Abstract
We study a new family of distributions defined by the minimum of the Poissonrandom number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of theproposed family.
Highlights
In many applied areas such as lifetime analysis, biomedical science, reliability, engineering, social sciences, finance and insurance, there is a clear need for extended forms of the classical models, i.e., new distributions which are more flexible to capture skewness and kurtosis behavior and to improve the goodness-of-fit of the generated family
We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al (2014))
Drobinski et al (2015) in their study, demonstrated that in modeling wind speed data, since the Weibull distribution is heavily relied on empirical perspective rather than physical justification, it might not be a good candidate in fitting to these types of environmental data
Summary
In many applied areas such as lifetime analysis, biomedical science, reliability, engineering, social sciences, finance and insurance, there is a clear need for extended forms of the classical models, i.e., new distributions which are more flexible to capture skewness and kurtosis behavior and to improve the goodness-of-fit of the generated family. All these above merits for finding a mixture of Weibull-G family of distribution, proposed and studied by Bourguignon et al (2014) (after adding more flexibility to Weibull model itself) with possibly a discrete probability distribution with the same support (0, ∞). This is why we considered Poisson distribution with the Weibull-G type models to capture more flexibility.
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