P. Yageen Thomas

A note on recurrence relations for the product moments of order statistics

In this work we provide simplified versions for some of the available recurrence relations on the product moments of order statistics.

Estimation of a Parameter of Bivariate Pareto Distribution by Ranked Set Sampling

Abstract Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we derive different estimators of a parameter associated with the distribution of the study variate Y, based on a ranked-set sample obtained by using an auxiliary variable X correlated with Y for ranking the sample units, when (X, Y) follows a bivariate Pareto distribution. Efficiency comparisons among these estimators are also made. Real-life data have been used to illustrate the application of the results obtained.

On an Application of Concomitants of Order Statistics in Characterizing a Family of Bivariate Distributions

In this article, we consider a family of bivariate distributions which includes the well-known Morgenstern family of bivariate distributions as its subclass. We identify some properties of concomitants of order statistics which characterize this generalized class of distributions. An application of the characterization result in modeling a bivariate distribution to a data is also explained.

Estimation of the Parameters of Triangular Distribution by Order Statistics

In this paper, we derive explicit expressions for the single and product moments of order statistics arising from the standard triangular distribution. Best linear unbiased estimators of the location and scale parameters of a triangular distribution based on order statistics are obtained. The efficiencies of these estimators are also compared with estimators based on U-statistics

Estimation of the Parameters of Type-I Generalized Logistic Distribution Using Order Statistics

In this work, we propose a technique of estimating the location parameter μ and scale parameter σ of Type-I generalized logistic distribution by U-statistics constructed by using best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to maximum likelihood estimators is also made.

Applications of Order Statistics of Independent Nonidentically Distributed Random Variables in Estimation

ABSTRACT Lloyds Best Linear Unbiased Estimators BLUEs of location and scale parameters of a distribution by order statistics is an extensively used method of estimation. In this article a method is proposed to estimate the common location and scale parameters of several distributions by order statistics. The method developed has been applied to estimate the common location and scale parameters of normal and double exponential distributions.

Estimation of the Scale Parameter of Generalized Exponential Distribution Using Order Statistics

In this paper we have developed an estimator for the scale parameter of generalized exponential distribution using an appropriate Ustatistic defined by the Best Linear Unbiased Estimator (BLUE) based on order statistics of a random sample of size 2 as the kernel. We have compared our estimator with the maximum likelihood estimator and an unbiased estimator based on sample mean.

Use of Spacings in the Estimation of Common Scale Parameter of Several Distributions

In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the common scale parameter of several distributions using spacing of the pooled sample of all observations of individual samples. We derived conditions for the non negativity of the scale estimator obtained by the above methods. Further, we obtained necessary and sufficient conditions for the derived estimators to be constant multiples of the pooled sample range.

On the moments of extremes from generalized gamma distribution

Two types of recurrence relations on the moments of the largest order statistic of a random sample of size n arising from the generalised gamma distribution are derived and their effective use in reducing the number of direct evaluation of tie integrals for the moments of order statistics arising from this distribution is pointed out.

Recurrence relations for moments of different orders of extremes from gamma distribution

Certain recurrence relations for the moments of different orders of the largest order statistic from a gamma distribution with shape parameter p are obtained. By using this it is shown that for obtaining the moment of any order of each order statistic of a sample of size n from the gamma distribution, one has to evaluate at most n-2 single integrals.