Abstract
A new distribution called
the gamma-generalized inverse Weibull distribution which includes inverse
exponential, inverse Rayleigh, inverse Weibull, Frechet, generalized inverse
Weibull, gamma-exponentiated inverse exponential, exponentiated inverse exponential,
Zografos and Balakrishnan-generalized inverse Weibull, Zografos and
Balakrishnan-inverse Weibull, Zografos and Balakrishnan-generalized inverse
exponential, Zografos and Balakrishnan-inverse exponential, Zografos and
Balakrishnan-generalized inverse Rayleigh, Zografos and Balakrishnan-inverse
Rayleigh, and Zografos and Balakrishnan-Fr'echet distributions as special
cases is proposed and studied in detail. Some structural properties of this new
distribution including density expansion, moments, R'enyi entropy,
distribution of the order statistics, moments of the order statistics and
L-moments are presented. Maximum likelihood estimation technique is used to
estimate the model parameters and applications to a real datasets to illustrate
its usefulness are presented.
Mathematics Subject Classification: 62E15; 60E05
Keywords: Zografos and Balakrishnan gamma generator; Gamma distribution; Inverse Weibull distribution; Maximum likelihood estimation
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