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This paper investigates interval estimation for measures of overlap, namely Matusita's measure, Weitzman's measure and based on Kullback–Leibler. Two types of sampling procedures, namely, Simple Random Sample and Upper Record Values from two exponential populations. Bootstrap method series approximation is used to construct confidence intervals for the overlap measures. To illustrate the performance of the likelihood confidence intervals obtained for this overlapping coefficient, under our proposal, we carry out some simulation studies that yield adequate coverage frequencies, this study conducts for comparing the performances of various competing estimators. A real data set is analysed to exemplify our proposal. [ABSTRACT FROM AUTHOR]

This paper presents interval estimation for the population mean and coefficient of variation in a two-parameter exponential distribution. The new generalized pivot, profile likelihood function and likelihood ratio statistic are derived and used to construct the confidence intervals. A highlight of this paper is that the generalized and likelihood ratio confidence intervals for the mean and coefficient of variation perform well in terms of coverage probability in many cases. Finally, two real-data applications on the air pollution of particulate matter (PM2.5) and the renewable energy through wind power of Thailand are used for illustration purposes. [ABSTRACT FROM AUTHOR]

Of interest in this paper is the development of a model that uses fixed, then inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false-positive misclassification rate may be estimated. Also, three first-order likelihood-based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the likelihood ratio interval is generally preferable over the Wald and score interval. Lastly, the model is applied to two different real-world medical data sets. [ABSTRACT FROM AUTHOR]

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach. [ABSTRACT FROM AUTHOR]

We introduce a newly developed R package AZIAD for analysing zero-inflated or zero-altered data. Compared with existing R packages, AZIAD covers a much larger class of zero-inflated and hurdle models, including both discrete and continuous cases. It provides more accurate parameter estimates, along with the corresponding Fisher information matrix and confidence intervals. It achieves significantly larger power for model identification and selection. To facilitate the potential users, in this paper we provide detailed formulae and theoretical justifications for AZIAD, as well as new theoretical results on zero-inflated and zero-altered models. We use simulation studies to show the advantages of AZIAD functions over existing R packages and provide real data examples and executable R code to illustrate how to use our package for sparse data analysis and model selection. [ABSTRACT FROM AUTHOR]

In this paper, the one-sided hypothesis testing and interval estimation problems for the fixed effect and variance component functions are considered in the skew-normal unbalanced heteroscedastic one-way classification random effects model. Firstly, the Bootstrap approach is used to establish test statistic for fixed effect. Secondly, the test statistics and confidence intervals for variance component functions are constructed by Bootstrap approach and generalized approach, and their theoretical properties are discussed. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with two real examples of the annual average concentrations of fine particulate matter and nitrogen dioxide. [ABSTRACT FROM AUTHOR]

Poisson distribution is a classic choice for modelling unbounded count data. However, count data arising in various fields of scientific research often have excess zeros and are under-reported. In such situations, Poisson distribution gives a poor fit and Poisson model based inferences lead to biased estimators and inaccurate confidence intervals. In this paper we develop a flexible model which can accommodate excess zeros and undercount. Internal validation data has been used for making likelihood based inferences. The impact of ignoring undercount and excess zeros are studied through extensive simulations. The finite sample behaviour of the estimators are investigated through bootstrap methodology. Finally, a real life data which is supposedly under-reported and known to have excess zeros is analysed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of variance estimation of predictions obtained from a subsampling-based ensemble estimator, such as subbagging and sub-random forest. We first recognize that a subsampling-based ensemble can be written as an infinite-order U-statistic of degree k n , where k n is the subsample size that may depend on the learning sample size n. As a result, one can study the uncertainty of predictions obtained from a subsampling-based ensemble under a U-statistic framework, such as approximating its asymptotic variance. However, existing methods used to estimate the asymptotic variance relies on some regularity conditions. In addition, they tend to yield variance estimations with large bias in finite sample scenarios. Motivated by the work of Wang and Lindsay (2014), we propose to construct an unbiased variance estimator for a subsampling-based ensemble. It is efficient to realize with the help of a partition-resampling scheme. We show by simulation studies that the proposed variance estimator yields better performance in terms of mean, standard deviation, and mean squared error compared to both the infinitesimal jackknife and internal variance estimation methods under either a simple linear regression model or a multivariate adaptive regression splines model. Furthermore, we present how to construct an asymptotic confidence interval for the expected prediction at a given test instance using the proposed variance estimator, and compare its coverage probability to that of competing methods. In the end, we demonstrate the practical applications of the methodology using two real data examples. [ABSTRACT FROM AUTHOR]

