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Bandwidth selection is key for kernel quantile estimators (KQEs), which estimate quantiles by averaging all of the order statistics with appropriate kernel-weighting functions. This paper provides a new data-driven bandwidth selection method for KQEs, named the exact bootstrap-based bandwidth selection (EBS) rule. By relying on the exact analytic expressions for the bootstrap mean and variance of KQEs, the error due to bootstrap resampling is eliminated, and thus the optimal bandwidth can be obtained by minimizing the mean squared error (MSE) estimate. The effectiveness of this EBS rule is confirmed by numerical experiments. First, the bandwidth selection performance of the EBS method is compared to that of a benchmark approach. Simulation studies show that the EBS method performs well, especially in selecting bandwidths for extreme quantiles and when applied to small sample sizes with skewed distributions and relatively large variances. Second, KQEs with a bandwidth determined by our EBS rule is compared with five other state-of-the-art quantile estimators over six typical distributions. The results further validate the efficiency of the EBS method. Third, the results of simulations of controlling actual type-I error rates that occur when two independent groups are compared through quantiles further demonstrate the precision of our EBS-based KQEs. [ABSTRACT FROM AUTHOR]

AbstractThe two-parameter standard two-sided power family of distributions on (0, 1) is considered in this article. We propose bootstrap standard errors for the maximum likelihood estimators, as well as bootstrap confidence intervals for its parameters, once these important statistical measures of accuracy cannot be computed based on first-order asymptotic theory. We consider Monte Carlo simulation experiments to verify the performance of the bootstrap methods, and the numerical results are quite promising. Applications to real data are also considered to illustrate the proposed methodology in practice. [ABSTRACT FROM AUTHOR]

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good enough. A more efficient alternative is the Harrell-Davis quantile estimator which uses a weighted sum of all order statistics. Whereas this approach provides more accurate estimations for the light-tailed distributions, it's not robust. To be able to customize the tradeoff between statistical efficiency and robustness, we could consider a trimmed modification of the Harrell-Davis quantile estimator. In this approach, we discard order statistics with low weights according to the highest density interval of the beta distribution. [ABSTRACT FROM AUTHOR]

We show that the expected value of the largest order statistic in Gaussian samples can be accurately approximated as (0.2069 ln (ln (n)) + 0.942) 4 , where n ∈ [ 2 , 10 8 ] is the sample size, while the standard deviation of the largest order statistic can be approximated as − 0.4205 arctan (0.5556 [ ln (ln (n)) − 0.9148 ]) + 0.5675. We also provide an approximation of the probability density function of the largest order statistic which in turn can be used to approximate its higher order moments. The proposed approximations are computationally efficient, and improve previous approximations of the mean and standard deviation given by Chen and Tyler (1999). [ABSTRACT FROM AUTHOR]

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results. [ABSTRACT FROM AUTHOR]

In this article, we propose two new scale invariant test statistics when the available data are subject to progressively Type-II censoring. The proposed tests are based on Gini index of spacings. It is observed thorough extensive Monte Carlo simulations that the proposed tests are quite powerful in compare to similar existing goodness-of-fit tests studied by Balakrishnan et al. and Wang. We also illustrate the method proposed here using a real data from reliability literature. [ABSTRACT FROM AUTHOR]

Let Poisson variables X 1 , ⋯ , X m be independent and Y 1 , ⋯ , Y n be also independent such that each X i ∼ P (λ i) , Y j ∼ P (μ j). We prove that if X m : m = max { X 1 , ⋯ , X m } and Y n : n = max { Y 1 , ⋯ , Y n } have the same distribution, then m = n and { λ 1 , ⋯ , λ m } = { μ 1 , ⋯ , μ m }. The weak version in term of minimum statistics is also derived. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character under investigation by means of visual inspection or other methods not requiring actual measurements. RSS performs better than simple random sampling (SRS) to estimate the population mean. In original RSS procedure, the units corresponding to each rank are used. In this article, we propose to use RSS method with lowest order statistics from each sample to estimate the population mean of Pareto distribution which is highly positively skew. The Pareto distribution is chosen due to its application in social and scientific phenomenon including the distribution of wealth in a society. The estimator based on lowest order statistics with bias correction term has been proposed. Two cases, known and unknown scale parameter, have been considered. The simulation-based methods have also been included. It is shown that the gains in the relative precisions of population mean based on our proposed method are uniformly higher than those based upon the RSS and extreme RSS procedures. The proposed method with bias correction term is recommended for real applications. [ABSTRACT FROM AUTHOR]

