Abstract
For a system, which is observed at timet, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.
Highlights
The Morgenstern family discussed in [1] provides a flexible family that can be used in such contexts, which is specified by the distribution function and the probability density function, respectively, as follows: FX,Y (x, y) (1)
We will consider the characterization results based on the entropy function for concomitants of ordered random variables based on residual lifetime distribution and the past life distribution
We will use the last equations to obtain and study the residual and past entropy of concomitants for Morgenstern family based on the types of gos
Summary
The Morgenstern family discussed in [1] provides a flexible family that can be used in such contexts, which is specified by the distribution function (df) and the probability density function (pdf), respectively, as follows: FX,Y (x, y) (1). = fY (y) [1 + αC∗ (r, n, m, k) (2FY (y) − 1)] , Journal of Probability and Statistics and the pdf of the concomitant of case-I of dgos Yd[r,n,m,k], 1 ≤ r ≤ n, is given by Nayabuddin [8] as follows: gd[r,n,m,k] (y) (5). We will obtain and study the residual and past entropy of the Morgenstern family for concomitants of ordered random variables. We will consider the characterization results based on the entropy function for concomitants of ordered random variables based on residual lifetime distribution and the past life distribution.
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