This paper considers the inference on the common mean and medians of a bivariate lognormal distribution. We propose point and interval estimators of the common mean in closed form. We derive confidence intervals of the common mean using the maximum likelihood method, generalized variable approach, method of variance estimate recovery and highest posterior density. The generalized confidence interval of the common mean under missing observations is also obtained. We obtain confidence limits for the difference of medians using first three techniques of interval estimation of the common mean and two bootstrap approaches. The coverage probability and expected length are used to assess the performance of the intervals. The proposed methodologies are exemplified through real-life data sets related to immunology, road accidents and vaccination programmes. [ABSTRACT FROM AUTHOR]

Gamma distribution plays an important role in applied fields due to its flexibility of accommodating right-skewed data. Although inference methods for single gamma mean and for difference of two independent gamma means have been well studied, inference methods for difference of two correlated gamma means are sparse. This paper considers the problem of interval estimation for the difference of two correlated gamma means. We propose several inference methods including a method based on the concepts of generalized inference and two hybrid methods based on the method of variance estimates recovery. An extensive Monte Carlo simulation study was conducted to assess the performance of the proposed methods in terms of coverage probabilities and average lengths of the estimated intervals. Two real data examples from medical and engineering studies are analyzed using the proposed methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Probability weighted moments (PWMs) are a generalization of the usual moments of a probability distribution. In this paper, the jackknife empirical likelihood (JEL), the adjusted JEL (AJEL), the transformed JEL, which combines the merits of jackknife and transformed empirical likelihoods (TJEL), the transformed adjusted JEL (TAJEL), the mean jackknife empirical likelihood (MJEL), the mean adjusted jackknife empirical likelihood (MAJEL), and the adjusted mean jackknife empirical likelihood (AMJEL) methods, are considered to construct confidence intervals for probability weighted moments. Simulation results under various distributions show that MAJEL method always gives the best performance in terms of the coverage probability and average length among these methods, and TJEL shows better performance than AJEL and MJEL for small sample sizes, while MJEL is relatively time-consuming. The tests based on the proposed methods for PWMs are also developed. Real datasets are used to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

This paper takes a deeper look into uncertainty assessment of the Mantel–Haenszel estimator (MHE). In the homogeneity case, all developed confidence intervals for the risk ratio and risk difference behave acceptably, even in therare events situation. For heterogeneity, the non-parametric bootstrap approachprovides confidence intervals for the risk difference with acceptable coverage,depending on the number of studies. For the risk ratio, the situation is morecomplex as typically distributions for the log-relative risk are considered. TheMHE overestimates the expected value of the distribution of the log-relativerisk whatever it may be. However, if we consider as true value the estimand ofMHE, reasonable coverage probabilities can be achieved with the bootstrap. Asource of this problem is that the moments of a non-linearly transformedrelative risk variable are not equal to the non-linearly transformed moments ofthe respective relative risk variable. [ABSTRACT FROM AUTHOR]

This paper studies simultaneous confidence intervals (SCIs) for the ratios of means of zero-heavy log-normal populations. We propose four SCIs by using the Bonferroni adjustment principle. Specifically, we integrate the fiducial generalized pivotal quantity (FGPQ) with the other two statistics to have two FGPQ-based methods and incorporate the variance estimates recovery (MOVER) with FGPQ to have two MOVER-based methods. We develop expedient algorithms to implement the methods, and conduct extensive simulation studies to evaluate and compare the performance of the four methods, which show that our methods perform well. We also apply the methods to analyse a real data set as an illustration. [ABSTRACT FROM AUTHOR]