In this paper, we derive the recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the exponential-geometric distribution. For a particular case, these results are reduced to the corresponding results for the usual order statistics. Next, we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the exponential-geometric distribution based on progressively Type-II right censored samples. The best linear unbiased predictors of future failure times are then discussed. Finally, an illustrative example is presented. [ABSTRACT FROM AUTHOR]

In this follow up article of Arnold and Ghosh, we re-visit and study in details one of the two special cases of multivariate hidden truncation -(a) single variable truncation from above in a trivariate scenario where the component random variables follow an appropriate Pareto (type II) distribution. The case with single variable truncation was not discussed in details earlier in Arnold and Ghosh, in particular the estimation under both the classical and the Bayesian paradigm. It is well known that the Pareto distribution is a simple model for nonnegative data with a power law probability tail. Accumulating experience rapidly pointed out the fact that it is only in the upper tail of the income distributions that Pareto-like behavior can be expected. In practice, it has been observed that in income modeling and in other medical studies, quite often the observed data has been truncated with respect to several other unobserved co-variable(s) attaining certain critical levels. In this paper, we consider both the classical and the Bayesian inference (under the non-informative priors set up) of the resulting hidden truncated model. For illustrative purposes, a real data set on abalone is considered to show the flexibility of a single variable truncated Pareto (type II) distribution in a trivariate setting. Finally, the large sample behavior of the smallest order statistic in the case of a single co-variable truncation from above is provided in the appendix. [ABSTRACT FROM AUTHOR]

Abstract Ranked set sampling (RSS) is a cost-efficient alternative to simple random sampling (SRS) when ranking small sets of population units is much simpler than effectively measuring them. Maximum likelihood estimation (MLE) in RSS is usually based on the restrictive assumption of perfect ranking, assuming that the sample units lead to order statistics. However, this procedure is not flexible and often produces highly biased estimators when ranking errors are present. To remedy these constraints, in this work we suggest and evaluate alternative MLE procedures for RSS: (i) MLE based on the perfect ranking assumption; (ii) MLE based on the SRS assumptions; (iii) a weighted estimator derived from (i) and (ii); (iv) the choice of (i) or (ii) by testing the null hypothesis of perfect ranking. We carried out extensive simulations to investigate the efficiency of each strategy, which allowed us to conclude that although (i) performed the best under perfect ranking, (ii-iv) are preferable under imperfect ranking. We have also evaluated a parametric bootstrap algorithm to obtain confidence intervals in RSS based on the suggested estimators. Two applications using data from age determination of fishes and anthropometric measures of athletes illustrate and corroborate our findings. [ABSTRACT FROM AUTHOR]

For highly reliable products and devices, conducting the life tests at normal usage conditions demands a great deal of time and cost, which can result in missed opportunities to introduce the product to the market in a timely manner and eventually loss of the market share. By subjecting test units at higher stress levels than normal operating conditions, accelerated life tests solve this problem and quickly produce information on the lifetime parameters. The lifetime at the design stress is then estimated through extrapolation using a regression model. Due to technical limitations and/or budgetary constraints, the exact failure times of test units may not be available in practice but only the failure counts are collected at certain time points during the life test. In this work, the design optimization of a general k-level step-stress accelerated life test under progressive Type-I censoring is considered with a uniform step duration Δ when the exact failure times are not observable ( i. e. , interval inspection). Allowing the intermediate censoring at each stress change time point (viz., i Δ , i = 1 , 2 , ... , k ), the optimal Δ is determined under various design criteria including D-optimality, T-optimality, C-optimality, A-optimality, and E-optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the design efficiency is compared to the situation when the exact failure times are available ( i. e. , continuous inspection). [ABSTRACT FROM AUTHOR]

