Bounds on Extropy With Variational Distance Constraint

Abstract

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].

Uncertainty and negation—Information theoretic applications

“…The extropy is generally referred as the the complementary dual of the shannon entropy function given by and has many properties similar to the . More details can be seen in Yang et al and Lad et al…”

“…The probability distribution given by has been used by Yang et al and Lad et al for defining the extropy of a probability distribution which they referred as the location and the scale transform the probability distribution . The extropy is generally referred as the the complementary dual of the shannon entropy function given by and has many properties similar to the .…”

“…The extropy is generally referred as the the complementary dual of the shannon entropy function given by (2.2) and has many properties similar to the (2.5). More details can be seen in Yang et al 8 Having developed a valid measure of entropy for negation of a probability distribution, we will now propose a new measure of dissimilarity between negations of two probability distributions. Consider two probability distributions P p p p = ( , , …, )…”

On Cumulative Residual Extropy

“…Qiu and Jia [15] proposed two estimators for extropy and they developed a goodness-of-fit test for standard uniform distribution. Yang et al [28] studied the relations between extropy and variational distance and determined the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution. Qiu et al [16] explored an expression of the extropy of a mixed systems lifetime.…”

On Dynamic Survival Past Extropy Properties‎

“…The properties of this measure such as the maximum extropy distribution and statistical applications were presented in their work. Yang et al (2018) studied the relations between extropy and variational distance. They determined the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution.…”