Journal of Statistical Theory and Applications

We present recurrence relations for single, inverse, product and ratio moments of Generalized Order Statistics when sample is available from an Inverse Weibull Distribution. These relations enable computation of higher order moments using corresponding lower order moments. Some Characterizations of the...

This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of the components and is unaffected by outliers. It is numerically compared...

Estimation of quantiles of two exponential populations is considered assuming equality of location parameters using censored samples from a decision theoretic point of view. Sufficient conditions for inadmissibility of estimators in certain classes have been derived. Consequently some complete class...

In this paper we modify nonparametric regression-based mean estimators in ranked set sampling using a covariate. We will show that our modified mean estimators perform well in comparison with their leading competitors.

In this note, we establish a law of iterated logarithm for a triangular array of a random number of independent random variables and apply it to obtain laws of iterated logarithm for the sequential nonparametric density estimators. We consider the case of Rosenblatt-Parzen kernel estimators and orthogonal...

In this paper, we consider a general form for the underlying distribution and a general conjugate prior, and develop a general procedure for Bayesian estimation based on an observed multiply Type-II censored sample. The problem of predicting the order statistics from a future sample are also discussed...

LINEX weighted k-means is a version of weighted k-means clustering, which computes the weights of features in each cluster automatically. Determining which entity is belonged to which cluster depends on the cluster centers. In this study, the asymmetric LINEX loss function is used to compute the dissimilarity...

The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for the data sets which exhibit heteroscedasticity mainly due to the lack of constant means rather than unequal variances, the existing models tend to overestimate the variance of the second level...

This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a three-parameter Burr XII distribution,...

This paper discusses the problem of how Monte-Carlo simulation method is deal with Bayesian estimation of reliability of system of n s-independent two-state component. Time-to-failure for each component is assumed to have Weibull distribution with different parameters for each component. The shape parameter...

By assuming that an underlying Gaussian-Log Gaussian (GLG) random field clipped to yield binary spatial data, we propose a new model which provides flexibility in capturing the effects of heavy tail in latent variables. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte...

The kernel approach has been applied using the adaptive kernel density estimation, to inference on the generalized gamma distribution parameters, based on the generalized order statistics (GOS). For measuring the performance of this approach comparing to the Asymptotic Maximum likelihood estimation,...

In this paper, we extend our investigations of a special class of perturbations of copulas introduced in [7]. Despite a surprising fact that this kind of perturbations does not change the value of tail dependence of the original copulas, their use yielded models with considerably improved fitting qualities.

For analysis of contingency tables with large sample size, classical approaches using approximate methods have high power. However, when the sample size is small or some cells have frequencies less than 5, classical approaches are so conservative. Also asymptotic behavior may be poor when the table contains...

In this paper, we present nonparametric tests for the two-sample scale problem. The proposed tests include as special case the B.V. Sukhatme, Ann. Math. Stat. 28 (1957), 188–194, and J.V. Deshpande, K. Kusum, Aust. J. Stat. 26 (1984), 16–24 tests. The asymptotic distribution of the test statistics is...

We deal with the normality asymptotic theory of empirical divergences measures based on wavelets in a series of three papers. In this first paper, we provide the asymptotic theory of the general of ϕ-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families...

Based on the goodness of fit approach, a new test is presented for testing exponentiality against "exponential Better than Used in moment generating function ordering class" (EBUmgf). The critical values and the powers of this test are calculated. It is shown that the proposed test enjoys good power...

In this paper we derive some general recurrence relations between moments of progressively Type-II right censored order statistics from a general class of doubly truncated distributions, thus unifying the earlier results in this direction due to several authors.

In the present paper, a two-sided test in a family of multivariate distribution according to the Mahalanobis distance with mean vector and positive definite matrix is considered. First, a family of multivariate distribution is introduced, then using the likelihood ratio method a test statistic is computed....

In this paper, a new extension of cumulative residual entropy is proposed. It contain the generalized cumulative residual entropy introduced by Psarrakos and Navarro (2013) and is related with the k-record values. We also consider a dynamic version of this new cumulative residual entropy using the residual...

