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A discrete distribution associated with a pure birth process

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Abstract

A discrete distribution associated with a pure birth process starting with no individuals, with birth rates λn=λ forn=0, 2, …,m−1 and λn forn≥m is considered in this paper. The probability mass function is expressed in terms of an integral that is very convenient for computing probabilities, moments, generating functions and others. Using this representation, the mean and the k-th factorial moments of the distribution are obtained. Some nice characterizations of this distribution are also given.

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References

  • Abad, J. andSesma, J. (1995). Computation of the Regular Confluent Hypergeometrin Function, Mathematika Jour. 5, pp. 74–76.

    Google Scholar 

  • Abramowitz, M. andSegun, I.A. (Eds.) (1972). Confluent Hypergeometric Functions, Chap 13 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, Dover, New York, pp. 503–515

    Google Scholar 

  • Gradshteyn, I.S. andRyzhik, I.M. (1965).Tables of Integrals Series and Products, Academic Press, New York.

    Google Scholar 

  • Janardan, K.G. (1980). A Stochastic Model for the Study of Oviposition Evolution of the Pest Callosobruchus Maculatus on Mung Beans, Phaseolus aureus, Math. Biosciences 50, pp. 231–238.

    Article  MathSciNet  Google Scholar 

  • Janardan, K.G., Schaeffer, D. J., andDuFrain, R.J. (1981). A Stochastic Model for the Study of Distribution of Chromosome Aberrations in Human and Animal Cells Exposed to Radiation or Chemicals,Statistical Distributions in Scientific Work (Editors: Taillie, C., Patil, G. P. and Baldessari, B. A. Publisher: D. Reidel Publishing Company, Boston, U. S. A.) Vol. 6, pp. 265–277.

    Google Scholar 

  • Janardan, K.G. andSchaeffer, D.J. (1977). Models for the Analysis of Aberrations in Human Leukocytes, Biometrical Journal 19, pp. 599–612.

    Article  MATH  MathSciNet  Google Scholar 

  • Janardan, K.G. (1993-94). A Modified Poisson Process Model For Couple's Desired Family Size, Journal of Mysore University, Section B: Science and Mathematics, Vol. 33, pp. 174–180.

    Google Scholar 

  • Janardan, K.G. (1997). A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite, Biometrical Journal, Vol. 39 (7), pp. 839–848.

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson, N.L., Kotz, S., andKemp, A.W. (1992).Univariate Discrete Distributions (Second Edition), Wiley & Sons, New York

    MATH  Google Scholar 

  • Koepf, W (1998).Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities, Braunschweuig, Germany. vieweg.

    MATH  Google Scholar 

Download references

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  1. Department of Mathematics, Eastern Michigan University, 48197, Ypsilanti, MI, USA

    Konanur G. Janardan

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  1. Konanur G. Janardan
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Janardan, K.G. A discrete distribution associated with a pure birth process. Statistical Papers 46, 587–597 (2005). https://doi.org/10.1007/BF02763007

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  • DOI: https://doi.org/10.1007/BF02763007

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