The two-parameter Birnbaum–Saunders distribution was derived to describe the failure time from a process of fatigue crack growth. The scale parameter is also the median of the distribution. The inferences for the median of the distribution are mostly based on the maximum likelihood methods and subject to large-sample requirements. In this paper, we develop the exact small-sample confidence intervals of the median of the distribution when the shape parameter is known and unknown, respectively. Moreover, an alternative consistent estimator with an explicit form for the median of the distribution is provided in this study. Finally, we develop the hypothesis testing for the median of the distribution based on a small sample. The Monte Carlo simulations are further carried out to prove the power of the proposed test well performance. [ABSTRACT FROM AUTHOR]

Process capability of simple linear profiles (SLPs) has been already measured by functional process capability indices ( C p (p r o f i l e) and C p k (p r o f i l e)), which are unable to distinguish between on-target and off-target processes. Hence, in this paper, we develop traditional loss-based indices for simple linear profiles using a functional approach. These new indices are based on the Taguchi loss function and can adequately reflect process mean deviations from the target value. The performance of the proposed indices and existing ones are studied using simulation studies. The simulation results show that the proposed methods outperform the existing functional indices regarding smaller mean absolute error (MAE) and mean square error (MSE) metrics. Also, a procedure is introduced to determine minimum number of profile samples for the estimation of proposed indices. In addition, bootstrap confidence intervals are constructed for the proposed indices. Finally, a real case study is given to show the application of the proposed indices. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in estimating the generalized process capability index ( C p y k ) proposed by Maiti et al. [On generalizing process capability indices. Qual Technol Quant Manag. 2010;7(3):279–300], when the underlying distribution is the generalized inverse Lindley (GIL) distribution. We estimate parameters of the GIL distribution using maximum likelihood (ML), bias-corrected maximum-likelihood (BCML) and bootstrap bias-corrected maximum-likelihood (BBCML) methodologies. C p y k are obtained using proposed estimators. Bootstrap confidence intervals called standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) 95 % are constructed based on the estimators of C p y k . We compare efficiencies of the parameter estimators and the performance of ML, BCML and BBCML based Cpyk via an extensive Monte Carlo simulation study. A simulation study is also described to compare the coverage probabilities (CP) and average lengths (AL) of SB, PB and BCPB confidence intervals for proposed C p y k . Finally, two real datasets are analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

The linear least-squares method has been applied to Weibull distribution for analysing the reliability, and the exact confidence intervals for Weibull parameters can be constructed from both Type-I and Type-II censored data. However, this method changes the shape of theoretical linear fit and estimates are highly biased for heavily censored data. Therefore, the nonlinear method (NLLSM) and transformation-based least-squares methods (TBLSM) are proposed in the literature. In this paper, I address confidence intervals for Weibull parameters based on the two methods and discuss the reliability and remaining lifetime with the right censored data. I propose the exact confidence intervals from pivotal quantities for the Weibull parameters based on NSLLM and approximate ones based on TBLLM. Further, different methods are compared through a Monte Carlo simulation study. Finally, these methods are applied to a data set as an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we consider Marshall-Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley’s approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate the results derived. [ABSTRACT FROM AUTHOR]

For substantiation of managerial decisions the forecasting results of dynamic indicators are used. Therefore, forecasting accuracy of these indicators must be acceptable. Consequently, forecasting algorithms are constantly improved to get the acceptable accuracy. This paper considers a variant of the method of forecasting binary outcomes. This method allows prediction of whether or not a future value of the indicator exceeds a predetermined value. This method ‘interval forecasting’ was named. In this paper a robust interval forecasting algorithm based on a probabilistic cluster model is proposed. The algorithm’s accuracy was compared with an algorithm based on logistic regression. The indicators with different statistical properties were chosen. The obtained results have shown the accuracy of both the algorithms is approximately similar in most cases. However, the cases when the algorithm based on logistic regression demonstrated unacceptable accuracy, unlike the presented algorithm have been identified. Thus, this new algorithm is more accurate. [ABSTRACT FROM AUTHOR]

