus lies in establishing the confidence interval (CI) for the variance of wind speed data. To achieve this, we will employ the delta-Birnbaum-Saunders (delta-BirSau) distribution. This statistical model allows for analyzing wind speed data and offers valuable insights into its variability and potential implications for air quality. The intervals are derived from ten different methods: generalized confidence interval (GCI), bootstrap confidence interval (BCI), generalized fiducial confidence interval (GFCI), and normal approximation (NA). Specifically, we apply GCI, BCI, and GFCI while considering the estimation of the proportion of zeros using the variance stabilized transformation (VST), Wilson, and Hannig methods. To evaluate the performance of these methods, we conduct a simulation study using Monte Carlo simulations in the R statistical software. The study assesses the coverage probabilities and average widths of the proposed confidence intervals. The simulation results reveal that GFCI based on the Wilson method is optimal for small sample sizes, GFCI based on the Hannig method excels for medium sample sizes, and GFCI based on the VST method stands out for large sample sizes. To further validate the practical application of these methods, we employ daily wind speed data from an industrial area in Prachin Buri and Rayong provinces, Thailand., Competing Interests: The authors declare that they have no competing interests., (© 2024 Ratasukharom et al.)

Purpose: Propensity score-weighting for confounder control and multiple imputation to counter missing data are both widely used methods in epidemiological research. Combination of the two is not trivial and requires a number of decisions to produce valid inference. In this tutorial, we outline the assumptions underlying each of the methods, present our considerations in combining the two, discuss the methodological and practical implications of our choices and briefly point to alternatives. Throughout we apply the theory to a research project about post-traumatic stress disorder in Syrian refugees. Patients and Methods: We detail how we used logistic regression-based propensity scores to produce "standardized mortality ratio"-weights and Substantive Model Compatible-Full Conditional Specification for multiple imputation of missing data to get the estimate of association. Finally, a percentile confidence interval was produced by bootstrapping. Results: A simple propensity score model with weight truncation at 1st and 99th percentile obtained acceptable balance on all covariates and was chosen as our model. Due to computational issues in the multiple imputation, two levels of one of the substantive model covariates and two levels of one of the auxiliary covariates were collapsed. This slightly modified propensity score model was the substantive model in the SMC-FCS multiple imputation, and regression models were set up for all partially observed covariates. We set the number of imputations to 10 and number of iterations to 40. We produced 999 bootstrap estimates to compute the 95-percentile confidence interval. Conclusion: Combining propensity score-weighting and multiple imputation is not a trivial task. We present considerations necessary to do so, realizing it is demanding in terms of both workload and computational time; however, we do not consider the former a drawback: it makes some of the underlying assumptions explicit and the latter may be a nuisance that will diminish with faster computers and better implementations. [ABSTRACT FROM AUTHOR]

We are mainly interested in estimating the stress–strength parameter, say R , when the parent distribution follows the well-known Marshall–Olkin model and the accessible data has the form of the progressively Type-II censored samples. In this case, the stress–strength parameter is free of the base distribution employed in the Marshall–Olkin model. Thus, we use the exponential distribution for simplicity. The maximum likelihood methods as well as some Bayesian approaches are used for the estimation purpose. The corresponding estimators of the latter approach are obtained by using Lindley's approximation and Gibbs sampling methods since the Bayesian estimator of R cannot be obtained as an explicit form. Moreover, some confidence intervals of various types are derived for R and then compared via a Monte Carlo simulation. Finally, the survival times of head and neck cancer patients are analyzed by two therapies for illustrating purposes. [ABSTRACT FROM AUTHOR]

In this article, to estimate the generalized process capability index (GPCI) Cpyk when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI Cpyk is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI Cpyk, and coverage probabilities (CPs), and average width (AW) for interval estimates. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding MSEs. Further, the Bayes estimates based on linear-exponential loss function are more efficient than the squared error loss function under informative prior. To illustrate the performance of the proposed methods, two real data sets are analyzed.In this article, to estimate the generalized process capability index (GPCI) C p y k when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI C p y k is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI C p y k , and coverage probabilities (CPs), and average width (AW) Abbreviations: AW : Average width; P B : Bias-corrected percentile bootstrap; BCI : Bootstrap confidence interval; CDF : Cumulative distribution function; CI : Confidence interval; CK : Coefficient of kurtosis; CP : Coverage probability; CS : Coefficient of skewness; GGD : Generalized gamma distribution; GPCI : Generalized process capability index; GLD : Generalized lindley distribution; SWCI : Shortest width credible interval; IS : Importance sampling; K-S : Kolmogorov-Smirnov; L : Lower specification limi; LD : Lindley distribution; LDL : Lower desired limit LLF : Linex loss function; MCMC : Markov Chain Monte Carlo; MH : Metropolis-Hastings; MPSE : Maximum product of spacings estimator; MLE : Maximum likelihood estimator; MSE : Mean squared error; OLSE : Ordinary least squares estimator; P B : Percentile bootstrap; PDF : Probability density function; PCI : Process capability index; PLD : Power Lindley distribution; Q i : i -th quartile; SD : Standard deviation; S B : Standard bootstrap; SELF : Squared error loss function; T : Target value; U : Upper specification limit; U D L : Upper desired limit; WD : Weibull distribution; WLSE : Weighted least squares estimator [ABSTRACT FROM AUTHOR]

