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The beta Laplace distribution. (English) Zbl 1221.60011
Summary: The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set.

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