A famiy of simple distribution functions to approximate complicted distributions

Abstract

For a general random variable with a continuous distribution function and known finite first four moments, a simple approach is proposed to find its approximate distribution having the correct first four moments. when applied to the classical Cramér-von Mises and Watson's statistics, the new method gives similar numerical results as the best known, but it is much simpler and can be directly used to obtain practical p-values of goodness-of-fit tests, instead of tabulating limited percentage points.

Keywords:

• Approximate Distribution
• Cramér-von Mises Statistic
• Waston's Statistic
• Skewness
• Kurtosis