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.
In this paper, we study Shannon's entropy and Fisher information number for concomitants of generalized order statistics from subfamilies of Farlie-Gumbel-Morgenstern when the marginal distributions are Weibull, exponential, Pareto and power function. Also, we provide some numerical results of Shannon entropy and Fisher information number for concomitants of order statistics.Mathematics Subject Classification 62B10 · 62H99 · 62P99
Extropy has been discussed in many works of literature as a complementary
dual of Shannon?s entropy function. In this paper, a replacement procedure
of uncertainty of random variable, constructed on the cumulative
distribution function F, called cumulative extropy is proposed. Some
properties and features of the deemed measure are obtained. Moreover, the
dynamic form of cumulative extropy is considered. Finally, non-parametric
estimators for the proposed measure are included.
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