Induced Ranked Set Sampling when Units are Inducted from Several Populations

The method of ranked set sampling when units are to be inducted from several bivariate populations is introduced in this work. The best linear unbiased estimation of a common parameter of two bivariate Pareto distributions is discussed based on the n ranked set observations, when a sample of size n1 is drawn from a bivariate Pareto population with shape parameter a1 and a sample of size n2 is drawn from another bivariate Pareto with shape parameter a2 such that n=n1+n2. The application of the results of this paper is illustrated with a real life data

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.Recurrence relations for order statistics

On Induced Generalized Record Ranked Set Sampling and its Role in Bivariate Model Building

A new variety of Ranked Set Sampling (RSS), namely Induced Generalized Record Ranked Set Sampling (IGRRSS), is introduced. In the proposed methodology, ranking is implemented by considering generalized (k) record values on the auxiliary variable X from each sequence of units. The selected units are further screened for measuring the variable of primary interest Y. Further, we propose estimators based on IGRRSS for the unknown parameters associated with the variable Y when the parent bivariate distribution belongs to the Morgenstern family of distributions. The proposed sampling scheme is utilized to collect primary data on the usable timber volume Y based on the ranking of units by generalized (2) record values on tree height X of acacia trees. Accordingly, Morgenstern type bivariate logistic distribution has been modelled for the distribution of the population random vector (X, Y) and estimated the average usable timber volume of the population

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

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,

Characterizations of bivariate distributions by properties of concomitants of order statistics

In this paper, we consider a family of bivariate distributions which forms a generalization of the Morgenstern family of bivariate distributions. We have derived two characteristic properties of concomitants of order statistics which characterize this generalized class of distributions. Some important conclusions based on the characterization results are also drawn.

Estimation of parameters of bivariate normal distribution using concomitants of record values

Record values, Concomitants of record values, Best linear unbiased estimators, Bivariate normal distribution,