On Two-Piece Double Exponential Distribution

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).