In this paper, several existing data-driven nonparametric methods including empirical likelihood, adjusted empirical likelihood and transformed empirical likelihood are considered to construct confidence intervals for the mean of a population containing many zeros and ones. Meanwhile, we propose a transformed adjusted empirical likelihood which combines the merits of adjusted and transformed empirical likelihoods. All five methods are compared to normal approximation in terms of coverage probabilities under various scenarios through simulations. All methods are applied to three datasets to illustrate the procedure of obtaining confidence intervals. [ABSTRACT FROM AUTHOR]

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage. [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]

In this paper, we consider the estimation reliability in multicomponent stress-strength (MSS) model when both the stress and strengths are drawn from Topp-Leone (TL) distribution. The maximum likelihood (ML) and Bayesian methods are used in the estimation procedure. Bayesian estimates are obtained by using Lindley's approximation and Gibbs sampling methods, since they cannot be obtained in explicit form in the context of TL. The asymptotic confidence intervals are constructed based on the ML estimators. The Bayesian credible intervals are also constructed using Gibbs sampling. The reliability estimates are compared via an extensive Monte-Carlo simulation study. Finally, a real data set is analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

The Conway–Maxwell–Poisson estimator is considered in this paper as the population size estimator. The benefit of using the Conway–Maxwell–Poisson distribution is that it includes the Bernoulli, the Geometric and the Poisson distributions as special cases and, furthermore, allows for heterogeneity. Little emphasis is often placed on the variability associated with the population size estimate. This paper provides a deep and extensive comparison of bootstrap methods in the capture–recapture setting. It deals with the classical bootstrap approach using the true population size, the true bootstrap, and the classical bootstrap using the observed sample size, the reduced bootstrap. Furthermore, the imputed bootstrap, as well as approximating forms in terms of standard errors and confidence intervals for the population size, under the Conway–Maxwell–Poisson distribution, have been investigated and discussed. These methods are illustrated in a simulation study and in benchmark real data examples. [ABSTRACT FROM AUTHOR]

The Lindley distribution is an important distribution for analysing the stress–strength reliability models and lifetime data. In many ways, the Lindley distribution is a better model than that based on the exponential distribution. Order statistics arise naturally in many of such applications. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the Lindley distribution. Then, we use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale parameters based on Type-II right-censored samples. Next, we use these results to determine the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics to develop Edgeworth approximate confidence intervals of the location and scale Lindley parameters. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set. [ABSTRACT FROM AUTHOR]

In this paper, we consider inference of the stress-strength parameter, R, based on two independent Type-II censored samples from exponentiated Fréchet populations with different index parameters. The maximum likelihood and uniformly minimum variance unbiased estimators, exact and asymptotic confidence intervals and hypotheses testing for R are obtained. We conduct a Monte Carlo simulation study to evaluate the performance of these estimators and confidence intervals. Finally, two real data sets are analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inferential procedures for the generalized inverted exponential distribution under progressive first failure censoring. The exact confidence interval for the scale parameter is derived. The generalized confidence intervals (GCIs) for the shape parameter and some commonly used reliability metrics such as the quantile and the reliability function are explored. Then the proposed procedure is extended to the prediction interval for the future measurement. The GCIs for the reliability of the stress-strength model are discussed under both equal scale and unequal scale scenarios. Extensive simulations are used to demonstrate the performance of the proposed GCIs and prediction interval. Finally, an example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In the paper, we present and discuss several methods of the construction of confidence intervals for the Laspeyres price index. We assume that prices of commodities are normally distributed and we consider both independent and dependent prices. Using Monte Carlo simulation, the paper compares the confidence interval computed from a simple econometric model with those obtained based on the Laspeyres density function. Our conclusions can be generalized to other price index formulas. [ABSTRACT FROM AUTHOR]

This paper is concerned with the estimation and inference in generalized semi-varying coefficient models. An orthogonal projection local quasi-likelihood estimation is investigated, which can easily be used to estimate the model parametric and nonparametric parts. Then an empirical likelihood logarithmic approach to construct the confidence regions/intervals of the nonparametric parts is developed. Under some mild conditions, the asymptotic properties of the resulting estimators are studied explicitly, respectively. Some simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by a real data set. [ABSTRACT FROM AUTHOR]

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given. [ABSTRACT FROM AUTHOR]

