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Transmuted Weibull distribution: a generalization of the Weibull probability distribution. (English) Zbl 1389.62150
Summary: In this article, the two parameter Weibull probability distribution is embedded in a larger family obtained by introducing an additional parameter. We generalize the two parameter Weibull distribution using the quadratic rank transmutation map studied by W. T. Shaw and I. R. C. Buckley [“The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map”, Preprint, arXiv:0901.0434] to develop a transmuted Weibull distribution. We provide a comprehensive description of the mathematical properties of the subject distribution along with its reliability behavior. The usefulness of the transmuted Weibull distribution for modeling reliability data is illustrated using real data.

##### MSC:
 62N05 Reliability and life testing 90B25 Reliability, availability, maintenance, inspection in operations research 62F10 Point estimation 62E15 Exact distribution theory in statistics 60E05 Probability distributions: general theory
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