Repeated measures designs are widely used in practice to increase power, reduce sample size, and increase efficiency in data collection. Correlation between repeated measurements is one of the first research questions that needs to be addressed in a repeated-measure study. In addition to an estimate for correlation, confidence interval should be computed and reported for statistical inference. The asymptotic interval based on the delta method is traditionally calculated due to its simplicity. However, this interval is often criticized for its unsatisfactory performance with regards to coverage and interval width. Bootstrap could be utilized to reduce the interval width, and the widely used bootstrap intervals include the percentile interval, the bias-corrected interval, and the bias-corrected with acceleration interval. Wilcox (Comput Stat Data Anal 22:89–98,1996) suggested a modified percentile interval with the interval levels adjusted by sample size to have the coverage probability close to the nominal level. For a study with repeated measures, more parameters in addition to sample size would affect the coverage probability. For these reasons, we propose modifying the percentiles in the percentile interval to guarantee the coverage probability based on simulation studies. We analyze the correlation between imaging volumes and memory scores from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study to illustrate the application of the considered intervals. The proposed interval is exact with the coverage probability guaranteed, and is recommended for use in practice. [ABSTRACT FROM AUTHOR]

A copula approach decomposes the joint distribution of random variables into marginal distributions of individual variables and the copula form that links the marginals together. When a researcher is dealing with a modeling problem, he is confronted with obtaining the best possible fit for the observed dependence structure. One possibility is to construct a new ideal copula that can describe the observed dependence. Finding a flexible multi-dimensional copula for modeling dependence is still quite challenging. In this paper, we will construct a new multi-dimensional Archimedean copula function that is characterized by a generator with two parameters which allows for more flexibility in modeling dependence. Moreover, we will apply the new constructed copula on step stress accelerated life testing with dependent competing risks under type II censoring. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the approximate and the parametric bootstrap confidence intervals are constructed. Numerical analysis including simulated data and a real life data about aerospace electrical connector is conducted to study the performance of our proposed copula function. [ABSTRACT FROM AUTHOR]

In this article we consider the analysis of progressively censored competing risks data obtained from a simple step‐stress experiment. It is assumed that there are only two competing causes of failures at each stress level and the lifetime distribution of each one of them is one parameter exponential distribution. Based on the cumulative exposure model assumption, the conditional maximum likelihood estimators (MLEs) of the unknown parameters can be obtained in explicit forms. Confidence intervals of the unknown parameters based on the exact distributions of the conditional MLEs and percentile bootstrap method, are constructed. Further we obtain Bayes estimates and the associated credible intervals based on a very flexible Beta‐gamma prior on the unknown parameters. A simulation experiment has been performed to observe the performances of the different estimators. [ABSTRACT FROM AUTHOR]

The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study.

In this paper, a multiple step-stress model is designed and analyzed when the data are Type-I censored. Lifetime distributions of the experimental units at each stress level are assumed to follow a two-parameter Weibull distribution. Further, distributions under each of the stress levels are connected through a tampered failure-rate based model. In a step-stress experiment, as the stress level increases, the load on the experimental units increases and hence the mean lifetime is expected to be shortened. Taking this into account, the aim of this paper is to develop the order restricted inference of the model parameters of a multiple step-stress model based on the frequentist approach. An extensive simulation study has been carried out and two real data sets have been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Sea level rise can bring disastrous outcomes to people living in coastal regions by increasing flood risk or inducing stronger storm surges. We study long‐term linear trends in monthly maximum sea levels by applying extreme value methods. The monthly maximum sea levels are extracted from multiple tide gauges around the coastal regions of the world over a period of as long as 169 years. Due to instrument changes, location changes, earthquakes, land reclamation, dredging, etc., the sea level data could contain inhomogeneous shifts in their means, which can substantially impact trend estimates if ignored. To rigorously quantify the long‐term linear trends and return levels for the monthly maximum sea level data, we use a genetic algorithm to estimate the number and times of changepoints in the data. As strong periodicity and temporal correlation are pertinent to the data, bootstrap techniques are used to obtain more realistic confidence intervals to the estimated trends and return levels. We find that the consideration of changepoints changed the estimated linear trends of 89 tide gauges (approximately 30% of tide gauges considered) by more than 20cmcentury‐1. Our results are summarized in maps with estimated extreme sea level trends and 50‐year return levels. [ABSTRACT FROM AUTHOR]