Recently, Zhang [Simultaneous confidence intervals for several inverse Gaussian populations. Stat Probab Lett. 2014;92:125–131] proposed simultaneous pairwise confidence intervals (SPCIs) based on the fiducial generalized pivotal quantity concept to make inferences about the inverse Gaussian means under heteroscedasticity. In this paper, we propose three new methods for constructing SPCIs to make inferences on the means of several inverse Gaussian distributions when scale parameters and sample sizes are unequal. One of the methods results in a set of classic SPCIs (in the sense that it is not simulation-based inference) and the two others are based on a parametric bootstrap approach. The advantages of our proposed methods over Zhang’s (2014) method are: (i) the simulation results show that the coverage probability of the proposed parametric bootstrap approaches is fairly close to the nominal confidence coefficient while the coverage probability of Zhang’s method is smaller than the nominal confidence coefficient when the number of groups and the variance of groups are large and (ii) the proposed set of classic SPCIs is conservative in contrast to Zhang’s method. [ABSTRACT FROM PUBLISHER]

In economics and government statistics, aggregated data instead of individual level data are usually reported for data confidentiality and for simplicity. In this paper we develop a method of flexibly estimating the probability density function of the population using aggregated data obtained as group averages when individual level data are grouped according to quantile limits. The kernel density estimator has been commonly applied to such data without taking into account the data aggregation process and has been shown to perform poorly. Our method models the quantile function as an integral of the exponential of a spline function and deduces the density function from the quantile function. We match the aggregated data to their theoretical counterpart using least squares, and regularize the estimation by using the squared second derivatives of the density function as the penalty function. A computational algorithm is developed to implement the method. Application to simulated data and US household income survey data show that our penalized spline estimator can accurately recover the density function of the underlying population while the common use of kernel density estimation is severely biased. The method is applied to study the dynamic of China's urban income distribution using published interval aggregated data of 1985–2010. [ABSTRACT FROM AUTHOR]

We investigate an isotonic parameterization for monotone polynomials previously unconsidered in the statistical literature. We show that this parameterization is more flexible than its alternatives through enabling polynomials to be constrained to be monotone over either a compact interval or a semi-compact interval of the form, in addition to over the whole real line. Furthermore, algorithms based on our new parameterization estimate the fitted monotone polynomials much faster than algorithms based on previous isotonic parameterizations which in turn makes the use of standard bootstrap methodology feasible. We investigate the use of the bootstrap under monotonicity constraints to obtain confidence bands for the fitted curves and show that an adjustment by using either the ‘mout ofn’ bootstrap or a post hoc symmetrization of the confidence bands is necessary to achieve more uniform coverage probabilities. We illustrate our new methodology with two real world examples which demonstrate not only the need for such techniques, but how restricting the monotonicity constraints to be over either a compact or semi-compact interval allows the fitting of even degree monotone polynomials. We also describe methods for using the ‘mout ofn’ bootstrap to select the degree of the fitted monotone polynomial. All algorithms discussed in this paper are available in the R packageMonoPoly(version 0.3-6 or later). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to estimate the parameters of the location-scale distribution family. As a special case, the method is used for estimating the parameters of the normal distribution and Cauchy distribution. For the Cauchy distribution, neither the moment estimation method nor the maximum likelihood estimation method works properly for estimating the parameters. The quantiles for obtaining confidence intervals and point estimates for the parameters of the two-parameter Cauchy distribution are given in the paper. It is shown that the estimators obtained in this paper are unbiased with respect to the median and possess some optimal properties. [ABSTRACT FROM AUTHOR]

For the complete sample and the right Type II censored sample, Chen [Joint confidence region for the parameters of Pareto distribution. Metrika 44 (1996), pp. 191-197] proposed the interval estimation of the parameter θ and the joint confidence region of the two parameters of Pareto distribution. This paper proposed two methods to construct the confidence region of the two parameters of the Pareto distribution for the progressive Type II censored sample. A simulation study comparing the performance of the two methods is done and concludes that Method 1 is superior to Method 2 by obtaining a smaller confidence area. The interval estimation of parameter ν is also given under progressive Type II censoring. In addition, the predictive intervals of the future observation and the ratio of the two future consecutive failure times based on the progressive Type II censored sample are also proposed. Finally, one example is given to illustrate all interval estimations in this paper. [ABSTRACT FROM AUTHOR]

