The Normal-Laplace Distribution and its Relatives
نویسنده
چکیده
The normal-Laplace (NL) distribution results from convolving independent normally distributed and Laplace distributed components. It is the distribution of the stopped state of a Brownian motion with normally distributed starting value if the stopping hazard rate is constant. Properties of the NL distribution discussed in the article include its shape and tail behaviour (fatter than the normal), its moments and its infinitely divisibility. The double Pareto-lognormal distribution is that of an exponentiated normal-Laplace random variable and provides a useful parametric form for modelling size distributions. The generalized normal-Laplace (GNL) distribution is both infinitely divisible and closed under summation. It is possible to construct a Lévy process whose increments follow the GNL distribution. Such a Lévy motion can be used to model the movement of the logarithmic price of a financial asset. An option pricing formula is derived for such an asset.
منابع مشابه
Asymmetric Uniform-Laplace Distribution: Properties and Applications
‎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 es...
متن کاملGeneralized Birnbaum-Saunders Distribution
The two-parameter Birnbaum–Saunders (BS) distribution was originally proposed as a failure time distribution for fatigue failure caused under cyclic loading. BS model is a positively skewed statistical distribution which has received great attention in recent decades. Several extensions of this distribution with various degrees of skewness, kurtosis and modality are considered. In particular, a...
متن کاملA New Modification in the Classical Laplace Distribution
‎Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day‎. ‎In this paper‎, ‎we introduce a modified symmetric version of the classical Laplace distribution‎. ‎We provide a comprehensive theoretical description of this distribution‎. ‎In particular‎, ‎we derive the formulas for th...
متن کاملAdmissible Estimators of ?r in the Gamma Distribution with Truncated Parameter Space
In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.
متن کاملOn the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
متن کامل