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We consider the random variable $Z_{n,\alpha}=Y_1+2^\alpha Y_2 +\ldots + n^\alpha Y_n$, with $\alpha\in\mathbb{R}$ and $Y_1,Y_2,\ldots$ independent and exponentially distributed random variables with mean one. The distribution function of $Z_{n,\alpha}$ is in terms of a series with alternating signs, causing great numerical difficulties. Using an extended version of the saddle point method, we derive a uniform asymptotic expansion for $\mathbb{P}(Z_{n,\alpha}

We consider the random variable $Z_{n,\alpha}=Y_1+2^\alpha Y_2 +\ldots + n^\alpha Y_n$, with $\alpha\in\mathbb{R}$ and $Y_1,Y_2,\ldots$ independent and exponentially distributed random variables with mean one. The distribution function of $Z_{n,\alpha}$ is in terms of a series with alternating signs, causing great numerical difficulties. Using an extended version of the saddle point method, we derive a uniform asymptotic expansion for $\mathbb{P}(Z_{n,\alpha}

We investigate mathematical tools, Edgeworth series expansion and the saddle point method, which are approximation techniques that help us to estimate the distribution function for the standardized mean of independent identical distributed random variables where we will take into consideration the lattice case. Later on we will describe one important application for these mathematical tools where game developing companies can use them to reduce the amount of time needed to satisfy their standard requests before they approve any game

We investigate mathematical tools, Edgeworth series expansion and the saddle point method, which are approximation techniques that help us to estimate the distribution function for the standardized mean of independent identical distributed random variables where we will take into consideration the lattice case. Later on we will describe one important application for these mathematical tools where game developing companies can use them to reduce the amount of time needed to satisfy their standard requests before they approve any game