The Exponentiated Gumbel Type-2 Distribution: Properties and Application

International Journal of Mathematics and Mathematical Sciences 2016  ·  Okorie, I. E. Akpanta, A. C. Ohakwe, J. ·

We introduce a generalized version of the standard Gumble type-2 distribution. The new lifetime distribution is called the ExponentiatedGumbel (EG) type-2 distribution. The EG type-2 distribution has three nested submodels, namely, theGumbel type2 distribution, the Exponentiated Fr´echet (EF) distribution, and the Fr´echet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. The usefulness and flexibility ofthe ExponentiatedGumbel (EG) type-2 distributionwere illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better fit to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. The EG type-2 distribution is therefore recommended for effective modelling of lifetime data.

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