Two modified ranked set sampling schemes are used to estimate the upper and lower quantiles of an underlying distribution. The performance of these sampling schemes is compared with that of ordinary ranked set sampling in view of Pitman's measure of closeness criterion. Actually, a way of choosing estimators is proposed in the paper based on Pitman closeness which demonstrates that the mentioned modifications on ranked set sampling are useful in the problem of quantile estimation. The results are applied to the location-scale family of distributions and the Pitman closeness probabilities are obtained numerically for the cases of exponential and uniform distributions. It is shown that the proposed sampling schemes would improve the performance of the point estimators of the population quantiles specially for extreme quantiles. The proposed procedure is used to estimate the quantiles of a real data set. [ABSTRACT FROM AUTHOR]

The half logistic-geometric (HLG) distribution derived here is a simple distribution with interesting properties and is therefore a useful distribution for analyzing lifetime data. Algorithm is derived for the computation of single and product moments of order statistics from this distribution. These recurrence relations enable the computation of means, variances and covariances of all order statistics for all sample size in a simple and efficient way. The results are of great importance in determining the best linear unbiased estimator of the scale parameter of a scaled-HLG distribution, and those of parameters of the more general location-scale HLG distribution based on complete and Type-II censored samples. Finally, an example is presented to illustrate the developed results. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference on the location parameter vector is studied in the multivariate skew-normal model with unknown scale parameter and known shape parameter. Based on the distribution of the generalized Hotelling's T2 statistic, confidence regions and hypothesis tests on the location parameter, μ , are obtained. The power function of the test is studied numerically as well. For illustration the effectiveness and applicability of our purposed methods, the traffic accident data from the National Highway Traffic Safety Administration (NHTSA) in U.S. Department of Transportation are analyzed. [ABSTRACT FROM AUTHOR]

In this note we provide a novel semi-parametric best linear unbiased estimator (BLUE) of location and its corresponding variance estimator under the assumption the random variate is generated from a symmetric location-scale family of distributions. The approach follows in a two-stage fashion and is based on the exact bootstrap estimate of the covariance matrix of the order statistic. We generalize our approach to add a robustness component in order to derive a trimmed BLUE of location under a semi-parametric symmetry assumption. [ABSTRACT FROM AUTHOR]

In this paper, it is investigated that the some statistical properties and the methods of estimation for transmuted record type Weibull (TRTW) distribution.The moments, variance, skewness and kurtosis coefficients, geometric mean, quantile function, median, incomplete moments, Rényi entropy, the moments of order statistics are obtained for TRTW distribution. Six different estimators are considered in order to estimate the parameters of TRTW distribution. Furthermore, Monte Carlo (MC) simulations are performed to evaluate the performances of these estimators. Finally, a real data example is presented to illustrate the usefullness of TRTW distribution. [ABSTRACT FROM AUTHOR]

This paper studies the prediction problem of future order statistics based on a mixture of exponential distributions. We suggest different scenarios to construct predictive intervals and point predictions for the future observations in two cases. In the first case, we assume fixed sample size, while in the second case, the sample size is assumed to be positive integer–valued random variable independent of the observations. [ABSTRACT FROM AUTHOR]

The results of the extropy of order statistics are applied to constructing a test statistic for symmetry. This test statistic has this advantage that we do not need to estimate the center of the symmetry. Through a simulation study, the power of the test is computed and then compared with the competing tests. The power results show that, for a wide variety of alternative asymmetric distributions, the proposed test is much more powerful than other tests. A real dataset is presented and analyzed. [ABSTRACT FROM AUTHOR]

The skew-normal distribution and various generalizations have received much attention in recent years in behalf of their non-normal characteristics, such as heavy right or left tail, which are appeared in many real data sets. So far, many mathematical results have been derived about the skew distributions. Nevertheless, less attention has been paid on the inferential aspects of the proposed distributions. Hence in this paper, we focus on some inferential results of the skew-normal distribution. The amount of Fisher information in the order statistics of a simple random sample is studied and some properties are discussed with respect to variations of skewness parameter. Also, the most informative part of a sample is determined via simulation. The maximum likelihood estimators of skewness parameter are derived based on both complete sample and the most informative part of the sample and their efficiencies are compared. Furthermore, a ranked based sampling scheme is introduced to do inference about the skewness parameter in populations with high right skewness. Finally, a real data set is used to illustrate the results of the paper. [ABSTRACT FROM AUTHOR]