In this paper, we introduce periodically correlated space-time autoregressive processes with values in Hilbert spaces. The existence conditions and the strong law of large numbers are established. Moreover, we present an estimator for the autocorrelation parameter of such processes.

In this paper, the researchers attempt to introduce a new generalization of the exponential distribution. This new model is obtained by compounding the exponential distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution....

In this paper, the Weibull-X family is proposed and some of its properties are discussed. A member of the Weibull-X family, the Weibull-logistic distribution, is defined and studied. Various properties of the Weibulllogistic distribution are obtained. The distribution is found to be unimodal and the...

In this article we derive the recurrence relations for the single and product moments based on progressively Type-II right-censored order statistics for the extended exponential (EE) distribution. The estimation of the model parameters under progressively Type-II right-censored order statistics are obtained...

In this paper some recurrence relations satisfied by single and product moments of generalized order statistics from Hjorth distribution have been obtained. Then we use these results to compute the first two moments of order statistics for some specific values of the parameters. Further, we use the results...

This paper proposes a moment-based approximation to the distribution of quadratic forms in gamma random variables. Quadratic forms in order statistics from an exponential population are considered as well. Actually,several test statistics can be expressed in terms of the latter. The density approximants...

The paper opens up a new aging class and a new stochastic orders which is depend on risk class, that plays vital role in the reliability theory, finance topics, stochastic orders, and the economic theory. The article presents some new interesting implications and characterizations concerning this class....

In certain experimental investigations involving discrete distributions external factors may induce measurement error in the form of misclassification. For instance, a situation may arise where certain values are erroneously reported; such a situation termed as modified or misclassified has been studied...

This article deals with the problem of estimating the parameters of the two-parameter exponential lifetime distribution based on Type-II hybrid censored samples from the Bayesian viewpoint. The scale and location parameters are assumed to have exponential and uniform priors respectively. Bayes point...

In this paper, the moment-based, maximum likelihood and Bayes estimators for the unknown parameter of the Lindley model based on Type II censored data are discussed. The expectation maximization (EM) algorithm and direct maximization methods are used to obtained the maximum likelihood estimator (MLE)....

Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. This paper deals with the...

We study a one-unit repairable system, supported by two identical spare units on cold standby, and serviced by two types of repairers. The model applies, for instance, to ANSI (American National Standard Institute) centrifugal pumps in a chemical plant, and hydraulic systems in aviation industry. The...

In analyzing most correlated outcomes, the popular multivariate Gaussian distribution is very restrictive and therefore dependence modeling using copulas is nowadays very common to take into account the association among mixed outcomes. In this paper, we use Gaussian copula to construct a joint distribution...

The Marshall-Olkin extended uniform distribution is introduced and studied by Jose and Krishna (2011). In this paper some moments properties of generalized order statistics (gos) for this distribution are investigated and results are deduced for order statistics and record values. In the last section,...

In this study, we propose a simple robust test for the mean of an exponential distribution by using the simplified version of “Forward Search” (FS) method. The FS method is a powerful general method for identifying outliers and their effects on inferences about the hypothesized model. The simulation...

In this paper some generalized exponential-type chain estimators have been proposed for the finite population mean in the presence of nonresponse under stratified two-phase sampling when mean of another auxiliary variable is readily available. The expressions for the bias and mean square error of proposed...

The concept of system signature is widely used for comparing of mixed (coherent) systems. In practical situa- tions, it is usually impossible to compare mixed systems. To do this, some partial orders are considered in the literature. In this paper, we define a new concept of stochastic order for comparing...

For analyzing longitudinal ordinal response data, many methods are available to take into account the correlations between responses of the same individual where different methods use different approaches. One of the methods to consider this correlation is the transition (Markov) model. In this paper,...

This paper considers the problem of estimating a variable mean for a population of elements where data are only available as aggregate sums for groups of multiple elements. The proposed model addresses an additional complication created when the group measure includes the contribution of diverse elements...

