A New More Flexible Class of Distributions on (0,1): Properties and Applications to Univariate Data and Quantile Regression

Abstract

In this paper, we will present a new, more flexible class of distributions with a domain in the interval (0,1), which presents heavier tails than other distributions in the same domain, such as the Beta, Kumaraswamy, and Weibull Unitary distributions. This new distribution is obtained as a transformation of two independent random variables with a Weibull distribution, which we will call the Generalized Unitary Weibull distribution. Considering a particular case, we will obtain an alternative to the Beta, Kumaraswamy, and Weibull Unitary distributions. We will call this new distribution of two parameters the type 2 unitary Weibull distribution. The probability density function, cumulative probability distribution, survival function, hazard rate, and some important properties that will allow us to infer are provided. We will carry out a simulation study using the maximum likelihood method and we will analyze the behavior of the parameter estimates. By way of illustration, real data will be used to show the flexibility of the new distribution by comparing it with other distributions that are known in the literature. Finally, we will show a quantile regression application, where it is shown how the proposed distribution fits better than other competing distributions for this type of application.