The present article is concerned with the comparison of representativeness of a random sample to the underlying population as a whole, obtained through ranked set sampling (RSS) with simple random sampling (SRS). This is done by defining the Bayesian score as a measure of representativeness corresponding to the units of the population. The proposed procedure shows that RSS is a better sampling method and the probability of having the most unrepresentative sample is very less in case of RSS than in case of SRS, irrespective of whether the ranking is perfect or imperfect. The proposed procedure is also illustrated through a real-life data on survivorship of children below one year in Empowered Action Groups (EAG) states of India. [ABSTRACT FROM AUTHOR]

In this note we propose a new semi-parametric bootstrap procedure for hypothesis tests about a statistical function and termed bootstrap warping. This procedure was motivated by empirical likelihood and bootstrap tilting techniques. The procedure is computationally efficient and has a fixed number of parameters. We show that the warping procedure has good type I error control and has monotone power as a function of sample size and shift alternatives. [ABSTRACT FROM AUTHOR]

In this paper, by considering an (n + 1) -dimensional random vector ( X 1 , X 2 , .... , X n , Y) T from the multivariate generalized hyperbolic (GH) distribution, we derive the joint distribution of Y and the order statistics from ( X 1 , X 2 , .... , X n) T. We show that this joint distribution is indeed a mixture of the selection GH distributions. The results were applied to some regression functions via the order statistics and established with a real data set. [ABSTRACT FROM AUTHOR]

Finding the optimal censoring scheme is a discrete optimization problem in the space of schemes. Under the entropy criterion, we examine optimal censoring schemes by preferring the choice of one-step censoring schemes as suggested by Balakrishnan. Exact one step optimal schemes for distributions with decreasing failure rate under entropy criterion are specified by Cramer and Bagh. We consider the distributions with increasing, right tailed and bath tub failure rates and compare the entropy of the one-step censoring schemes with the optimal ones, and observed that the loss in entropy is very negligible. [ABSTRACT FROM AUTHOR]

Pareto distribution is one of the well known distributions used to fit heavy-tailed data. Various generalizations of this distribution have been reported in the literature by several authors. An obvious reason for generalizing a standard distribution is that the generalized form provides greater flexibility in modeling real data. In this article, we introduce a new four parameter distribution called New Generalized Pareto distribution, which is a generalization of the classical Pareto distribution. The structural properties of the new distribution are discussed. It is shown that the distribution is heavy-tailed and belongs to the class of subexponential distributions. Certain characterizations of the new distribution are obtained. We also derive the distribution of order statistics. The method of maximum likelihood is used for estimating the model parameters. We provide simulation results to assess the performance of the maximum likelihood estimates of the model parameters. Autoregressive time series model with the new generalized Pareto distribution as marginal is developed. An application of a real data set shows the performance of the new distribution over other generalizations of Pareto distribution. [ABSTRACT FROM AUTHOR]

The value-at-risk (VaR) at a small level q, 0 < q < 1 , is the size of the loss that occurs with a probability q. Semi-parametric partially reduced-bias (PRB) VaR-estimation procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p any real number, are put forward. After the study of their asymptotic behavior, these PRB VaR-estimators are altogether compared with the classical ones for finite samples, through a large-scale Monte-Carlo simulation study. A brief application to financial log-returns is provided, as well as some final remarks. [ABSTRACT FROM AUTHOR]

We introduce a new family of distributions using truncated discrete Linnik distribution. This family is a rich family of distributions which includes many important families of distributions such as Marshall–Olkin family of distributions, family of distributions generated through truncated negative binomial distribution, family of distributions generated through truncated discrete Mittag–Leffler distribution etc. Some properties of the new family of distributions are derived. A particular case of the family, a five parameter generalization of Weibull distribution, namely discrete Linnik Weibull distribution is given special attention. This distribution is a generalization of many distributions, such as extended exponentiated Weibull, exponentiated Weibull, Weibull truncated negative binomial, generalized exponential truncated negative binomial, Marshall-Olkin extended Weibull, Marshall–Olkin generalized exponential, exponential truncated negative binomial, Marshall–Olkin exponential and generalized exponential. The shape properties, moments, median, distribution of order statistics, stochastic ordering and stress–strength properties of the new generalized Weibull distribution are derived. The unknown parameters of the distribution are estimated using maximum likelihood method. The discrete Linnik Weibull distribution is fitted to a survival time data set and it is shown that the distribution is more appropriate than other competitive models. [ABSTRACT FROM AUTHOR]

