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The transmuted Birnbaum-Saunders distribution. (English) Zbl 1380.62057

Summary: The Birnbaum-Saunders distribution has been largely studied and applied because of its attractive properties. We introduce a transmuted version of this distribution. Various of its mathematical and statistical features are derived. We use the maximum likelihood method for estimating its parameters and determine the score vector and Hessian matrix for inference and diagnostic purposes. We evaluate the performance of the maximum likelihood estimators by a Monte Carlo study. We illustrate the potential applications of the new transmuted Birnbaum-Saunders distribution by means of three real-world data sets from different areas.

MSC:

62E15 Exact distribution theory in statistics
62N05 Reliability and life testing
62F10 Point estimation
62J20 Diagnostics, and linear inference and regression

Software:

Ox; R
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