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Moments of order statistics of the standard two-sided power distribution. (English) Zbl 1508.62130

Summary: The standard two-sided power distribution is a flexible distribution having uniform, power function and triangular as subdistributions, and it is a reasonable alternative to the Laplace distribution in some cases. In this work, computationally efficient expressions for moments of order statistics, expressions for L-moments, and asymptotic results for sample extrema are derived. Then a simulation study is performed for the location-scale estimation problem of a small data set by considering the maximum likelihood estimation method and the best linear unbiased estimation method based on the moments of order statistics.

MSC:

62G30 Order statistics; empirical distribution functions
60E05 Probability distributions: general theory
62E15 Exact distribution theory in statistics

Software:

LBFGS-B; LMOMENTS; R
PDFBibTeX XMLCite
Full Text: DOI

References:

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