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Applied Mathematics and Computation
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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.
Hamedani, Gholamhossein; Javanshiri, Z.; Maadooliat, Mehdi; and Yazdani, A., "Remarks on Characterizations of Malinowska and Szynal" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 226.
NOTICE: This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, VOL 246, November 1, 2014, PGS. 377-388. DOI. © 2014 Elsevier. Used with permission.