The unit-improved second-degree Lindley distribution: inference and regression modeling

Abstract

We define a new one-parameter model on the unit interval, called the unit-improved second-degree Lindley distribution, and obtain some of its structural properties. The methods of maximum likelihood, bias-corrected maximum likelihood, moments, least squares and weighted least squares are used to estimate the unknown parameter. The finite sample performance of these methods are investigated by means of Monte Carlo simulations. Moreover, we introduce a new regression model as an alternative to the beta, unit-Lindley and simplex regression models and present a residual analysis based on Pearson and Cox-Snell residuals. The new models are proved empirically to be competitive to the beta, Kumaraswamy, simplex, unit-Lindley, unit-Gamma and Topp-Leone models by means of two real data sets. Empirical findings indicate that the proposed models can provide better fits than other competitive models when the data are close to the boundaries of the unit interval.