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The Exponentiated Power Generalized Weibull: Properties and Applications.

Fernando A Peña-Ramírez¹, Renata R Guerra¹, Gauss M Cordeiro²

¹Departamento de Estatística, Universidade Federal de Santa Maria, Cidade Universitária, Av. Roraima, 1000, 97105-900 Santa Maria, RS, Brazil.

Anais Da Academia Brasileira De Ciencias

|October 11, 2018

Summary

We introduce the exponentiated power generalized Weibull (EPGW) distribution, a flexible new lifetime model. This model offers a competitive alternative to existing distributions for various hazard rate functions.

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Area of Science:

Statistics
Probability Theory
Reliability Engineering

Background:

The power generalized Weibull (PGW) distribution has unstudied structural properties.
Existing lifetime models like Weibull and exponentiated Weibull have limitations in flexibility.

Purpose of the Study:

Introduce the novel exponentiated power generalized Weibull (EPGW) distribution.
Investigate the mathematical properties and flexibility of the EPGW distribution.
Provide a new, competitive lifetime model for various hazard rate functions.

Main Methods:

Derivation of the EPGW distribution from the exponentiated family applied to the PGW distribution.
Exploration of structural properties inherited from the PGW distribution.
Mathematical investigation of the EPGW distribution's properties.

Main Results:

The EPGW distribution is highly flexible, accommodating all common hazard rate function types.
The EPGW distribution demonstrates competitiveness against established models like Weibull and exponentiated exponential.
Estimation methods using maximum likelihood are discussed and validated.

Conclusions:

The EPGW distribution is a valuable addition to the field of lifetime modeling.
The proposed model offers enhanced flexibility and performance compared to existing distributions.
The study provides a foundation for applying the EPGW distribution in real-world scenarios.