Nearly Gaussian Distributions and Application

Abstract

We consider the random variable X that is not Gaussian but for which X ^c , where c = (2k + 1)/(2j + 1) with k, j ∊ {0, 1,…}, is approximately Gaussian. A variable of this type is used to model the errors made by meteorologists when forecasting temperatures.

Keywords:

• Goodness of fit
• Kurtosis
• Meteorology
• Power transformation

Mathematics Subject Classification:

• Primary 62E17
• Secondary 62P30

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada. The author is grateful to the Associate Editor and the reviewers for pertinent and constructive comments. In particular, a reviewer provided the point estimates of the four parameters of the DPU distribution. Finally, thanks are also due to Serge Lefebvre for his help in performing the Kolmogorov–Smirnov tests with MATLAB.