Abstract
In this paper, we try to contribute to the distribution theory literature by incorporating 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 statistical 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 Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters 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 distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius 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
Highlights
An integral part of many statistical studies is the collection of information about the form of population from which the data is obtained
We obtain a new distribution with support on (0, 1), which we refer to as unit generalized inverse Weibull distribution (UGIWD)
The unknown parameters of the UGIW distribution are estimated by six different frequentist methods of estimation and obtained their CIs
Summary
An integral part of many statistical studies is the collection of information about the form of population from which the data is obtained For this purpose, statisticians often use goodness of fit (GOF) tests so as to determine whether the observed sample data âfitsâ some proposed model. The above cited distributions are extended form of inverse Weibull distribution and have been derived by incorporating some additional parameters to the original probability distribution They are based on the support over positive part of the real line. We obtain a new distribution with support on (0, 1), which we refer to as unit generalized inverse Weibull distribution (UGIWD) This distribution is capable of modelling increasing and bathtub shaped hazard rate.
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