Mixture Models and the Krätzel Integral Transform

Abstract

Continuous mixture Weibull models arise in many areas of sciences such as reliability studies, communications theory, etc. Due to its wide applicability, we introduce a class of continuous mixture Weibull models which is a combination of Weibull and generalized gamma distributions. Some characteristics of the distribution are obtained. It is seen that Krätzel integral enters into the model naturally, and then the model can be called as a Krätzel density. Applications of the density function related to fading channels and ultrasonic backscatter signals modeling are discussed. A real data analysis is given to illustrate the use of this distribution.

Keywords:

• Generalized gamma distribution
• Krätzel function
• Mixture Weibull distribution
• Weibull distribution

Mathemetics Subject Classifications:

• 62H10
• 33E20
• 60E07