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This paper consider a new exponential parametric distortion measurement errors model for the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted with exponential parametric distortion measurement errors models, which are exponential functions of an observed confounding variable. The nonlinear least squares estimation and weighted nonlinear least squares estimation are used to estimate parameters in the multiplicative distortion functions. We use the fully parametrical calibration and mixed calibration to estimate the correlation coefficient, and show that the proposed estimators of correlation coefficient are all asymptotically efficient. Moreover, we suggest several asymptotic normal approximation statistics to construct the confidence intervals. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators. These methods are applied to analyse a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

In this paper, the problem of estimating unknown parameters of a two-parameter Kumaraswamy-Exponential (Kw-E) distribution is considered based on progressively type-II censored sample. The maximum likelihood (ML) estimators of the parameters are obtained. Bayes estimates are also obtained using different loss functions such as squared error, LINEX and general entropy. Lindley's approximation method is used to evaluate these Bayes estimates. Monte Carlo simulation is used for numerical comparison between various estimates developed in this paper. [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]

In this paper an extension of the piecewise exponential distribution based on the distribution of the maximum of a random sample is considered. Properties of its density and hazard function are investigated. Maximum likelihood inference is discussed and the Fisher information matrix is identified. Results of two real data applications are reported, where model fitting is implemented by using maximum likelihood. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models. [ABSTRACT FROM AUTHOR]

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected. [ABSTRACT FROM PUBLISHER]

This paper deals with a new censoring scheme, called ‘Block Censoring’ which reduces considerably the total time on test in the life testing experiments with respect to the common used experimental tests such as rightly censored data. This new scheme is analysed when the lifetimes of products follow the two-parameter exponential distribution. Specially, it is proved that the respective spacings are independently distributed exponential. The problem of estimating parameters is investigated in details.A Monte Carlo simulation is conducted for obtaining the optimal block censoring scheme in the sense of the shortest expected test time. Finally, a real data set on times to breakdown of an insulating fluid between electrodes from Nelson [Applied life data analysis. New York: Wiley; 1982. p.105] is analysed. [ABSTRACT FROM AUTHOR]

In this paper, the reliability properties of two-component parallel and series systems are considered for bivariate generalized exponential (BVGE) distribution introduced by Kundu and Gupta [Bivariate generalized exponential distribution. J Multivar Anal. 2009;100:581–593]. For this model, the moments and mean residual life functions of these systems and the regression mean residual life function are derived. Stochastic comparisons of series and parallel systems of BVGE distribution are investigated. Moreover, various ordering results for the comparisons of series and parallel systems arising from BVGE random vectors are obtained with respect to the usual stochastic, reversed hazard rate and likelihood ratio orderings. [ABSTRACT FROM AUTHOR]

In this paper, a generalization of inverted exponential distribution is considered as a lifetime model [A.M. Abouammoh and A.M. Alshingiti,Reliability estimation of generalized inverted exponential distribution, J. Statist. Comput. Simul. 79(11) (2009), pp. 1301–1315]. Its reliability characteristics and important distributional properties are discussed. Maximum likelihood estimation of the two parameters involved along with reliability and failure rate functions are derived. The method of least square estimation of parameters is also studied here. In view of cost and time constraints, type II progressively right censored sampling scheme has been used. For illustration of the performance of the estimates, a Monte Carlo simulation study is carried out. Finally, a real data example is given to show the practical applications of the paper. [ABSTRACT FROM AUTHOR]

In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

This paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function. [ABSTRACT FROM AUTHOR]

In this paper, a new mixed bivariate geometric-exponential distribution is introduced. We present the properties and numerical characteristics of the distribution. In addition, the applications of this new bivariate distribution are given in a two-unit series system. Through an intensive Monte-Carlo simulation study, we assess the precision of the proposed estimation methods for the parameter inference. A real data is analysed for illustrative purpose. [ABSTRACT FROM PUBLISHER]

Whenever a practitioner is not sure about the underlying process distribution, alternative monitoring schemes that may be used are called nonparametric charts. A nonparametric scheme mostly used to monitor the difference in the means of two samples is called the Wilcoxon rank-sum (WRS). In this paper, we propose nonparametric (or distribution-free) cumulative sum and exponentially weighted moving average charts based on the WRS using ranked set sampling. We thoroughly discuss the performance of the proposed control charts in terms of run-length properties through intensive simulations. Moreover, we conduct an overall performance comparison using the relative mean index and a variety of quality loss functions (for instance, the average extra quadratic loss, average ratio of the average run-length and performance comparison index). The newly proposed charts have very attractive run-length properties and they have better overall performance than their counterparts. An illustrative example is given, as well as an easy-to-use table with optimal design parameters to aid practical implementation. [ABSTRACT FROM AUTHOR]

