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Ardalan, A.; Sadooghi-Alvandi, S. M.; Nematollahi, A. R.

The two-piece normal-Laplace distribution. (English) Zbl 1253.60011

Commun. Stat., Theory Methods 41, No. 19-20, 3759-3785 (2012).
Summary: This article considers the two-piece normal-Laplace (TPNL) distribution, a split skew distribution consisting of a normal part and a Laplace part. The distribution is indexed by three parameters, representing location, scale and shape. As illustrated by several examples, the TPNL family of distributions provides a useful alternative to other families of asymmetric distributions on the real line. However, because the likelihood function is not well behaved, the standard theory of maximum-likelihood (ML) estimation does not apply to the TPNL family. In particular, the likelihood function can have multiple local maxima. We provide a procedure for computing ML estimators, and prove consistency and asymptotic normality of ML estimators, using non standard methods.

Cited in 2 Documents

MSC:

60E05 Probability distributions: general theory
62F12 Asymptotic properties of parametric estimators

Keywords:

asymmetric distribution; asymptotic normality; consistency; maximum likelihood estimation; two-piece Laplace distribution; two-piece normal distribution

Software:

faraway
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Full Text: DOI

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