Quantile-Based Entropy function in past lifetime for Order Statistics and its properties
Abstract
In this paper, we introduce a quantile version of past entropy for order statistics and study its properties.
It is shown that this measure uniquely determine the quantile function.
Also, we define two nonparametric classes of distribution based the proposed measure. The closure of these classes under increasing convex (concave) transformations and weighted variables are discussed. Moreover, a new stochastic order based this measure is defined and some features of it are investigated.
We give desirable conditions for a function of a random variable
to have more quantile past entropy for order statistics
than original random variable.
It is shown that this measure uniquely determine the quantile function.
Also, we define two nonparametric classes of distribution based the proposed measure. The closure of these classes under increasing convex (concave) transformations and weighted variables are discussed. Moreover, a new stochastic order based this measure is defined and some features of it are investigated.
We give desirable conditions for a function of a random variable
to have more quantile past entropy for order statistics
than original random variable.
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