Using Modern Computing Tools to Fit the Pearson Type III Distribution to Aviation Loads Data;Final rept

摘要

The question of obtaining a relatively simple and at the same time accurate functional representation of asymmetric frequency distributions gives rise to one of the most important practical problems in mathematical statistics. The famous mathematician Karl Pearson solved this with a considerable degree of success in the development of his Type III frequency function. This function is a comparatively simple exponential expression, which is completely defined in terms of the mean, standard deviation, and the skewness of the distribution. The Type III function produces, with considerable accuracy, a large number of different distributions, both skew and symmetric, and reduces to the standard normal frequency function when skewness is zero. The Pearson Type III distribution is used by the U.S. Army Corps of Engineers in flood frequency analysis, by the National Oceanic and Atmospheric Administration in the analysis of precipitation data, and by the U.S. Navy in specifying airplane touchdown sink speed of non-carrier-based airplanes. A derivation of the Pearson Type III probability function, a table containing a complete set of Pearson Type III probability values for skewness values up to 1.1, an example describing how to use the tables, and a procedure and example for setting up an Excel spreadsheet and graphical applications are presented herein.