Extended Gumbel type-2 distribution: properties and applications. (English) Zbl 1499.62067
Summary: In this paper, we proposed a new four-parameter Extended Gumbel type-2 distribution which can further be split into the Lehman type I and type II Gumbel type-2 distribution by using a generalized exponentiated \(G\) distribution. The distributional properties of the proposed distribution have been studied. We derive the \(p\)th moment; thus, we generalize some results in the literature. Expressions for the density, moment-generating function, and \(r\)th moment of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix of the developed distribution. Two life data, which consist of data on cancer remission times and survival times of pigs, were used to show the applicability of the Extended Gumbel type-2 distribution in modelling real life data, and we found out that the new model is more flexible than its submodels.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 60E05 | Probability distributions: general theory |
| 62F10 | Point estimation |
| 62E15 | Exact distribution theory in statistics |
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