Process capability indices have been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The distribution of the estimator of the process capability index Cpmk is very complicated and the asymptotic distribution is proposed by Chen and Hsu [The asymptotic distribution of the processes capability index Cpmk, Comm. Statist. Theory Methods 24(5) (1995), pp. 1279-1291]. However, we found a critical error for the asymptotic distribution when the population mean is not equal to the midpoint of the specification limits. In this paper, a correct version of the asymptotic distribution is given. An asymptotic confidence interval of Cpmk by using the correct version of asymptotic distribution is proposed and the lower bound can be used to test if the process is capable. A simulation study of the coverage probability of the proposed confidence interval is shown to be satisfactory. The relation of six sigma technique and the index Cpmk is also discussed in this paper. An asymptotic testing procedure to determine if a process is capable based on the index of Cpmk is also given in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of determining non-parametric confidence intervals for quantiles when available data are in the form of k-records. Distribution-free confidence intervals as well as lower and upper confidence limits are derived for fixed quantiles of an arbitrary unknown distribution based on k-records of an independent and identically distributed sequence from that distribution. The construction of tolerance intervals and limits based on k-records is also discussed. An exact expression for the confidence coefficient of these intervals are derived. Some tables are also provided to assist in choosing the appropriate k-records for the construction of these confidence intervals and tolerance intervals. Some simulation results are presented to point out some of the features and properties of these intervals. Finally, the data, representing the records of the amount of annual rainfall in inches recorded at Los Angeles Civic Center, are used to illustrate all the results developed in this paper and also to demonstrate the improvements that they provide on those based on either the usual records or the current records. [ABSTRACT FROM AUTHOR]

This paper encompasses three parts of validating risk models. The first part provides an understanding of the precision of the standard statistics used to validate risk models given varying sample sizes. The second part investigates jackknifing as a method to obtain a confidence interval for the Gini coefficient and K-S statistic for small sample sizes. The third and final part investigates the odds at various cutoff points as to its efficiency and appropriateness relative to the K-S statistic and Gini coefficient in model validation. There are many parts to understanding the risk associated with the extension of credit. This paper focuses on obtaining a better understanding of present methodology for validating existing risk models used for credit scoring, by investigating the three parts mentioned. The empirical investigation shows the precision of the Gini coefficient and K-S statistic is driven by the sample size of the smaller, either successes or failures. In addition, a simple adaption of the standard jackknifing formula is possible to use to get an understanding of the variability of the Gini coefficient and K-S statistic. Finally, the odds is not a reliable statistic to use without a considerably large sample of both successes and failures. [ABSTRACT FROM AUTHOR]

In this paper exact confidence intervals (CIs) for the shape parameter of the gamma distribution are constructed using the method of Bølviken and Skovlund [Confidence intervals from Monte Carlo tests. J Amer Statist Assoc. 1996;91:1071–1078]. The CIs which are based on the maximum likelihood estimator or the moment estimator are compared to bootstrap CIs via a simulation study. [ABSTRACT FROM AUTHOR]

In this article bootstrap confidence intervals of process capability index as suggested by Chen and Pearn [An application of non-normal process capability indices. Qual Reliab Eng Int.1997;13:355–360] are studied through simulation when the underlying distributions are inverse Rayleigh and log-logistic distributions. The well-known maximum likelihood estimator is used to estimate the parameter. The bootstrap confidence intervals considered in this paper consists of various confidence intervals. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Application examples on two distributions for process capability indices are provided for practical use. [ABSTRACT FROM AUTHOR]