The foundations of statistics have evolved over many centuries, perhaps millennia, with major paradigm shifts of the form described in Kuhn (1962). We briefly consider these important transitions and how they have led to major shifts in the foundations of statistical inference. Clearly there is no conventional...

The distribution theory and applications of concomitants from the Morgenstern family of bivariate distributions are discussed in Scaria and Nair, Biom. J. 41 (1999), 483–489. In the present study, some dependence concepts of concomitants of order statistics from the Morgenstern family are discussed....

We show that the Fisher information matrix of the Birnbaum–Saunders distribution can present numerical problems for some values of the shape parameter. To overcome this problem, we provide a simple analytical approximation which works very well.

In this paper, the maximum likelihood estimates (MLE's) of the parameters of a finite mixture of modified Weibull (MW (alpha, beta, gamma)) distributions are obtained based on type-I and type-II censored samples using the EM algorithm. A simulation study is carried out to study the behavior of the mean...

The output of an engineering process is the result of several inputs, which may be homogeneous or heterogeneous and to study them, we need a model which should be flexible enough to summarize efficiently the nature of such processes. As compared to simple models, mixture models of underlying lifetime...

Recently, Mahmoudi and Mahmoodian [7] introduced a new class of distributions which contains univariate normal–geometric distribution as a special case. This class of distributions are very flexible and can be used quite effectively to analyze skewed data. In this paper we propose a new bivariate distribution...

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this paper, we derive the bivariate and multivariate weighted Kumaraswamy distributions via the construction method as discussed in...

In this article, we consider a measure of inaccuracy between distributions of the i-th order statistics and parent random variable. It is shown that the inaccuracy measure characterizes the distribution function of parent random variable uniquely. We also discuss some properties of the proposed measure.

Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators...

Some distributional properties of Levy distribution are presented. Limiting distributions of the extreme order statistics are given. Based on the distributional properties a characterization of the Levy distribution is shown.

The representations of record ranges via sums of independent identically distributed exponential random variables are obtained for asymmetrical Laplace distributions. This result generalizes the corresponding relations for record values in the cases of exponential and negative exponential distributions

In this study, we have discussed various statistical properties for 3-component mixture of Rayleigh distributions. Here initially, the main properties of mixture distributions are presented and analyzed. Second, some of the famous entropies, measures of inequality are also discussed. Also, the statistical...

Several distributional properties of semicircular distribution are presented. The limiting distributions of the standardized extreme order statistics are given. Some characterizations of the distribution are shown.

There are multiple tests of homogeneity of binomial proportions in the statistics literature. However, when working with sparse data, most test procedures may fail to perform well. In this article we review nine classical and recent testing procedures, including the standard Pearson and likelihood ratio...

To find the change point of a normal process monitored by an X control chart, the first and most important step is to find a good estimate of the change point. Different from all the previous studies in which the MLE of the change point is computed from a conditional likelihood function given the signal...

The strength-reliability of equipment is defined as the probability that the strength of the equipment exceeds its stress. Augmentation of strength-reliability of equipments gives better service protection and longevity. In this paper, the concept of Augmentation Strategy Plan (ASP) is introduced under...

Two important papers of Worsley, Siegmund and coworkers consider rotation and scale space random fields for detecting signals in fMRI (functional magnetic resonance imaging) brain images. They use the global maxima of images for detection of a signal. In the current work, we utilize a reproducing kernel...

A class of estimator based on dual to ratio and dual to product-type estimator in double sampling for estimating finite population mean is proposed. The bias and mean square error of the proposed estimator are obtained in two different cases. A comparative study has been made with usual estimators, dual...

This study investigates the simultaneous optimization of multiple correlated responses that involve mixed ordinal and continuous responses. The proposed approach is applicable for responses that have either an all ordinal categorical form are continuous but have different marginal distributions, or when...

