Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data
Samuel U. Enogwe *
Department of Statistics, Michael Okpara University of Agriculture, Umudike, Nigeria. 2Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
Chisimkwuo John
Department of Statistics, Michael Okpara University of Agriculture, Umudike, Nigeria. 2Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
Happiness O. Obiora-Ilouno
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
Chrisogonus K. Onyekwere
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.
Keywords: Weighted Rama distribution, hazard rate function, maximum likelihood method, order statistics.