Year-end Sale % OFF 
Abstract
This paper presents a new class of probability distributions generated from the gamma distribution. For the new class proposed, we present several statistical properties, such as the risk function, the density expansions, Moment-generating function, characteristic function, the moments of order m, central moments of order m, the log likelihood and its partial derivatives and also entropy, kurtosis, symmetry and variance. These same properties are determined for a particular distribution within this new class that is used to illustrate the capability of the proposed new class through an application to a real data set. The database presented in Choulakian and Stephens (2001) was used. Six models are compared and for the selection of these models were used the Akaike Information Criterion (AIC), the Akaike Information Criterion corrected (AICc), Bayesian Information Criterion (BIC), Hannan Quinn Information Criterion (HQIC) and tests of Cramer-Von Mises and Anderson-Darling to assess the models fit. Finally, we present the conclusions from the analysis and comparison of the results obtained and the directions for future work.
Highlights
The gamma distribution is used in a variety of applications including queue, financial and weather models
Due to the importance of this distribution, recently some new distributions as well as families of probability distributions based on generalizations of the gamma distribution have been proposed
We note that the class of gamma-[(1 G) G] probability distributions developed in this work is a novel way of generalizing the gamma distribution and can be applied in different areas depending on the choice of the distribution G
Summary
The gamma distribution is used in a variety of applications including queue, financial and weather models. It can naturally be considered as the distribution of the waiting time between events distributed according to a Poisson process. It is a two-parameter distribution, whose density is given by:. Due to the importance of this distribution, recently some new distributions as well as families of probability distributions based on generalizations of the gamma distribution have been proposed. Given a distribution with continuous distribution function G x its generalization or exponentiated form. Gupta, Gupta, and Gupta (1998) proposed and studied some properties exponentiated gamma distribution G x is obtained by F x Ga x , with a 0 (power parameter). Gupta, Gupta, and Gupta (1998) proposed and studied some properties exponentiated gamma distribution
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
