Fitting Mixture Distributions Using a Mixture of Generalized Lambda Distributions with Computer Code

Authored by: Wei Ning , Yunchuan Gao , Edward J. Dudewicz

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-11

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Abstract

In this chapter, we will discuss the problems of fitting data with the mixture of two generalized lambda distributions (GLDs) and its application. Finite mixture distributions have provided an approach to the statistical modeling of a wide variety of random phenomena. Most of the work has been done using mixtures of normal distributions. The most striking property of a mixture distribution is that the shape of the density is extremely flexible. Because of its flexibility, it has been applied to many fields such as: biology, genetics, medicine, and the social sciences. In these applications, finite mixture distributions underpin a variety of techniques in major areas of statistics including: cluster analysis, discriminant analysis, image analysis and survival analysis, in addition to their more direct role in data analysis and inference of providing descriptive models for distributions. Mixture distributions also play an important role in neural networks.

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