Stochastic Comparisons of Residual Entropy of Order Statistics and Some Characterization Results

Abstract

In this paper, we have presented some results for the residual and past entropies of order statistics. Results on the stochastic comparisons based on residual entropy of order statistics are presented. Characterization results for these dynamic entropies based on the sufficient condition for the uniqueness of the solution of an initial value problem have been considered.

Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons

“…Several authors have studied the stochastic comparisons. For example, Ebrahimi and Kirmani (1996), Raqab and Amin (1996), Kochar (1999), Abbasnejad and Argami (2011), Di Crescenzo and Longobardi (2013), Psarrakos and Navarro (2013), Gupta et al (2014). We continue this line of researches by exploring some properties of stochastic comparisons based on Tsallis entropy of order statistics.…”

“…Abbasnejad and Arghami (2011) provided some bounds for Renyi entropy of order statistics. Gupta et al (2014), derived the upper bounds for residual entropy. In this section, we derive upper and lower bounds for Tsallis entropy of order statistics.…”

Probabilistic mean value theorems for conditioned random variables with applications

“…for any > 0. Condition (25) is equivalent to the following relation for the distribution function of X( ):…”

“…Theorem 5. Let {X( ); > 0} be a family of absolutely continuous random variables having support (0, r), with 0 < r ≤ ∞, and satisfying the proportional reversed hazards model as indicated in Equations (25) and (26). Let Z be a random variable with conditional PDF for t ∈ (0, r), with 0 < 1 < 2 .…”

“…In analogy with Theorem 3.2 in the work of Gupta et al, 25 in the following theorem, we show that the results of Section 2 are useful to compare the residual entropies of random lifetimes. We recall that a random lifetime Y is said to be 'decreasing failure rate' (DFR) if Y (t) is decreasing in t or, equivalently, if F Y (t) is logconvex.…”