On Explicit Expressions for Moments of Gamma Order Statistics

Abstract

Naradajah and Pal (Bull Braz Math Soc New Ser 39(1):45–60, 2008) derived explicit closed-form expressions for moments of order statistics from the gamma and generalized gamma distributions. However, the closed-form expressions provided by these authors are not correct and hence cannot be used to compute the moments of order statistics. We provide, therefore, an alternative closed-form expression for moments of gamma order statistics.

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References

  1. Exton, H.: Handbook of Hypergeometric Integrals: Theory, Applications, Tables. Computer Programs. Halsted Press, New York (1978)

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  2. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, New York (2007)

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  3. Naradajah, S., Pal, M.: Explicit expressions for moments of gamma order statistics. Bull. Braz. Math. Soc. New Ser. 39, 45–60 (2008)

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Acknowledgements

Both authors would express their gratitude to the Editor.

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Correspondence to Artur J. Lemonte.

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Fredy Castellares gratefully acknowledges the financial support from FAPEMIG (Belo Horizonte/MG, Brazil). Artur Lemonte gratefully acknowledges the financial support of the Brazilian agency CNPq (Grant 304776/2019-0).

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Castellares, F., Lemonte, A.J. On Explicit Expressions for Moments of Gamma Order Statistics. Bull Braz Math Soc, New Series (2021). https://doi.org/10.1007/s00574-020-00238-1

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Keywords

  • Gamma distribution
  • Lauricella function
  • Order statistics

Mathematics Subject Classification

  • 60E05
  • 62E10