Different Classical Methods of Estimation and Chi-squared Goodness-of- t Test for Unit Generalized Inverse Weibull Distribution
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Date
2021-07
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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