Properties of Generalized Log Pearson Type VII Distribution.

      Аннотация: In this book we consider generalized log Pearson (GLP) type VII distribution which is more flexible than log Pearson of type VII distribution in data fitting. The goal of curve fitting is to find out the parameter values that most closely match the data. So different choices of combinations of parameters make GLP type VII distribution more useful in curve fitting. The GLP type VII distribution is closed under inversion which produces many distributions after replacing some special transformations. The objective of this dissertation is to develop theoretical properties of the GLP type VII distribution. Characterization of the GLP type VII distribution is presented through conditional expectation. The proposed extension is utilized to model a data set. The GLP type VII distribution provides a fit to data set measured by the Anderson-Darling and Cramer-von Mises statistics. The generalized log normal (GLN) distribution is proved as the limiting form of GLP type VII distribution. Averages of the mixed random variables containing algebraic, logarithmic and trigonometric functions with respect to the limiting distribution of the GLP type VII distribution are found.

Ключевые слова: characterization, type, GLP, VII distribution, scale mixture distribution, mixed distribution