Morgenstern Family Of Distributions Research Articles

Extropy properties of ranked set sample when ranking is not perfect

In this article, extropy properties of the ranked set sample (RSS) when ranking is not perfect are considered. By deriving the expression for extropy of concomitant order statistic, the expression for extropy of RSS of the study variable Y in which an auxiliary variable X is used to rank the units in each set, under the assumption that ( X , Y ) follows Morgenstern family of distributions is obtained. The upper and lower bounds of extropy of RSS are obtained. The cumulative residual extropy of concomitant of order statistic and RSS arising from Morgenstern family of distributions are also obtained. The discrimination informations between the distribution of rth RSS statistic and the parent distribution are also obtained.

Concomitant record ranked set sampling

ABSTRACTIn this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.

Concomitants of k-record values arising from Morgenstern family of distributions and their applications in parameter estimation

In this paper, we have obtained the marginal and joint distributions of concomitants of k-record values for the Morgenstern family of distributions (MFD) and hence obtained the moments and product moments of concomitants of k-record values. Applying this results we have derived the best linear unbiased estimators of some parameters involved in Morgenstern type bivariate logistic distribution which belongs to MFD based on concomitants of k-record values.

Concomitants of Record Values Arising from Morgenstern Type Bivariate Logistic Distribution and Some of their Applications in Parameter Estimation

In this paper we have obtained the joint probability density function of concomitants of two record values and hence obtained an explicit expression for the product moment of concomitants of two record values arising from Morgenstern family of distributions. Appling this expression for the product moments of concomitants of record values we have derived the best linear unbiased estimators based on concomitants of record values of some parameters involved in Morgenstern type bivariate logistic distribution which is a subfamily of the Morgenstern family of distributions. The efficiencies of these estimators based on the first n concomitants of record values for n≤10 are also obtained.