On a muted family of bivariate distributions

This paper introduces 'muted bivariate distribution (MBD)' as a new family of bivariate distributions possessing the property (P) that the concomitant of nth record value on one variable arising from any distribution of this family is distributed identically as the largest order statistic of a sample of size n arising from the marginal distribution of the same variable. Also if the property P is observed on any distribution, then we illustrate a process of impounding the probability density function (pdf) of the nth record value on one variable resulting due to P with the known form of the marginal pdf on the other variable to build up an appropriate MBD of the parent population. Some properties of the newly defined MBD are further derived. We identify the forms of the pdf of the concomitant of generalized upper record value and the pdf of the concomitant of the smallest order statistic of a sample of size n in order that each of the above pdf s again can be used to generate MBD of the parent population, alternatively. We further observe MBD as a suitable model for describing an astronomical bivariate dataset relating to the galaxy luminosity measurements made under two conditions on globular clusters. For illustrative purposes, a real-life dataset on acacia trees obtained via concomitant record ranked set sampling methodology is considered as an application of this new family of bivariate distributions. (C) 2018 Elsevier Inc. All rights reserved.