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The Discrete Half-Normal Distribution

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Advances in Mathematical and Statistical Modeling

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

The discrete half-normal distribution is derived as the maximum entropy distribution on 0,1,. . . with specified mean and variance. It is a limiting q-hyper-Poisson- I distribution that arises from the Morse M/M/1 queue with service-dependent balking. Success runs models are reviewed. A new derivation as a mixture of Heine distributions is given. Finally the moment and other properties are examined.

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References

  • Benkherouf, L. and Bather, J. A. (1988). Oil exploration: sequential decisions in the face of uncertainty.Journal of Applied Probability, 25:529–543.

    Article  MATH  MathSciNet  Google Scholar 

  • Gasper G. and Rahman M. (2004).Basic Hypergeometric Series (2e). Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Gupta, P. L., Gupta, R. C., and Tripathi, R. C. (1997). On the monotone properties of discrete failure rates.Journal of Statistical Planning and Inference, 6:255–268.

    Article  MathSciNet  Google Scholar 

  • Johnson, N. L., Kemp, A. W., and Kotz, S. (2005).Univariate Discrete Distributions (3e). Wiley, Hoboken, New Jersey.

    MATH  Google Scholar 

  • Kapur, J. N. (1989).Maximum Entropy Models in Science and Engineering. Wiley Eastern, New Delhi.

    MATH  Google Scholar 

  • Kemp, A. W. (1997). Characterizations of a discrete normal distributions.Journal of Statistical Planning and Inference, 63:223–229.

    Article  MATH  MathSciNet  Google Scholar 

  • Kemp, A. W. (1992a). Heine-Euler extensions of the Poisson distribution.Communications in Statistics, Theory and Methods, 21:571–588.

    Article  MATH  MathSciNet  Google Scholar 

  • Kemp, A. W. (1992b). Steady state Markov chain models for the Heine and Euler distributions.Journal of Applied Probability, 29:869–876.

    Article  MATH  MathSciNet  Google Scholar 

  • Kemp, A. W. (2005). Steady state Markov chain models for certain q-confluent hypergeometric distributions.Journal of Statistical Planning and Inference, 135:107–120.

    Article  MATH  MathSciNet  Google Scholar 

  • Kemp, A. W. (2002). q-Analogues of the hyper-Poisson distribution.Journal of Statistical Planning and Inference, 101:179–183.

    Article  MATH  MathSciNet  Google Scholar 

  • Liang, T. -C. (1999). Monotone empirical Bayes tests for a discrete normal distribution.Statistics and Probability Letters, 44:241–249.

    Article  MATH  MathSciNet  Google Scholar 

  • Lisman, J. H. C. and van Zuylen, M. C. A. (1972). Note on the generation of the most probable frequency distribution.Statistica Neerlandica, 26:19–23.

    Article  MATH  Google Scholar 

  • Morse, P. M. (1958).Queues, Inventories and Maintenance. Wiley, New York.

    Google Scholar 

  • Navarro, J. and Ruiz, J.M. (2005). A note on the discrete normal distribution.Advances and Applications in Statistics, 5(2):229–245.

    MATH  MathSciNet  Google Scholar 

  • Szablowski, P. J. (2001). Discrete normal distribution and its relationship with Jacobi Theta functions.Statistics and Probability Letters, 52:289–299.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of St. Andrews, Scotland

    Adrienne W. Kemp

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  1. Adrienne W. Kemp
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© 2008 Birkhäuser Boston

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Kemp, A.W. (2008). The Discrete Half-Normal Distribution. In: Advances in Mathematical and Statistical Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4626-4_27

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