In this paper, we introduce two new flexible families of unimodal circular distributions obtained by wrapping onto the unit circle two recently explored heavytailed distributions defined on the real line. The first, the four-parameter wrapped normal–Laplace distribution, is nested within the second, the five-parameter wrapped generalized normal–Laplace distribution. Both families contain the wr...

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails often observed in practical data, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. ...

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties ...

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investiga...

We consider deconvolution problems where the observations are equal in distribution to Here the random variables in the sums are independent, the E i are exponentially distributed, the L i are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants i or i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion ...

In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace tran...

From a suitable integral representation of the Laplace transform of a positive semi–definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furth...

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Lapla...

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.