In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling (RRSS) scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased estimator, and Bayesian estimators of R are derived. Also, we compared this point estimators with their counterparts obtained by well-known sampling scheme in record values known as inverse sampling scheme. Various confidence intervals for the parameter R are constructed, and compared based on the simulation study. Moreover, the RRSS scheme is compared with ordinary records in case of interval estimations. We observed that our proposed point and interval estimations perform well in the estimation of R based on RRSS. We also proved that all calculations do not depend on the baseline distribution in the proportional reversed hazard rate model. Finally, a data set has been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

We develop a saddlepoint-based method and several generalized Bartholomew methods for generating confidence intervals about the hazard rate of exponential survival times in the presence of heavy random right-censoring. Butler's conditional moment generating function (MGF) formula is used to derive the MGF for the hazard rate score function which provides access to a saddlepoint-based bootstrap method. MGFs also play a key role in the generalized Bartholomew methods we develop. Since heavy censoring is assumed, the possible nonexistence of the rate parameter maximum likelihood estimate (MLE) is nonignorable. The overwhelming majority of existing methods condition upon the event that the number of observed failures is non-zero (rate parameter MLE exists). With heavy censoring these methods may not be able to produce a confidence interval an appreciable percentage of times. Our proposed methods are unconditional in the sense that they can produce confidence intervals even when the hazard rate MLE does not exist. The unconditional saddlepoint method in particular defaults in a natural way to a proposed generalized Bartholomew method when the hazard rate MLE fails to exist. We find in our Monte Carlo studies that the proposed saddlepoint method outperforms the four competing Bartholomew methods in the presence of heavy censoring and small sample sizes. [ABSTRACT FROM AUTHOR]

A major winter storm brought up to 42 inches of snow in parts of the Mid-Atlantic and Northeast states for January 22–24, 2016. The blizzard of January 2016 impacted about 102.8 million people, claiming at least 55 lives and $500 million to $3 billion in economic losses. This article studies two important aspects of extreme snowfall events: 1. trends in annual maxima and threshold exceedances and 2. return levels for extreme snowfall. Applying extreme value methods to the extreme snow data in the New York City area, we quantify linear trends in extreme snowfall and assess how severe the 2016 blizzard is in terms of return levels. To find a more realistic standard error for the extreme value methods, we extend Smith's method to adapt to both spatial and temporal correlations in the snow data. Our results show increasing, but insignificant trends in the annual maximum snowfall series. However, we find that the 87.5th percentile snowfall has significantly increased by 0.564 inches per decade, suggesting that, while the maximum snowfall is not significantly increasing, there have been increases in the snowfall among the larger storms. We also find that the 2016 blizzard is indeed an extreme snow event equivalent to about a 40-year return level in the New York City area. The extreme value methods used in this study are thoroughly illustrated for general readers. Data and modularized programming codes are to be available online to aid practitioners in using extreme value methods in applications. [ABSTRACT FROM AUTHOR]

The Asian economic crises of 1997 and the 2008 Global Financial Crisis (GFC) had far-reaching impacts on Asian and other global economies. Turmoil in the banking and finance sectors led to downturns in stock markets, resulting in bankruptcies, house repossessions and high unemployment. These crises have been shown to be correlated with a deterioration in mental health and an increase in suicides, and it is important to understand the implication of these impacts and how such recessions affect the health of affected populations. With the benefit of hindsight, did lessons learned from the negative effects of the 1997 Asian economic recession impact the aftermath of the 2008 GFC in Asian countries? Utilising a framework based on a simple strata-bootstrap algorithm using daily data – where available – we investigate the trend in suicide rates over time in three different populations (Hong Kong, Taiwan and South Korea), and examine whether there were any changes in the pattern of suicide rates in each country subsequent to both the 1997 Asian and 2008. We find that each country responded differently to each of the crises and the suicide rates for certain age-gender specific groups in each country were more affected. [ABSTRACT FROM AUTHOR]