We apply the result of conditional independence of blocked ordered data established by Iliopoulos and Balakrishnan, together with the algorithm of Huffer and Lin, to obtain exact expressions for the distributions of linear combinations of Laplace order statistics. These expressions can then be evaluated using symbolic math package Maple. Finally, we illustrate the computational method with some examples. [ABSTRACT FROM AUTHOR]

This work is concerned with the distributions of spacings from a two-parameter gamma distribution, when the shape parameter is a positive integer (or Erlang Distribution). We express the probability density functions of spacings and their moments in closed forms that are easy to implement using computer algebra systems like Mathematica. [ABSTRACT FROM AUTHOR]

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek's estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives. [ABSTRACT FROM AUTHOR]

In this article, we consider the prediction of future failure times based on Type-I hybrid censored samples. Point predictors and prediction intervals using different procedures are discussed for a general model. The exponential and Rayleigh distributions are used as illustrative examples to show the most simplified forms of the so obtained predictors as well as prediction intervals. Intensive simulation study and a real life dataset are presented to illustrate our findings and results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extension of the Gompertz-Makeham distribution. This distribution is called the transmuted Gompertz-Makeham (TGM). The new model which can handle bathtub-shaped, increasing, increasing-constant and constant hazard rate functions. This property makes TGM is useful in survival analysis. Various statistical and reliability measures of the model are obtained, including hazard rate function, moments, moment generating function (mgf), quantile function, random number generating, skewness, kurtosis, conditional moments, mean deviations, Bonferroni curve, Lorenz curve, Gini index, mean inactivity time, mean residual lifetime and stochastic ordering; we also obtain the density of the ith order statistic. Estimation of the model parameters is justified by the method of maximum likelihood. An application to real data demonstrates that the TGM distribution can provides a better fit than some other very well known distributions. [ABSTRACT FROM AUTHOR]

We introduce the best unbiased prediction of missing order statistics of a stable distribution, based on conditional expected value. We present necessary and sufficient conditions for the existence of conditional moments of stable order statistics. These conditions enable us to compute unknown parameters using the expectation-maximization algorithm. We reveal the efficiency of the presented method through a simulation study. [ABSTRACT FROM AUTHOR]

The aim of this paper is to estimate parameters of generalized Pareto distribution based on generalized order statistics. Some non-Bayesian methods, such as MLE, bootstrap and unbiased estimators have been obtained to develop point and interval estimations. Bayesian estimations have also been derived under LSE and LINEX loss functions. To compare the performances of the employed methods, numerical results have been computed. To illustrate dependence and association properties of generalized order statistics, correlation coefficient and some informational measures in closed form have been obtained. [ABSTRACT FROM AUTHOR]

This article focuses on the improvement of a well-celebrated randomized response technique of Kuk. A generalized randomized response technique is suggested. In particular, the generalized geometric distribution of orderkis introduced as a randomization device for estimating the population proportion of a rare sensitive attribute. The proposed randomized response technique includes Singh and Grewal and Hussain et al. techniques as its special cases. Through numerical illustrations, it is established that the suggested technique is superior to the Kuk, Singh and Grewal, and Hussain et al. techniques. Flexibility of the proposed technique is also discussed. [ABSTRACT FROM PUBLISHER]

This article introduces a new generalization of the transmuted Weibull distribution introduced by Aryal and Tsokos in 2011. We refer to the new distribution as exponentiated transmuted Weibull geometric (ETWG) distribution. The new model contains 22 lifetime distributions as special cases such as the exponentiated Weibull geometric, complementary Weibull geometric, exponentiated transmuted Weibull, exponentiated Weibull, and Weibull distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. To examine the performance of our new model in fitting several data we use two real sets of data, censored and uncensored, and then compare the fitting of the new model with some nested and nonnested models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples. This model is capable of modeling various shapes of aging and failure criteria. [ABSTRACT FROM AUTHOR]

