Using Pearson Type IV and other cinderella distributions in simulation

Univariate continuous distributions with unbounded range of variation have not been so widely used in simulation as those that are bounded (usually to the left). However situations do occur when they are needed, particularly in operations research and financial applications. Two distributions that have such unbounded range are the Pearson Type IV and Johnson SU distributions. Though both are well known in statistics, there is still a lack of methods in the literature for fitting these distributions to data which are both efficient and comprehensively reliable. Indeed the Pearson Type IV has the reputation of being difficult to fit. In this paper we identify the pitfalls and propose a fitting method that avoids them. We also show how to test the goodness of fit of estimated distributions. All the procedures described are included as VBA code in an accompanying Excel workbook available online. Two numerical examples are described in detail.