UNIT BURR-HATKE DISTRIBUTION WITH A NEW QUANTILE REGRESSION MODEL

Abstract

In this study, a new distribution is introduced. The Burr-Hatke distribution is considered the baseline distribution. Since the baseline distribution has one parameter, the new unit distribution also has one parameter. Some distributional properties such as moments, coefficients of skewness and kurtosis, stochastic ordering, etc. of the new distribution are studied. Five estimators such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, and Cramer-von Mises are examined to estimate the unknown parameter of the new model. The performances of the estimators are analyzed according to the bias and mean square error criteria calculated by Monte Carlo simulation. Two numerical data analyses are performed. A new quantile regression model is also introduced based on the new distribution as an alternative to beta and Kumaraswamy regression. A Monte Carlo simulation is also conducted for the new regression model.