Characterizations of the Pareto and related distributions

Some Characterization and Relations Based on K-th Lower Record Values

“…For the sufficiency part, we have from (16) and 17 Differentiating both sides in (18) with respect to y and substituting (19), we have hence, the theorem is proved.…”

“…Many authors have considered characterization of distributions through conditional expectation of record values, for instance, Nagaraja [4], Franco and Ruiz [5,6], Khan and Alzaid [7], Khan, Faizan, and Haque [8], and Lopez-Blazques and Moreno-Rebollo [9]. For more information in the theory of records and its distributional properties and some characterizations of k-th record values can be found in, for example, Ahsanullah [10,11], Arnold, Balakrishnan, and Nagaraja [12], Nevzorov [13], Deheuvels [14], Nagaraja [15], Raqab and Awad [16] and references therein.…”

Some Characterizations Based on Entropy of Order Statistics and Record Values

“…Several authors have studied the subject of characterization of F based on properties of order statistics and record values. We mention the work of Raqab and Awad (2000) dealing with the generalized Pareto distribution, and that of Hofmann et al (2005) studied characterization of two classes of exponential families, by the property of Fisher information in minima and upper record values. Park and Zheng (2004) derived a necessary and sufficient condition under which two distributions have equal Fisher information in any order statistics.…”

Characterization of the power distribution based on the lower records

“…We will just confine our attention to lower record values. Many authors have studied characterization of records values from different kind of distributions; for example,Ahsanullah [1], Kamps [9], Balakrishnan and Chan [7], Balakrishnan and Ahsanullah [6], Pawlas and Szynal [8], Raqab and Awad [5], Raqab [4], and AlZaid and Ahsanullah [2].…”