The exponentiated generalized inverse Gaussian distribution. (English) Zbl 1207.62028

Lemonte, Artur J.; Cordeiro, Gauss M.

Stat. Probab. Lett. 81, No. 4, 506-517 (2011).

Summary: The modeling and analysis of life time data is an important aspect of statistical work in a wide variety of scientific and technological fields. I. J. Good [Biometrika 40, 237–264 (1953; Zbl 0051.37103)] introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution [S. Nadarajah and S. Kotz, Acta Appl. Math. 92, No. 2, 97–111 (2006; Zbl 1128.62015)]. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set.

MSC:

62E10	Characterization and structure theory of statistical distributions
62G30	Order statistics; empirical distribution functions
62N05	Reliability and life testing

Keywords:

exponentiated gamma distribution; generalized inverse Gaussian distribution; inverse Gaussian distribution; lifetime data; maximum likelihood estimation

Citations:

Zbl 0051.37103; Zbl 1128.62015

Software:

Mathematica; LMOMENTS; Ox

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