Abstract
In the present communication, based on two extensions of Shannon entropy cumulative entropy by Rao, et al, 2004 and Kerridge’s inaccuarcy by Kerridge, (1961), we study and obtain some properties of weighted cumulative residual (past) inaccuracy for truncated random variables. Several properties, including monotonicity, bounds and their connections to proportional (reversed) hazard model are obtained for left, right and doubly truncated random variables.
Highlights
In order to modelling the best probability density function based on the data given via information theory, many researchers have been introduced and studied some measures
We study characterization problem for the proposed measures (6) and (7) under the proportional hazard model (PHM) and proportional reversed hazard model (PRHM)
The following theorem describes the relationship between interval Shannon entropy and the interval weighted cumulative residual entropy and we prove that the weighted interval cumulative residual inaccuracy (WICRI) is exponentially larger than interval Shannon entropy
Summary
In order to modelling the best probability density (mass) function based on the data given via information theory, many researchers have been introduced and studied some measures. Nath (1968) extended this measure to the case of continuous lifetime random variables by, Characterizations and extentions of the inaccuracy measure of form (2) have been obtained by many authors such as, Nair and Gupta (2007), Taneja et al (2009), Kumar et al (2011) and Kundu and Nanda (2015). Taneja and Tuteja (1986), defined the weighted inaccuracy measure n
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