For square contingency tables with ordered categories, there would be some situations that one would like to analyze them by using collapsed 3×3 tables combining some adjacent categories in the original table. This paper considers the marginal homogeneity for collapsed tables and proposes a measure which...

We introduce a new three-parameter extension of the exponential distribution called the odd exponentiated half-logistic exponential distribution. Various of its properties including quantile and generating functions, ordinary and incomplete moments, mean residual life, mean inactivity time and some characterizations...

The effect of heterogeneity on order statistics has attracted much attention in recent decades. In this paper, first, we discuss stochastic comparisons of extreme order statistics from independent heterogeneous exponentiated scale samples. These comparisons are made with respect to usual stochastic,...

RNA-seq technology has been widely used as an alternative approach to traditional microarrays in transcript analysis. Sometimes gene expression by sequencing, which generates RNA-seq data set, may have missing read counts. These missing values can adversely affect downstream analyses. Most of the methods...

If we know the statistics of central tendency and dispersion, we still cannot nature a complete design about the distribution. About these measures we should know more information's of skewness and kurtosis, which are enables us to have a design the distribution. However, there is evidence that...

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions...

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions....

We consider the purely sequential procedure for estimating the scale parameter of a gamma distribution with known shape parameter, when the risk function is bounded by the known preassigned number. In this paper, we provide asymptotic formulas for the expectation of the total sample size. Also, we propose...

The log-logistic distribution (also known as the Fisk distribution in economics) is widely used in survival analysis when the failure rate function presents a unimodal shape. In this paper, we introduce the Zografos- Balakrishnan log-logistic distribution, which contains the log-logistic distribution...

This paper proposes a new flexible four-parameter model called Marshall–Olkin power generalized Weibull (MOPGW) distribution which provides symmetrical, reversed-J shaped, left-skewed and right-skewed densities, and bathtub, unimodal, increasing, constant, decreasing, J shaped, and reversed-J shaped...

In this paper, a new class of distributions called the odd log-logistic Burr-X family with two extra positive parameters is introduced and studied. The new generator extends the odd log-logistic and Burr X distributions among several other well-known distributions. We provide some mathematical properties...

Explicit expressions for the densities of S = X1 + X2 , D = X1 − X2 , P = X1X2 and R = X1/X2 are derived when X1 and X2 are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in...

Reinforced balanced incomplete block designs (BIBDs) are very useful in statistical planning of experiments as they can be constructed for any number of treatments for given numbers of replications. Das (1958) was first to introduce the statistical analysis of variance (ANOVA) of these designs, and in...

For square contingency tables with ordered categories, the present paper proposes an asymmetry model with m-additional parameters, which indicates (1) the generalized marginal homogeneity and (2) the structure of quasi-symmetry for cumulative probabilities. The proposed model includes a modified palindromic...

This paper is concerned with using the E-Bayesian method for computing estimates for the parameter and reliability function of the Exponential distribution based on a set of upper record statistics values. The estimates are derived based on a conjugate prior for the scale parameter and squared error...

This article deals with using E-Bayesian method under progressively type-II censored sample from the Rayleigh distribution (RD) for computing the estimates of the parameter. The Bayesian and E-Bayesian estimators are obtained under squared error and LINEX loss functions. A comparison between E-Bayesian...

In this paper probability density function of single concomitant and joint probability density function of two concomitants of dual generalized order statistics from bivariate Burr III distribution are obtained and expressions for single and product moments are derived. Further, results are deduced for...

A new test statistic is proposed to test the equality of two normal means when the data is partially paired and partially unpaired. The test statistic is based on a linear combination of the differences of both paired and unpaired sample means. Using t-distribution as the approximate null distribution,...

Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of items under use condition follows the modified Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are...

The presence of the multicollinearity problem in the predictor data causes the variance of the ordinary linear regression coefficients to be increased so that the prediction power of the model not to be satisfied and sometimes unacceptable results be predicted. The ridge regression has been proposed...

A semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability alpha1. It is also assumed that the failure...