This paper presents likelihood and Bayesian estimation of stress–strength reliability parameter (say R ) based on lower record ranked set sampling scheme from the generalized exponential distribution. Maximum likelihood, uniformly minimum variance unbiased as well as the Bayesian estimators of R are derived and their properties are studied. Constructing and comparing various confidence intervals for the parameter R is also examined. Finally, the rocket-motor experiment data is analysed for illustrating purposes. [ABSTRACT FROM AUTHOR]

Modern problems in statistics often include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such assumptions are often not applicable for available sample sizes, due to dependencies in the data. A common alternative is the use of resampling procedures, such as bootstrapping, but these may be computationally intensive to an extent that renders them impractical for modern problems. In this article, we develop a method for fast construction of test-inversion bootstrap confidence intervals. Our approach uses quantile regression to model the quantile of an estimator conditional on the true value of the parameter. We apply this to the Watterson estimator of mutation rate in a standard coalescent model. We demonstrate an improved efficiency of up to 40% from using quantile regression compared to state of the art methods based on stochastic approximation, as measured by the number of simulations required to achieve comparable accuracy. for this article are available online. [ABSTRACT FROM AUTHOR]

The process capability index (PCI) is a quality control–related statistic mostly used in the manufacturing industry, which is used to assess the capability of some monitored process. It is of great significance to quality control engineers as it quantifies the relation between the actual performance of the process and the preset specifications of the product. Most of the traditional PCIs performed well when process follows the normal behaviour. However, using these traditional indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, Cpy, suggested by Maiti et al, which can be used for normal as well as non‐normal random variables. This article addresses the different methods of estimation of the PCI Cpy from both frequentist and Bayesian view points of generalized Lindley distribution suggested by Nadarajah et al. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, least square and weighted least square estimators, and maximum product of spacings estimators. Next, we consider Bayes estimation under squared error loss function using gamma priors for both shape and scale parameters for the considered model. We use Tierney and Kadane's method as well as Markov Chain Monte Carlo procedure to compute approximate Bayes estimates. Besides, two parametric bootstrap confidence intervals using frequentist approaches are provided to compare with highest posterior density credible intervals. Furthermore, Monte Carlo simulation study has been carried out to compare the performances of the classical and the Bayes estimates of Cpy in terms of mean squared errors along with the average width and coverage probabilities. Finally, two real data sets have been analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Recently Mondal and Kundu [Mondal S, Kundu D. A new two sample type-II progressive censoring scheme. Commun Stat Theory Methods. 2018. doi:] introduced a Type-II progressive censoring scheme for two populations. In this article, we extend the above scheme for more than two populations. The aim of this paper is to study the statistical inference under the multi-sample Type-II progressive censoring scheme, when the underlying distributions are exponential. We derive the maximum likelihood estimators (MLEs) of the unknown parameters when they exist and find out their exact distributions. The stochastic monotonicity of the MLEs has been established and this property can be used to construct exact confidence intervals of the parameters via pivoting the cumulative distribution functions of the MLEs. The distributional properties of the ordered failure times are also obtained. The Bayesian analysis of the unknown model parameters has been provided. The performances of the different methods have been examined by extensive Monte Carlo simulations. We analyse two data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper presents the Bayesian analysis of the stress–strength reliability of a parallel system with active and mixed standby components. The Bayesian estimators of the parameters of exponential and Weibull stress–strength distributions are obtained by assuming informative and noninformative prior for the parameters of the respective distributions. The Gibbs sampling procedure is used to compute the Bayesian stress–strength reliability. The asymptotic distributions, of the maximum likelihood estimators of the parameters of the corresponding distributions, and of the respective system reliabilities are presented. The bootstrap estimate and confidence interval are also obtained. The procedures are illustrated based on certain datasets. [ABSTRACT FROM AUTHOR]

This paper deals with construction of confidence intervals for process capability index using bootstrap method (proposed by Chen and Pearn in Qual Reliab Eng Int 13(6):355–360, 1997) by applying simulation technique. It is assumed that the quality characteristic follows type-II generalized log-logistic distribution introduced by Rosaiah et al. in Int J Agric Stat Sci 4(2):283–292, (2008). Discussed different bootstrap confidence intervals for process capability index. Maximum likelihood method is considered for obtaining the estimators of the parameter. Monte Carlo simulation technique is applied to find out the coverage probabilities and average widths of the bootstrap confidence intervals. The results are illustrated with real data sets. [ABSTRACT FROM AUTHOR]