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Asymmetric uniform-Laplace distribution: properties and applications. (English) Zbl 1412.62024

Summary: The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution. We present a detailed theoretical description of this distribution. We try to estimate the parameters of AUL distribution using the maximum likelihood method. Since the likelihood approach results in complicated forms, we suggest a bootstrap-based approach for estimating the parameters. The proposed method is mainly based on the shape of the empirical density. We conduct a simulation study to assess the performance of the proposed procedure. We also fit the AUL distribution to real data sets: daily working time and Pontius data sets. The results show that AUL distribution is a more appropriate choice than the skew-normal, skew t, asymmetric Laplace and uniform-normal distributions.

MSC:

62E15 Exact distribution theory in statistics
62E10 Characterization and structure theory of statistical distributions
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