Some Properties of Laplace Process

Laplace Process

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

Laplace process was introduced in Satheesh (1990) as a possible alternative to Wiener process. Here we discuss some properties of this process viz. correlation, martingales, finite dimensional distributions and sample paths. A review of the rich theoretical developments over Laplace process, driven by data, over the years is also given.