Characterizations of Certain Continuous Distributions
In designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will vitally depend on the characterizations of the selected distribution. The Amoroso, SSK (Shakil–Singh–Kibria), SKS (Shakil–Kibria–Singh), SK (Shakil–Kibria), and SKS-type distributions have been suggested to have potential applications in modeling and are characterized here based on either a simple relationship between two truncated moments or a truncated moment of a function of the first order statistic or of a function of the nth order statistic, the two more interesting order statistics. We also present a characterization of SKS-type distribution based on the conditional expectation of adjacent generalized order statistics.
- 7.Crooks GE (2010) The Amoroso distribution. arXiv:1005.3274v1 [math.ST]Google Scholar
- 8.Galambos J, Kotz S (1978) Characterizations of probability distributions. In: A unified approach with an emphasis on exponential and related models, Lecture Notes in Mathematics, vol 675. Springer, BerlinGoogle Scholar
- 9.Glänzel W (1987) A characterization theorem based on truncated moments and its application to some distribution families. Math Stat Probab Theor (bad Tatzmannsdorf, 1986):75–84Google Scholar
- 18.Johnson NI, Kotz S (1970) Distributions in statistics. Continuous univariate distributions, vols 1 and 2. Houghton Miffin Co., Boston, MassGoogle Scholar
- 19.Kamps U (1995) A concept of generalized order statistics. In: Teubner BG, Stuttgart Teubner Skripten zur Mathematischen Stochastik. [Teubner Texts on Mathematical Stochastics]Google Scholar
- 24.Shakil M, Kibria BM, Singh JN (2010) A new family of distributions based on the generalized Pearson differential equation with some applications. Austrian J Stat 39:259–278Google Scholar