We derive the best linear unbiased interpolation for the missing order statistics of a random sample using the well-knownprojection theorem. The proposed interpolation method only needs the first two moments on both sides of a missing order statistic. A simulation study is performed to compare the proposed method with a few interpolation methods for exponential and Lévy distributions. [ABSTRACT FROM AUTHOR]

The logistic distribution is a simple distribution possessing many useful properties and has been used extensively for analyzing growth. Recently, van Staden and King proposed a quantile-based skew logistic distribution. In this paper, we introduce an alternative skew logistic distribution. We then establish recurrence relations for the computation of the single and product moments of order statistics from the standard skew logistic distribution by using the moments of order statistics from the standard half logistic distribution. These enable an efficient computation of means, variances and covariances of order statistics from the skew logistic distibution for all sample sizes. The results become useful in determining the best linear unbiased estimators of the location and scale paramters of the skew logistic distribution. Finally, we provide an example to illustrate the usefulness of the developed model and then compare its fit with that provided by the model of van Staden and King. [ABSTRACT FROM AUTHOR]

An empirical distribution function estimator for the difference of order statistics from two independent populations can be used for inference between quantiles from these populations. The inferential properties of the approach are evaluated in a simulation study where different sample sizes, theoretical distributions, and quantiles are studied. Small to moderate sample sizes, tail quantiles, and quantiles which do not coincide with the expectation of an order statistic are identified as problematic for appropriate Type I error control. [ABSTRACT FROM AUTHOR]

This article introduces a new generalization of the transmuted exponentiated modified Weibull distribution introduced by Eltehiwy and Ashour in 2013, using Kumaraswamy distribution introduced by Cordeiro and de Castro in 2011. We refer to the new distribution as Kumaraswamy-transmuted exponentiated modified Weibull (Kw-TEMW) distribution. The new model contains 54 lifetime distributions as special cases such as the KumaraswamyWeibull, exponentiated modified Weibull, exponentiated Weibull, exponentiated exponential, transmuted Weibull, Rayleigh, linear failure rate, and exponential distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. This model is capable of modeling various shapes of aging and failure criteria. [ABSTRACT FROM AUTHOR]

A goodness-of-fit test procedure is proposed for some lifetime distributions when the available data are subject to Type-I censoring. The proposed method extends the test procedure of Pakyari and Balakrishnan to other lifetime distributions. The extension toWeibull and log-normal models is studied in details. The new test recovers the nominal level of significance and exhibits more power in comparison to the existing tests for several alternative distributions by means of Monte Carlo simulations. Finally, a real dataset is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this study some new unbiased estimators based on order statistics are proposed for the scale parameter in some family of scale distributions. These new estimators are suitable for the cases of complete (uncensored) and symmetric doubly Type-II censored samples. Further, they can be adapted to Type II right or Type II left censored samples. In addition, unbiased standard deviation estimators of the proposed estimators are also given. Moreover, unlike BLU estimators based on order statistics, expectation and variance-covariance of relevant order statistics are not required in computing these new estimators. Simulation studies are conducted to compare performances of the new estimators with their counterpart BLU estimators for small sample sizes. The simulation results show that most of the proposed estimators in general perform almost as good as the counterpart BLU estimators; even some of them are better than BLUin some cases. Furthermore, a real data set is used to illustrate the new estimators and the results obtained parallel with those of BLUE methods. [ABSTRACT FROM AUTHOR]

Viewing the future order statistics as latent variables at each Gibbs sampling iteration, several Bayesian approaches to predict future order statistics based on type-II censored order statistics, X(1),X(2), . . ., X(r), of a size n(>r) random sample from a four-parameter generalized modifiedWeibull (GMW) distribution, are studied. Four parameters of the GMW distribution are first estimated via simulation study. Then various Bayesian approaches, which include the plug-in method, the Monte Carlo method, the Gibbs sampling scheme, and the MCMC procedure, are proposed to develop the prediction intervals of unobserved order statistics. Finally, four type-II censored samples are utilized to investigate the predictions. [ABSTRACT FROM AUTHOR]