In this paper, we consider some problems of point estimation and point prediction when the competing risks data from a class of exponential distribution are progressive type-I interval censored. The maximum likelihood estimation and mid-point approximation method are proposed for the estimations of parameters. Also several point predictors of censored units such as the maximum likelihood predictor, the best unbiased predictor and the conditional median predictor are obtained. The methods discussed here are applied when the lifetime distributions of the latent failure times are independent and Weibull-distributed. Finally a simulation study is given by using Monte-Carlo simulations to compare the performances of the different methods and one data analysis has been presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Recently, Ristić and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets. [ABSTRACT FROM PUBLISHER]

In this paper, we present new one-stage multiple comparison procedures with the average for location parameters of two-parameter exponential distributions under heteroscedasticity by modifying the existing one proposed by Wu [One stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. Comput Stat Data Anal. 2013;68:352–360] with unequal sample sizes. A simulation study is done and the results show that the proposed procedures have shorter confidence length with coverage probabilities closer to the nominal ones. At last, an example of comparing the survival days of patients for four categories of lung cancer is given to demonstrate the proposed procedures. [ABSTRACT FROM PUBLISHER]

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here. [ABSTRACT FROM PUBLISHER]

In this paper, we conduct a simulation study to investigate the performance of three popular weighted estimators, namely the Imbens' weighted estimator, the propensity score weighted estimator, and the generalized doubly robust (GDR) estimator for estimating average treatment effects of multiple treatments when the outcome variable is generated from one of the seven commonly seen non-normal distributions: lognormal, student'st, exponential, uniform, gamma, beta, and Weibull. When outcome variables are non-normally distributed, simulation results show that the GDR estimator has a better performance compared to the other two estimators. [ABSTRACT FROM AUTHOR]

The exponential–Poisson (EP) distribution with scale and shape parameters β>0 and λ∈ℝ, respectively, is a lifetime distribution obtained by mixing exponential and zero-truncated Poisson models. The EP distribution has been a good alternative to the gamma distribution for modelling lifetime, reliability and time intervals of successive natural disasters. Both EP and gamma distributions have some similarities and properties in common, for example, their densities may be strictly decreasing or unimodal, and their hazard rate functions may be decreasing, increasing or constant depending on their shape parameters. On the other hand, the EP distribution has several interesting applications based on stochastic representations involving maximum and minimum of iid exponential variables (with random sample size) which make it of distinguishable scientific importance from the gamma distribution. Given the similarities and different scientific relevance between these models, one question of interest is how to discriminate them. With this in mind, we propose a likelihood ratio test based on Cox's statistic to discriminate the EP and gamma distributions. The asymptotic distribution of the normalized logarithm of the ratio of the maximized likelihoods under two null hypotheses – data come from EP or gamma distributions – is provided. With this, we obtain the probabilities of correct selection. Hence, we propose to choose the model that maximizes the probability of correct selection (PCS). We also determinate the minimum sample size required to discriminate the EP and gamma distributions when the PCS and a given tolerance level based on some distance are before stated. A simulation study to evaluate the accuracy of the asymptotic probabilities of correct selection is also presented. The paper is motivated by two applications to real data sets. [ABSTRACT FROM AUTHOR]

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration. [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]

In this paper, we consider the distribution of life length of a series system with random number of components, sayZ. Considering the distribution ofZas generalized Poisson, an exponential-generalized Poisson (EGP) distribution is developed. The generalized Poisson distribution is a generalization of the Poisson distribution having one extra parameter. The structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated. Extensive simulation studies are carried out to study the performance of the estimates. The score test is developed to test the importance of the extra parameter. For illustration, two real data sets are examined and it is shown that the EGP model, presented here, fits better than the exponential–Poisson distribution. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce an efficient Bayesian sampling procedure for exponential distribution with type-I censoring. An online inspection method is suggested to reach a Bayes decision prior the termination time of life test. Bayesian sampling plans (BSPs) with quadratic loss function are established to illustrate the use of the proposed method. Some BSPs are tabulated, and the performance of the proposed BSPs is compared with two existing competitive methods. Numerical results indicate that a significant reduction in the experimental time over the conventional BSP can be achieved when the online inspection method is applied. [ABSTRACT FROM AUTHOR]

