The unit extended Weibull families of distributions and its applications

Abstract

In this paper, two new general families of distributions supported on the unit interval are introduced. The proposed families include several known models as special cases and define at least twenty (each one) new special models. Since the list of well-being indicators may include several double bounded random variables, the applicability for modeling those is the major practical motivation for introducing the distributions on those families. We propose a parametrization of the new families in terms of the median and develop a shiny application to provide interactive density shape illustrations for some special cases. Various properties of the introduced families are studied. Some special models in the new families are discussed. In particular, the complementary unit Weibull distribution is studied in some detail. The method of maximum likelihood for estimating the model parameters is discussed. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Applications to the literacy rate in Brazilian and Colombian municipalities illustrate the usefulness of the two new families for modeling well-being indicators.

Keywords:

• Extended Weibull distribution
• maximum likelihood estimation
• moments
• unit distributions
• well-being indicators

AMS CLASSIFICATION:

• 60E05

Acknowledgements

We gratefully acknowledge partial financial support from CAPES.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 https://newdists.shinyapps.io/UEWfamilies/#section-models.