Beta Burr XII OR Five Parameter Beta Lomax Distribution: Remarks and Characterizations

The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated moments of certain functions of the random variable

Remarks on Characterizations of Malinowska and Szynal

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Malinowska and Szynal (2008) for certain general classes of distributions are revisited and simpler proofs of them are presented. These characterizations are not based on conditional expectation of the kth lower record values (as in Malinowska and Szynal), they are based on: (i) simple truncated moments of the random variable, (ii) hazard function