Marginal Laplace and Linnik Processes

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.

Kozubowski et al. (2005) introduced and studied a class of multivariate distributions called operator geometric stable (OGS) laws by generalizing operator stable and geometric stable laws and as a special case they studied marginal Laplace and Linnik (MLL) distributions. In this paper, corresponding to MLL distributions time series models with autoregressive structure is developed and some properties of the process are discussed.