Abstract
In this paper, we study a new four-parameter distribution called the odd gamma Weibull-geometric distribution. Having the qualities suggested by its name, the new distribution is a special member of the odd-gamma-G family of distributions, defined with the Weibull-geometric distribution as baseline, benefiting of their respective merits. Firstly, we present a comprehensive account of its mathematical properties, including shapes, asymptotes, quantile function, quantile density function, skewness, kurtosis, moments, moment generating function and stochastic ordering. Then, we focus our attention on the statistical inference of the corresponding model. The maximum likelihood estimation method is used to estimate the model parameters. The performance of this method is assessed by a Monte Carlo simulation study. An empirical illustration of the new distribution is presented by the analyses two real-life data sets. The results of the proposed model reveal to be better as compared to those of the useful beta-Weibull, gamma-Weibull and Weibull-geometric models.
Highlights
The parametric models based on standard distributions are not always suitable to reveal the finer detail of the underlying structure of a data set
One can remark that he odd gamma Weibull-geometric distribution (OGWG) distribution is special case of the general gamma-Weibull-Weibull distribution introduced by ([7], Section 6) (with the notations of [7], it corresponds to β = 1, simplifying the complexity of the distribution, α = 1/(1 − p), λ = 1/β and k = c)
We investigate the empirical bias (Bias), mean square error (MSE) and coverage probability (CP) at the nominal level 95%
Summary
The parametric models based on standard (probability) distributions are not always suitable to reveal the finer detail of the underlying structure of a data set This limitation has triggered the creation of new families of distributions, often defined as compounding or weighting existing distributions. We focus our attention on a new distribution with cdf defined by the compounding of the odd-gamma-G cdf given by (1) and the Weibull-geometric cdf given by (2). We show that the OGWG pdf can have reversed-J, right skewed shapes, left-skewed and approximately symmetric, and the OGWG hrf can have increasing failure rate, decreasing failure rate and bathtub shapes These aspects are welcome to the construction of new flexible models for a wide variety of data sets.
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