Single Moments Of Order Statistics Research Articles

On the theory of order statistics of the flexible Lomax distribution

This paper studies the flexible Lomax distribution’s order statistics with graphical and numerical findings. Along with the quantitative measurements, some plots are furnished, including those for the skewness and kurtosis measures. We will dwell on the numerous results that relate to statistics of moments of order. We consider the single and product moment of order statistics from the new distribution. Further, we establish some recurrence relation for single moments of order statistics. We have sought to apply the derived relations to empirically evaluate the moments of smallest (largest) order statistics to establish well-known moments and related measures. For order statistics of a flexible Lomax distribution, exact analytical expressions of entropy, residual entropy, and past latent entropy are determined.

Exact Moments of Order Statistics and Parameter Estimation for Sushila Distribution

In this paper, we have obtained the exact expression and recurrence relations for single moments of order statistics arising from Sushila distribution. We have also obtained L-moments, TL-moments of Sushila distribution and used them to find the L-moment and TL-moment estimators of the parameters of the distribution. The estimators of the parameters are also obtained using the method of moments and maximum likelihood. Further, by using these maximum likelihood estimators (MLEs), we have also obtained the MLEs of the measures of reliability of the considered distribution. Monte Carlo simulation has been carried out to investigate the performance of the estimators.

Moments of order statistics from DNID discrete random variables with application in reliability

In this paper, we present methods of obtaining single moments of order statistics arising from possibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical evaluation of such moments. To demonstrate their use, we tabulate means and second moments of order statistics from random vectors having some typical discrete distributions with selected parameter values. Next, we apply our results in reliability theory. We establish moments of discrete lifetimes of coherent systems consisting of heterogeneous and not necessarily independently working components. In particular, we obtain expression for expectations and variances of lifetimes of such systems. We give some illustrative examples.

Order Statistics Properties of the Two Parameter Lomax Distribution

In this paper we study the distribution of order statistics of the two parametric Lomax distribution. We consider the single and product moment of order statistics from Lomax distribution. Also, we establish some recurrence relation for single moments of order statistics. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Lomax distribution is derived.

A rank test based on the moments of order statistics of the modified Makeham distribution

Single moments of order statistics from the modified Makeham distribution (MMD) are derived, an identity about the single moments of order statistics is given, and the specific expected value and variance of the single moments of order statistics from the MMD are calculated. In this study, the order statistic from the MMD was applied to the rank sum test in a two-sample problem. The exact critical values of the designated statistics were evaluated. Simulations were used to investigate the power of these statistics for the two-sided alternative with several population distributions. The powers of the statistics were compared with the Wilcoxon rank sum statistic, the Lepage statistic, the modified Baumgartner statistic, the Savage test and the normal score test. The Edgeworth expansion was used to evaluate the upper tail probability for the preferred statistic, given finite sample sizes.

Nonparametric Bayesian estimation on the exponentiated inverse Weibull distribution with record values

Abstract The inverse Weibull distribution (IWD) is the complementary Weibull distributionand plays an important role in many application areas. In Bayesian analysis, Soland’smethod can be considered to avoid computational complexities. One limitation of thisapproach is that parameters of interest are restricted to a nite number of values. Thispaper introduce nonparametric Bayesian estimator in the context of record statisticsvalues from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland’sconjugate piror, stick-breaking prior is considered and the corresponding Bayesian esti-mators under the squared error loss function (quadratic loss) and LINEX loss functionare obtained and compared with other estimators. The results may be of interest espe-cially when only record values are stored.Keywords: Exponentiated inverse Weibull distribution, nonparametric Bayesian esti-mation, record statistics, stick-breaking prior. 1. Introduction The inverse Weibull distribution (IWD) is the complementary Weibull distribution andplays an important role in many applications including the dynamic components of dieselengines, the times to breakdown of an insulating uid subject to the action of constanttensioin and ood data (Nelson, 1982; Maswadah, 2003). Also, it has been used quite exten-sively when the data indicate a monotone hazard function beacuse of the exibility of thepdf and its corresponding hazard function. Studies for the inverse Weibull distribution wereconducted by many authors. Calabria and Pulcini (1994) studied Bayes 2-sample predictionfor the inverse Weibull distribution. Mahmoud et al. (2003) considered the order statisticsarising from the inverse Weibull distribution and derived the exact expression for the singlemoments of order statistics. They also obtained the variances and covariances based on themoments of order statistics.

Computing the moments of order statistics from nonidentically distributed phase-type random variables

In this paper, we derive a recurrence relation for the single moments of order statistics (o.s.) arising from n independent nonidentically distributed phase-type (PH) random variables (r.v.’s). This recurrence relation will enable one to compute all single moments of all o.s. in a simple recursive manner.

Moments of order statistics of Topp–Leone distribution

We derive explicit algebraic expressions for both of the single and product moments of order statistics from Topp–Leone distribution. We also give an identity about single moments of order statistics. These expressions will be useful for computational purposes.

Some General Identities among Single Moments of Order Statistics

Some General Identities among Single Moments of Order Statistics

Relations for order statistics from non-identical logistic random variables and assessment of the effect of multiple outliers on the bias of linear estimators

In this paper, we establish some relations for the single moments of order statistics arising from n independent and non-identically distributed logistic random variables. These relations are then used to deduce a set of recurrence relations for the moments of order statistics from the multiple-outlier logistic model (with a slippage of p observations). The moments of order statistics from the p-outlier model are expressed in terms of the corresponding quantities from ( p - 1 ) -outlier and ( p - 2 ) -outlier models. We then use these recurrence relations along with the corresponding i.i.d. results originally derived by Shah [1970. Note on moments of a logistic order statistics, Ann. Math. Statist. 41, 2151–2152.] and the results for the single outlier model discussed by Balakrishnan [1992a. Relationships between single moments of order statistics from non-identically distributed variables. In: Sen, P.K., Salama, I.A. (Eds.), Order Statistics and Nonparametrics: Theory and Applications. Elsevier, Amsterdam, pp. 65–78.] to compute the bias of various linear estimators of the location and scale parameters of the logistic distribution in the presence of multiple outliers.

Order statistics from inverse weibull distribution and associated inference

Order statistics arising from inverse Weibull (IW) distribution are considered. Exact expression for the single moments of order statistics are derived. Also, the variances and covariances are calculated. Based on the moments of order statistics, the best linear unbiased estimates (BLUEs) for the location and scale parameters of IW distribution are obtained. In addition, these BLUEs are applied to draw inferences for the location and scale parameters of the underlying model. To show the usefulness of our results a simulation study is carried out.

Some New Identities for Single Moments of Order Statistics

In this paper we derive some new identities among cumulative distribution functions and moments of order statistics and use them to obtain some new combinatorial identities.

Two identities involving order statistics in the presence of an outlier

In this note, we derive two simple identities involving order statistics from a sample of size n in the presence of an outlier. These generalize the results of Joshi (1973). These identities will be quite useful in checking the computation of the single moments of order statistics from an outlier model.

Recurrence relations between moments of order statistics

AbstractA general result for obtaining recurrence relations between single moments of order statistics is obtained and has been used to establish the recurrence relations between moments of some doubly truncated distributions. The examples considered are Weibull, exponential, Pareto, power function, Cauchy, and logistic. Recurrence relations are also obtained for nontruncated gamma and beta distributions.

A note on order statistics from Weibull distribution

Summary We establish a recurrence relation for the moments of order statistics from a two-parameter Weibull distribution. This enables us to obtain all the single moments of order statistics for which exact and explicit expressions are given by Lieblein (1955).