Error Bounds for Exponential Approximations of Geometric Convolutions
Error Bounds for Exponential Approximations of Geometric Convolutions
Define $Y_0$ to be a geometric convolution of $X$ if $Y_0$ is the sum of $N_0$ i.i.d. random variables distributed as $X$, where $N_0$ is geometrically distributed and independent of $X$. It is known that if $X$ is nonnegative with finite second moment, then as $p \rightarrow 0, Y_0/EY_0$ converges …