When the shape parameter is a non-integer of the generalized exponential (GE) distribution, the analytical renewal function (RF) usually is not tractable. To overcome this, the approximation method has been used in this paper. In the proposed model, then-fold convolution of the GE cumulative distribution function (CDF) is approximated byn-fold convolutions of gamma and normal CDFs. We obtain the GE RF by a series approximation model. The method is very simple in the computation. Numerical examples have shown that the approximate models are accurate and robust. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via numerical experiments. [ABSTRACT FROM PUBLISHER]

In this paper, a new sampling method is suggested, namely truncation-based ranked set samples (TBRSS) for estimating the population mean and median. The suggested method is compared with the simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS) and median-ranked set sampling (MRSS) methods. It is shown that for estimating the population mean when the underlying distribution is symmetric, TBRSS estimator is unbiased and it is more efficient than the SRS estimator based on the same number of measured units. For asymmetric distributions considered in this study, TBRSS estimator is more efficient than the SRS for all considered distributions except for exponential distribution when the selection coefficient gets large. When compared with ERSS and MRSS methods, TBRSS performs well with respect to ERSS for all considered distributions except for U(0, 1) distribution, while TBRSS efficiency is higher than that of MRSS for U(0, 1) distribution. For estimating the population median, the TBRSS estimators have higher efficiencies when compared with SRS and ERSS. A real data set is used to illustrate the suggested method. [ABSTRACT FROM PUBLISHER]

In this paper, we study some mathematical properties of the beta Weibull (BW) distribution, which is a quite flexible model in analysing positive data. It contains the Weibull, exponentiated exponential, exponentiated Weibull and beta exponential distributions as special sub-models. We demonstrate that the BW density can be expressed as a mixture of Weibull densities. We provide their moments and two closed-form expressions for their moment-generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and two entropies. The density of the BW-order statistics is a mixture of Weibull densities and two closed-form expressions are derived for their moments. The estimation of the parameters is approached by two methods: moments and maximum likelihood. We compare the performances of the estimates obtained from both the methods by simulation. The expected information matrix is derived. For the first time, we introduce a log-BW regression model to analyse censored data. The usefulness of the BW distribution is illustrated in the analysis of three real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a Bayesian estimation procedure for the parameters in a Moran–Downton bivariate exponential distribution based on complete and censored samples. A Markov-chain Monte Carlo method is used to obtain the Bayes estimates of the parameters. An intensive simulation experiment is conducted to study the performance of the proposed Bayesian estimation procedure. Discussions and suggestions are provided based on the simulation results. A numerical example is presented to illustrate the Bayesian estimation procedure developed here and some concluding remarks are provided. [ABSTRACT FROM PUBLISHER]

The paper introduces an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Ebrahimiet al. [Two measures of sample entropy, Statist. Probab. Lett. 20 (1994), pp. 225–234]. The consistency of the estimator is proved and comparisons are made with Vasicek's estimator [A test for normality based on sample entropy, J. R. Stat. Soc. Ser. B 38 (1976), pp. 54–59], van Es estimator [Estimating functionals related to a density by class of statistics based on spacings, Scand. J. Statist. 19 (1992), pp. 61–72], Ebrahimiet al. estimator and Correa estimator [A new estimator of entropy, Comm. Statist. Theory Methods 24 (1995), pp. 2439–2449]. The results indicate that the proposed estimator has smaller mean-squared error than above estimators. A real example is presented and analysed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce thep-generalized polar methods for the simulation of thep-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate thep-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of thep-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider the situations in which a middle part of the sample is lost or removed from the experiment. The left-censored sample and Type-II right-censored sample are special cases of this scheme. Point and interval reconstructors for lost failure times are obtained, while the underlying distribution is exponential. To illustrate the performance of the proposed procedures, two numerical examples based on the real data sets are presented. In the case of two-parameter, a simulation study has been done and also the sensitivity of the results to deviations from the true distribution is investigated. [ABSTRACT FROM AUTHOR]

Recently, Sanjel and Balakrishnan [A Laguerre Polynomial Approximation for a goodness-of-fit test for exponential distribution based on progressively censored data, J. Stat. Comput. Simul. 78 (2008), pp. 503–513] proposed the use of Laguerre orthogonal polynomials for a goodness-of-fit test for the exponential distribution based on progressively censored data. In this paper, we use Jacobi and Laguerre orthogonal polynomials in order to obtain density approximants for some test statistics useful in testing for outliers in gamma and exponential samples. We first obtain the exact moments of the statistics and then the density approximants, based on these moments, are expressed in terms of Jacobi and Laguerre polynomials. A comparative study is carried out of the critical values obtained by using the proposed methods to the corresponding results given by Barnett and Lewis [Outliers in Statistical Data, 3rd ed., John Wiley & Sons, New York, 1993]. This reveals that the proposed techniques provide very accurate approximations to the distributions. Finally, we present some numerical examples to illustrate the proposed approximations. Monte Carlo simulations suggest that the proposed approximate densities are very accurate. [ABSTRACT FROM PUBLISHER]

