On shift-dependent generalized entropies for doubly truncated random variable

Abstract

Recently, Das (2017) studied the importance of weighted generalized entropy for one sided truncation problems. There are some situations in survival study, where data are usually truncated from both sides. In such cases, individuals whose event-time lies within a certain time interval are only observed. The concept of first kind as well as second kind weighted doubly truncated generalized entropy measures is studied in this paper. It is showed that they characterize the distribution function uniquely. Further, the effect of monotone transformations on these measures is discussed. Uncertainty orders and its relation with the usual stochastic order are presented. Nonparametric class of lifetime distributions is introduced and some inequalities are obtained. Various examples are provided for illustration purpose.

Subject Classification:

• 62N05
• 90B25

Keywords:

• Weighted generalized entropy
• Doubly truncated random variable
• Usual stochastic order
• Monotone transformation
• Nonparametric class