Approximations to Risk Theory's F(x,t) by Means of the Gamma Distribution

It seems that there are people who are prepared to accept what the numerical analyst would regard as a shockingly poor approximation to F(x, t), the distribution function of aggregate claims in the interval of time (o, t), provided it can be quickly produced on a desk or pocket computer with the use of standard statistical tables. The so-called NP (Normal Power) approximation has acquired an undeserved reputation for accuracy among the various possibilities and we propose to show why it should be abandoned in favor of a simple gamma function approximation.