The selection of the form of the transformation to normality from the Johnson system has proved to be confusing in many cases where nothing is known about the underlying distribution. In this paper we investigate how the choice made by the investigator of the Z-value in the Slifker and Shapiro (1980) procedure affects the form of the transformation given by the Slifker and Shapiro procedure. Our investigation centers around simulations of an exponential distribution.

The Pearson. deviance and Anscombe overall goodness of fit statistics for gamma regression are considered. Approximate moments of the null distributions of the statistics are given and used to develop various chi—square approximations for the percentiles. A detailed evaluation of the approximations is made for the case of a logarithmic link function.

This article gives a comparative study among several prediction intervals for the future sample mean. The observed sample, used in the techniques and the future sample for which the prediction intervals were established share the same underlying distribution. Two assumed underlying distributions were used. The first underlying distribution is the exponential with parameter θ. Five different intervals were set for the prediction of the future sample mean. The second underlying distribution is the normal with the parameter θ as the common value for the mean and the variance. Seven intervals were compared. A simulation validation was done. Some criteria were set for the “best” interval in both cases. Moreover, the merits of the techniques were given, and a table of results of the simulations is supplied.