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.Ranked set sampling, bivariate Pareto distribution, best linear unbiased estimator,

Estimation of parameter of Morgenstern type bivariate exponential distribution using concomitants of order statistics

“…Concomitants of order statistics appear naturally in the estimation of correlation and regression coefficients in a variety of situations, most importantly in censored bivariate samples where the censoring is practiced on the basis of X values. They also play an important role in ranked set sampling (see [7,8]), double sampling and in certain selection procedures. For a detailed review of work on concomitants of order statistics see, [11].…”

A flexible ranked set sampling schemes: Statistical analysis on scale parameter

“…The same results were obtained by [12] by considering errors in judgment ranking. Some results of parametric RSS were presented by [22], [15], and [8]. The RSS scheme has been developed into various procedures.…”

Aggregation and Capital Allocation Formulas for Bivariate Distributions

“…We consider 18 families of bivariate distributions each defined on (0, ∞) × (0, ∞) or (β, ∞) × (β, ∞) for some β > 0. They include mixtures of independent exponential distributions, Crovelli [12] bivariate exponential distribution, Lawrance and Lewis' [17] bivariate exponential distribution, Block and Basu [5] bivariate exponential distribution, Arnold and Strauss [1] bivariate exponential distribution, Becker and Roux [4] bivariate gamma distribution, Cheriyan [7] bivariate gamma distribution, bivariate Liouville distributions, bivariate equilibrium distributions due to Unnikrishnan Nair and Sankaran [22], Chacko and Thomas [6] bivariate Pareto distribution, bivariate Pareto distribution in Eq. (10.68) of Balakrishnan and Lai [2], bivariate Pareto distribution with equal scale parameters, generalized bivariate Pareto distribution, Lee and Cha [18] bivariate distribution and truncated bivariate normal distribution.…”