On order statistics from Laplace-type distributions. (English) Zbl 1437.62169

Aly, Emad-Eldin A. A.

Stat. Probab. Lett. 160, Article ID 108706, 10 p. (2020).

Summary: We obtain the probability density function (pdf) of a single order statistic (OS) and the joint pdf of two OS based on a random sample \(\{Z_i\}_{i = 1}^n\) from \(Z = U X - (1 - U) Y\), where \(U, X\) and \(Y\) are independent with \(U \sim B e r n o u l l i (\beta)\). We drive formulas for calculating the moments and the product moments of OS based on \(\{ Z_i\}_{i = 1}^n\). We apply the obtained results to the important class of Double distributions. This class includes the Double Exponential, the Double Logistic and the Double Pareto distributions.

MSC:

62G30	Order statistics; empirical distribution functions
62E15	Exact distribution theory in statistics
60E05	Probability distributions: general theory
62J12	Generalized linear models (logistic models)

Keywords:

random sign mixture transformation; moments and product moments of order statistics

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