Different Classical Methods of Estimation and Chi-squared Goodness-of- t Test for Unit Generalized Inverse Weibull Distribution

Abstract

In this paper, we try to contribute to the distribution theory literature by incorporat ing a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits increasing and bathtub shaped hazard rate function. We derive some basic statis tical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cramer-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap condence intervals of the param eters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distri butions. Further, we construct chi-squared goodness-of- t tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modi cation. The criterion test used is the modi ed chi-squared statistic Y 2, developed by Bagdon avicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set