For the general stochastic regression analysis of complete data, Bindele and Abebe [Bounded influence nonlinear signed-rank regression. Can J Stat. 2012;40(1):172–189. Available from:http://dx.doi.org/10.1002/cjs.10134  ] proposed the signed-rank (SR) estimator. However, there exists an over-coverage problem for the confidence intervals of the regression parameters when the sample size is small. In this paper, we investigate an empirical likelihood (EL) approach to construct confidence intervals for the regression parameters based on the SR estimating equation. The limiting distribution of log-empirical likelihood ratio isdistribution. We carry out extensive simulation studies to compare the proposed method with the normal approximation-based method. The simulation results show that the proposed method outperforms the existing method in terms of the coverage probability and average length of confidence intervals. We illustrate the EL method using a real data example. [ABSTRACT FROM PUBLISHER]

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probabilitypof the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of constructing different kinds of confidence intervals for the coefficient of variationof a normal distribution. Firstly, the construction of a confidence interval that bounds the reciprocal of the coefficient of variation away from zero is considered. This confidence interval provides a directional decision as to whether the coefficient of variation is positive or negative, and provides a lower bound on the magnitude of. Secondly, the construction of a confidence interval that provides an upper bound on the absolute value of the reciprocal of the coefficient of variation is considered. This confidence interval provides an upper bound on the magnitude of, which could be either negative or positive. These procedures are developed using inferences on the non-centrality parameter of a non-central t-distribution. Several applications are considered, such as financial analyses with Sharpe ratios and the measurement of signal-to-noise ratios, with specific attention being directed towards assessing win-probabilities for comparing two normal treatments. In the context of win-probabilities, the first confidence interval can be used to determine which treatment is better and by how much, while the second confidence interval can be used to provide an upper bound on how different the two treatments may be. Examples of the implementations of these procedures are provided together with illustrations of the improvements over standard procedures, and R code is available from the author. [ABSTRACT FROM AUTHOR]

In this paper, a small-sample asymptotic method is proposed for higher order inference in the stress–strength reliability model,R=P(Y

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints. [ABSTRACT FROM AUTHOR]

Accelerated life testing is widely used in product life testing experiments since it provides significant reduction in time and cost of testing. In this paper, assuming that the lifetime of items under use condition follow the two-parameter Pareto distribution of the second kind, partially accelerated life tests based on progressively Type-II censored samples are considered. The likelihood equations of the model parameters and the acceleration factor are reduced to a single nonlinear equation to be solved numerically to obtain the maximum-likelihood estimates (MLEs). Based on normal approximation to the asymptotic distribution of MLEs, the approximate confidence intervals (ACIs) for the parameters are derived. Two bootstrap CIs are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply Markov chain Monte Carlo method to tackle this problem, which allows us to construct the credible interval of the involved parameters. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and to compare the performance of different corresponding CIs considered. [ABSTRACT FROM AUTHOR]

Exact confidence intervals for variances rely on normal distribution assumptions. Alternatively, large-sample confidence intervals for the variance can be attained if one estimates the kurtosis of the underlying distribution. The method used to estimate the kurtosis has a direct impact on the performance of the interval and thus the quality of statistical inferences. In this paper the author considers a number of kurtosis estimators combined with large-sample theory to construct approximate confidence intervals for the variance. In addition, a nonparametric bootstrap resampling procedure is used to build bootstrap confidence intervals for the variance. Simulated coverage probabilities using different confidence interval methods are computed for a variety of sample sizes and distributions. A modification to a conventional estimator of the kurtosis, in conjunction with adjustments to the mean and variance of the asymptotic distribution of a function of the sample variance, improves the resulting coverage values for leptokurtically distributed populations. [ABSTRACT FROM AUTHOR]

Recently, exact inference under hybrid censoring scheme has attracted extensive attention in the field of reliability analysis. However, most of the authors neglect the possibility of competing risks model. This paper mainly discusses the exact likelihood inference for the analysis of generalized type-I hybrid censoring data with exponential competing failure model. Based on the maximum likelihood estimates for unknown parameters, we establish the exact conditional distribution of parameters by conditional moment generating function, and then obtain moment properties as well as exact confidence intervals (CIs) for parameters. Furthermore, approximate CIs are constructed by asymptotic distribution and bootstrap method as well. We also compare their performances with exact method through the use of Monte Carlo simulations. And finally, a real data set is analysed to illustrate the validity of all the methods developed here. [ABSTRACT FROM AUTHOR]

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method. [ABSTRACT FROM AUTHOR]