In this paper, we first present two characterizations of the exponential distribution and next introduce three exact goodness-of-fit test for exponentiality. By simulation, the powers of the proposed tests under various alternatives are compared with the existing tests. [ABSTRACT FROM PUBLISHER]

Doostparast and Balakrishnan (Pareto record-based analysis, Statistics, under review) recently developed optimal confidence intervals as well as uniformly most powerful tests for one- and two-sided hypotheses concerning shape and scale parameters, for the two-parameter Pareto distribution based on record data. In this paper, on the basis of record values and inter-record times from the two-parameter Pareto distribution, maximum-likelihood and Bayes estimators as well as credible regions are developed for the two parameters of the Pareto distribution. For illustrative purposes, a data set on annual wages of a sample of production-line workers in a large industrial firm is analysed using the proposed procedures. [ABSTRACT FROM PUBLISHER]

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88-95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhya Ser. B 48 (1986), pp. 10-18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties. [ABSTRACT FROM AUTHOR]

In this paper the collective risk model with Poisson-Lindley and exponential distributions as the primary and secondary distributions, respectively, is developed in a detailed way. It is applied to determine the Bayes premium used in actuarial science and also to compute the regulatory capital in the analysis of operational risk. The results are illustrated with numerous examples and compared with other approaches proposed in the literature for these questions, with considerable differences being observed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a test for uniformity and use it as the second stage of an exact goodness-of-fit test of exponentiality. By simulation, the powers of the proposed test under various alternatives are compared with exponentiality test based on Kullback-Leibler information proposed by Ebrahimi et al. [N. Ebrahimi, M. Habibullah, and E.S. Soofi, Testing exponentiality based on Kullback-Leiber information, J. R. Statist. Soc. Ser. B 54 (1992), pp. 739-748]. The results are impressive, i.e. the proposed test has higher power than the test based on entropy. [ABSTRACT FROM AUTHOR]

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains Op(N-3/2), which is the best convergence rate in the case of only additive noise and constant amplitude. [ABSTRACT FROM AUTHOR]

Recently, many standard families of distributions have been generalized by exponentiating their cumulative distribution function (CDF). In this paper, test statistics are constructed based on CDF-transformed observations and the corresponding moments of arbitrary positive order. Simulation results for generalized exponential distributions show that the proposed test compares well with standard methods based on the empirical distribution function. [ABSTRACT FROM AUTHOR]

The generalized exponential distribution proposed by Gupta and Kundu [Gupta, R.D and Kundu, D., 1999, Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41(2), 173-188.] is an important lifetime distribution in survival analysis. In this paper, we consider the maximum likelihood estimation procedure of the parameters of the generalized exponential distribution when the data are left censored. We obtain the maximum likelihood estimators of the unknown para-meters and the Fisher information matrix. Simulation studies are carried out to observe the performance of the estimators in small sample. [ABSTRACT FROM AUTHOR]

Statistical inference methods for the Weibull parameters and their functions usually depend on extensive tables, and hence are rather inconvenient for the practical applications. In this paper, we propose a general method for constructing confidence intervals for the Weibull parameters and their functions, which eliminates the need for the extensive tables. The method is applied to obtain confidence intervals for the scale parameter, the mean-time-to-failure, the percentile function, and the reliability function. Monte-Carlo simulation shows that these intervals possess excellent finite sample properties, having coverage probabilities very close to their nominal levels, irrespective of the sample size and the degree of censorship. [ABSTRACT FROM AUTHOR]

Inference concerning the ratio of two means based two independent two-parameter gamma models with common shape parameter was examined in Booth et al. (1999) and a computationally intensive bootstrap calibration method was developed. In this paper, a likelihood based method is proposed for small sample inference about the ratio of two means of the two-parameter gamma models when the shape parameters may or may not be equal. The proposed method is very simple to use and, as illustrated in simulation studies, gives extremely accurate results. [ABSTRACT FROM AUTHOR]

