On the generalized extended exponential-Weibull distribution: properties and different methods of estimation

ABSTRACT

We consider the generalized extended exponential-Weibull distribution, which can be very useful for modelling non-monotonic failure rate function, and provide a detailed study of its structural properties. This model includes at least thirteen sub-models and some of them are very known such as the Weibull, generalized Weibull, exponential-Weibull, and exponentiated generalized linear exponential distributions. We also consider different estimation procedures for estimating the model parameters, namely: maximum likelihood, least-square, weighted least-square, maximum product of spacings, Cramér-von-Mises, and Anderson-Darling methods. We also conduct Monte Carlo simulation experiments to assess the finite sample properties of the proposed estimation methods. The usefulness of the distribution is illustrated by means of two real data sets to prove its versatility in practical applications.

Keywords:

• Lifetime data
• generalized extended distributions
• maximum likelihood estimation

2010 Mathematics Subject Classifications:

• 62E10
• 62E15
• 62N05

Acknowledgements

We are very grateful to the anonymous referees for useful comments and suggestions on an early version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Gauss M. Cordeiro  http://orcid.org/0000-0002-3052-6551

Additional information

Funding

Artur Lemonte gratefully acknowledges the financial support of the Brazilian agency CNPq (grant 301808/2016–3).