In this article we introduce a new generalization of skew-tdistributions, which contains the standard skew-tdistribution, as a special case. This new class of distributions is an adequate model for modeling some dataset rather than the standard skew-tdistributions. This kind of distributions can be represented as a scale-shape mixture of the extended skew-normal distributions. The main properties of this family of distributions are studied and a recurrence relation for the cumulative distribution functions (cdf) of them is presented. We derive the distribution of the order statistics from the trivariate exchangeablet-distribution in terms of our distribution and then an exact expression for the cdf of order statistics is derived. Likelihood inference for this distribution is also examined. The method is illustrated with a numerical example via a simulation study. [ABSTRACT FROM AUTHOR]

Baker (2008) introduced a new method for constructing multivariate distributions with given marginals based on order statistics. In this paper, we provide a test of independence for a pair of absolutely continuous random variables (X,Y) jointly distributed according to Baker’s bivariate distributions. Our purpose is to test the hypothesis thatXandYare independent versus the alternative thatXandYare positively (negatively) quadrant dependent. The asymptotic distribution of the proposed test statistic is investigated. Also, the powers of the proposed test and the class of distribution-free tests proposed by Kochar and Gupta (1987) are compared empirically via a simulation study. [ABSTRACT FROM AUTHOR]

In this study, new unbiased and nonlinear estimators based on order statistics are proposed for the family of symmetric location-scale distributions and these estimators can be computed from both uncensored and symmetric doubly Type II censored samples. In addition, other relevant unbiased estimators are proposed to estimate standard deviations of these new estimators. A simulation study has been performed to evaluate the performance of the new estimators compared to BLU estimators for small sample sizes. As a result of the simulation study, the new estimators proposed for the location-scale family in general performed nearly as good as BLU estimators. Furthermore, the computational advantage of the proposed estimators over BLU and ML estimators are worthy of notice. In addition, these new estimators have been applied to real data, and the estimation results obtained have been compatible with those of BLUE methods. [ABSTRACT FROM PUBLISHER]

In this article, the simple step-stress model is considered based on generalized Type-I hybrid censored data from the exponential distribution. The maximum likelihood estimators (MLEs) of the unknown parameters are derived assuming a cumulative exposure model. We then derive the exact distributions of the MLEs of the parameters using conditional moment generating functions. The Bayesian estimators of the parameters are derived and then compared with the MLEs. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs, Bayesian, and the parametric bootstrap methods. The problem of determining the optimal stress-changing point is discussed and the MLEs of thepth quantile and reliability functions at the use condition are obtained. Finally, Monte Carlo simulation and some numerical results are presented for illustrating all the inferential methods developed here. [ABSTRACT FROM PUBLISHER]

The maximum likelihood estimator is widely used in estimating the population proportion using group testing. However, it is positive biased and some alternatives have been raised in literatures. In this study, we propose a new estimator by weighted combination of order statistics. Two rules are supplied to determine the unknown weight. Using the rule of minimizing the absolute bias, our estimator is almost unbiased in most cases shown by simulations. Using the rule of minimizing the mean square error, a simple estimator with weight 1 is recommended for its good performance. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to develop a Monte-Carlo simulation algorithm for computing mean time to failure (MTTF) of weighted-k-out-of-n:G and linear consecutive-weighted-k-out-of-n:G systems. Our algorithm is based on the use of appropriately defined stochastic process which represents the total weight of the system at timet. These stochastic processes are explicitly defined and used along with the ordered component lifetimes to simulate MTTF of the systems with weighted components. [ABSTRACT FROM PUBLISHER]

Boxplots are among the most widely used exploratory data analysis (EDA) tools in statistical practice. Typical applications of boxplots include eliciting information about the underlying distribution (shape, location, etc.) as well as identifying possible outliers. This article focuses on a modification using a type of lower and upper fences similar in concept to those used in a traditional boxplot; however, instead of constructing the upper and lower fences using the upper and lower quartiles, respectively, and a multiple of the interquartile range (IQR), multiples of the upper and the lower semi-interquartile ranges (SIQR), respectively, measured from the sample median, are used. Any observation beyond the proposed fences is labeled a potential outlier. An exact expression for the probability that at least one sample observation is wrongly classified as an outlier, the so-called “some-outside rate per sample” (Hoaglin et al. (1986)), is derived for the family of location-scale distributions and is used in the determination of the fence constants. Tables for the fence constants are provided for a number of well-known location-scale distributions along with some illustrations with data; the performance of the outlier detection rule is explored in a simulation study. [ABSTRACT FROM AUTHOR]