Recently the two-parameter generalized exponential distribution was introduced by the authors. It is observed that a generalized exponential distribution has several properties which are quite similar to a gamma distribution. It is also observed that a generalized exponential distribution can be used quite effectively in many situations where a skewed distribution is needed. In this paper, we use the ratio of the maximized likelihoods in choosing between a generalized exponential distribution and a gamma distribution. We obtain asymptotic distributions of the logarithm of the ratio of the maximized likelihoods under null hypotheses and use them to determine the sample size needed to discriminate between two overlapping families of distributions for a user specified probability of correct selection and a tolerance limit. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new type of censoring scheme which combines the features of grouped censoring and Type-II censoring. Statistical analysis of exponentially distributed lifetimes observed under this scheme is considered. The MLE of the model parameter and its asymptotic variance are derived. Furthermore, expressions for the expected experiment time and the expected number of failures are given. A numerical study is conducted to study these quantities and the results are compared with those under a Type-II censored plan. This comparison provides useful insight on the choice of these plans in designing a life test. [ABSTRACT FROM AUTHOR]

This paper investigates a new family of goodness-of-fit tests based on the negative exponential disparities. This family includes the popular Pearson's chi-square as a member and is a subclass of the general class of disparity tests (Basu and Sarkar, 1994) which also contains the family of power divergence statistics. Pitman efficiency and finite sample power comparisons between different members of this new family are made. Three asymptotic approximations of the exact null distributions of the negative exponential disparity family of tests are discussed. Some numerical results on the small sample performance of this family of tests are presented for the symmetric null hypothesis. It is shown that the negative exponential disparity family, like the power divergence family, produces a new goodness-of-fit test statistic that can be a very attractive alternative to the Pearson's chi-square. Some numerical results suggest that, application of this test statistic, as an alternative to Pearson's chi-square, could be preferable to the I[sup2/3] statistic of Cressie and Read (1984) under the use of chi-square critical values. [ABSTRACT FROM AUTHOR]

Left-censored data with one or more detection limits (DLs) often arise in environmental contexts. The computational procedure for the calculation of maximum likelihood estimators of the parameter for Type I multiply left-censored data from underlying exponential distribution is suggested and used considering various numbers of DLs. The expected Fisher information measure (FIM) is analytically determined and its performance is compared with sample (observed) FIM using simulations. Simulations are focused primarily on the properties of estimators for small sample sizes. Moreover, the simulations follow the possible applications of the results in the statistical analysis of real chemical data. [ABSTRACT FROM PUBLISHER]

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the parameters and Kolmogorov–Smirnov type statistics. Simple explicit representations for the boundaries and for the coverage probabilities of the confidence bands are analytically derived, and the performance of the bands is compared in terms of band width and area by means of a data example. As a by-product, a novel confidence region for the location-scale parameter is obtained. Extensions of the results to related models for ordered data, such as sequential order statistics, as well as to other underlying location-scale families of distributions are discussed. [ABSTRACT FROM AUTHOR]

Features a parametric study involving simulations to determine which of the inverse-sampling and the random-sampling schemes is more efficient for the maximum likelihood estimates of the parameters of the exponential distribution. Sampling schemes used to collect record-breaking data; Weibull distribution; Type I extreme value or Gumbel distribution; Pareto distribution; Mean square errors.

The aim of this article is to review existing goodness-of-fit tests for the exponential distribution under progressive Type-II censoring and to provide some new ideas and adjustments. In particular, we consider two-parameter exponentially distributed random variables and adapt the proposed test procedures to our scenario if necessary. Then, we compare their power by an extensive simulation study. Furthermore, we propose five new test procedures that provide reasonable alternatives to those already known. [ABSTRACT FROM AUTHOR]

In this study, we discuss the classical, Bayesian, and generalized inference of the reliability parameter At least s of the exceed of an s-out-of-k:G system with strength components subjected to a common stress Y whose probability densities are independent two-parameter general class of exponentiated inverted exponential distributions. These statistical analyses are carried out based on the progressively type-II right censored data with uniformly random removals. Under squared error and LINEX loss functions, Bayes estimates are developed by using Lindley's approximation and the Markov Chain Monte Carlo method due to the lack of closed forms of the posterior distributions. Generalized inferences are performed based on the generalized variable method. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed. Comparison and contrast among the classical, Bayesian, and generalized inferences of the reliability parameter in the multicomponent stress-strength model are performed. [ABSTRACT FROM AUTHOR]

This article mainly considers interval estimation of the scale and shape parameters of the generalized exponential (GE) distribution. We adopt the generalized fiducial method to construct a kind of new confidence intervals for the parameters of interest and compare them with the frequentist and Bayesian methods. In addition, we give the comparison of the point estimation based on the frequentist, generalized fiducial and Bayesian methods. Simulation results show that a new procedure based on generalized fiducial inference is more applicable than the non-fiducial methods for the point and interval estimation of the GE distribution. Finally, two lifetime data sets are used to illustrate the application of our new procedure. [ABSTRACT FROM AUTHOR]