Abstract
Nassar (2016) considers an interesting univariate continuous distribution called Kumaraswamy-Laplace which has different forms on two subintervals. He studies certain properties and applications of this distribution. Shahbaz et al. (2016) consider another interesting distribution called McDonald Inverse Weibull distribution. They present some basic properties of their distribution and study the estimations of the parameters as well as discussing its application via an illustrative example. What is lacking in both papers, in our opinion, is the characterizations of these two interesting distributions. the present work is intended to complete, in some way, the works of Nassar and Shahbaz et al. via establishing certain characterizations of these distributions in four directions. We also introduce several New generalized Exponential distributions and present their characterizations as well.
Highlights
The problem of characterizing a distribution is an important problem which can help the investigator to see if their model is the correct one
This work deals with various characterizations of Kumaraswamy-Laplace (KL) and McDonald Inverse Weibull (MIW) distributions to complement the works of Nassar (2016) and Shahbaz et al (2016)
These characterizations are presented in three directions: (i) based on the ratio of two truncated moments; (ii) in terms of the reverse hazard function and (iii) based on the conditional expectation of certain functions of the random variable
Summary
The problem of characterizing a distribution is an important problem which can help the investigator to see if their model is the correct one. This work deals with various characterizations of Kumaraswamy-Laplace (KL) and McDonald Inverse Weibull (MIW) distributions to complement the works of Nassar (2016) and Shahbaz et al (2016). These characterizations are presented in three directions: (i) based on the ratio of two truncated moments; (ii) in terms of the reverse hazard function and (iii) based on the conditional expectation of certain functions of the random variable. The cdf and pdf of our second NGE distribution (denoted by NGE2) are given, respectively, by. The cdf and pdf of our third NGE distribution (denoted by NGE3) are given, respectively, by. Characterizations We present our characterizations (i) − (iv) in four subsections
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