The presence of outliers, skewness, kurtosis, and dependency are well-known challenges while fitting distributions to many data sets. Developing multivariate distributions that can properly accomodate all these aspects has been the aim of several researchers. In this regard, we introduce here a new multivariate...

The Marshall–Olkin Extended Exponential distribution is introduced and reliability properties are studied. The p.d.f.’s of nth record value, joint p.d.f.’s, of mth and nth record values are derived to obtain the expression for mean, variance and covariance of reord values. The entropy of jth record value...

Ranked set sampling (RSS) is applicable whenever ranking of a set of sampling units can be done easily by a judgment method or based on the measurement of an auxiliary variable which can be measured easily. In this work, a modification of RSS called ordered extreme ranked set sampling is considered for...

The Kumaraswamy InverseWeibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy InverseWeibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive...

The problems of comparing several exponential distributions based on type II censored samples are considered. Likelihood ratio tests (LRTs) for comparing several location parameters, comparing several scale parameters and for homogeneity of distributions are derived. The LRTs for all three problems are...

We consider six different estimators of residual heterogeneity in random-effects meta-regression, five estimators already known and implemented in the R package metaphor and one estimator not yet considered in random-effects meta-regression. In a numerical study, we investigate the properties of these...

In this paper, the exact and explicit expressions for single, product, and conditional moments for inverted Kumaraswamy distribution using dual generalized order statistics (dgos) are derived. Further, the expression for maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator...

In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three

In this paper, we establish some recurrence relations for marginal and joint moment generating functions of generalized order statistics from a new class of Pareto distributions. For a particular case these results verify the corresponding results of Athar et al. (2012).

The present investigation is an attempt to estimate the population mean on current occasion in two-phase successive (rotation) sampling over two occasions. Utilizing information on two auxiliary variables one chain-type estimator has been proposed to estimate the population mean on the current occasion....

For a continuous random variable X, M. Shakil, B.M.G. Kibria, J. Stat. Theory Appl. 9 (2010), 255–282, introduced a generalized Burr increasing, decreasing, and upside-down bathtub failure rate life-testing model. In this paper, we provide some characterizations of this life-testing model by truncated...

Considered is a linear ‘interactive’ model in the context of survey sampling. This situation arises when investigator and/or supervisor interventions are contemplated in the responses. An appropriate linear model is introduced to represent the response profile(s) arising out of each respondent-cum-investigator-cum-supervisor...

Marshall and Olkin [Biometrika199784641652] introduced a method for constructing a new distribution by adding a new parameter, called tilt parameter, to a parent distribution. It is observed that adding this parameter leads to a more flexible model than the parent model. In this paper, different estimators...

Doubly truncated data are sometimes encountered in several applications, mainly in survival and astronomical data analysis. This occurs when the data falls between two points. In this study, we focus on the Shannon entropy measure of doubly truncated random variables. We propose ordering and various...

We introduce a new generalization of Weibull distribution by making use of a transformation of the standard two- sided power distributed random variable. Weibull and the exponentiated Weibull distributions are submodels of this new distribution.We show that this newly defined distribution is in fact...

In this paper, we discuss the optimal accelerated life test plans for Burr type X distribution with log-linear model under periodic inspection and Type I censoring. We obtain the maximum likelihood estimators, the Fisher information and the asymptotic covariance matrix of the maximum likelihood estimators....

In this paper we have tried to present an alternative approach for two discrete distributions such as Binomial and Multinomial with a new concept of sampling having a more general form apart from the traditional methods of sampling. The existing distributions may be obtained as a special case of our...

An extended version of exponential distribution is considered in this paper. This lifetime distribution has increasing, decreasing and constant hazard rates. So it can be considered as another useful two-parameter extension/generalization of the exponential distribution. It can be used as an alternative...

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the...

Here we develop an order k version of the alpha-logarithmic series distribution of Kumar and Riyaz (South African Statist. J., 2014) through its probability generating function and derive its probability mass function, mean and variance. The parameters of the model are estimated by the method of maximum...