In this paper, we study the Exponential-Gamma distribution obtained by the convolution of independent Exponential and Gamma random variables. First order autoregressive model with Exponential-Gamma distribution as stationary marginal distribution is developed and properties of the process are studied. As a generalization, Generalized Exponential-Gamma distribution, Geometric Exponential-Gamma distribution and Geometric Generalized Exponential-Gamma distribution are introduced and studied and the corresponding time series models are developed. An extension to higher order is also given. Exponential-Mittag-Leffler distribution and processes is introduced.

autoregressive process, convolution, exponential distribution, Gamma distribution, linear combination of random variables, Mittag-Leffler distribution.