×
Nadarajah, Saralees; Kotz, Samuel

The exponentiated type distributions. (English) Zbl 1128.62015

Acta Appl. Math. 92, No. 2, 97-111 (2006).
Summary: R. C. Gupta et al. [Commun. Stat., Theory Methods 27, No. 4, 887–904 (1998; Zbl 0900.62534)] introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. We introduce four more exponentiated type distributions that generalize the standard gamma, standard Weibull, standard Gumbel and the standard Fréchet distributions in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. A treatment of the mathematical properties is provided for each distribution.

Cited in 2 Reviews
Cited in 107 Documents

MSC:

62E10 Characterization and structure theory of statistical distributions
62E15 Exact distribution theory in statistics
33C90 Applications of hypergeometric functions

Citations:

Zbl 0900.62534
PDF BibTeX XML Cite
\textit{S. Nadarajah} and \textit{S. Kotz}, Acta Appl. Math. 92, No. 2, 97--111 (2006; Zbl 1128.62015)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 6th edn. Academic, San Diego, California (2000) · Zbl 0981.65001
[2] Gupta, R.C., Gupta, P.L., Gupta, R.D.: Modeling failure time data by Lehman alternatives. Comm. Statist.,Theory Methods 27, 887–904 (1998) · Zbl 0900.62534
[3] Gupta, R.D., Kundu, D.: Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom. J. 43, 117–130 (2001) · Zbl 0997.62076
[4] Kotz, S., Nadarajah, S.: Extreme Value Distributions: Theory and Applications. Imperial College, London, UK (2000) · Zbl 0960.62051
[5] Mudholkar, G.S., Hutson, A.D.: The exponentiated Weibull family: some properties and a flood data application. Comm. Statist., Theory Methods 25, 3059–3083 (1996) · Zbl 0887.62019
[6] Mudholkar, G.S., Srivastava, D.K., Freimer, M.: The exponentiated Weibull family. Technometrics 37, 436–445 (1995) · Zbl 0900.62531
[7] Nassar, M.M., Eissa, F.H.: On the exponentiated Weibull distribution. Comm. Statist., Theory Methods 32, 1317–1336 (2003) · Zbl 1140.62308
[8] Nadarajah, S., Kotz, S.: On the exponentiated exponential distribution, to appear in Statistica (2003) · Zbl 1048.62014
[9] Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series (vol. 1–3). Gordon and Breach Science, Amsterdam, Netherlands (1986) · Zbl 0606.33001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.