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

Abstract

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.

Keywords

• generalized (k) record values
• record ranked set sampling
• induced generalized upper record ranked set sampling (igurrss)
• induced generalized lower record ranked set sampling
• concomitants of generalized record values
• morgenstern family of distributions
• morgenstern type bivariate logistic distribution
• best linear unbiased estimation
• modelling bivariate distribution by igurrss data