# An alternative hyper-Poisson distribution

## DOI:

https://doi.org/10.6092/issn.1973-2201/3652## Abstract

An alternative form of hyper-Poisson distribution is introduced through its probability mass function and studies some of its important aspects such as mean, variance, expressions for its raw moments, factorial moments, probability generating function and recursion formulae for its probabilities, raw moments and factorial moments. The estimation of the parameters of the distribution by various methods are considered and illustrated using some real life data sets.## References

M. ABRAMOWITZ, I.A. STEGUN, (1965), Hand book of Mathematical Functions, Dover, New York.

M. AHMAD, (2007), A short note on Conway-Maxwell-hyper Poisson distribution, “Pakistan Journal of Statistics”, 23, pp. 135-137.

P.S. ALBERT, (1991), A two state Markov mixture model for a time series of epileptic seizure counts, “Biometrics”, 47, pp. 1371-1381.

G.E. BARDWELL, E.L. CROW, (1964), A two parameter family of hyper-Poisson distributions, “Journal of American Statistical Association”, 59, pp. 133-141.

C.I. BLISS, (1953), Fitting the negative binomial distribution to biological data, “Biometrics”, 9, pp. 176-200.

S. CHAKRAVORTHY, (2010), On some distributional properties of the family of weighted generalized Poisson distribution, “Communications in Statistics-Theory and methods”, 39, pp. 2767-2788.

E.L. CROW, G.E. BARDWELL, (1965), Estimation of the parameters of the hyper-Poisson distributions, “Classical and Contagious Discrete Distributions”. G. P. Patil (editor), pp. 127-140, Pergamon Press, Oxford.

D.J. HAND, F. DALY, A.D. LUNN, K.J. McCONWAY, E. OSTROWSKI, (1994), A Hand Book of Small Data Sets, Chapman and Hall, London.

N.L. JOHNSON, A.W. KEMP, S. KOTZ, (2005), Univariate Discrete Distributions, Wiley, New York.

C.D. KEMP, (2002), q-analogues of the hyper-Poisson distribution, “Journal of Statistical Planning and Inference”, 101, pp. 179-183.

C.S. KUMAR, (2009), Some properties of Kemp family of distributions, “Statistica”, 69, pp. 311-316.

C.S. KUMAR, B.U. NAIR, (2011), A modified version of hyper Poisson distribution and its applications, “Journal of Statistics and Applications”, 6, pp. 25-36.

C.S. KUMAR, B.U. NAIR, (2012), An extended version of hyper Poisson distribution and some of its applications, “Journal of Applied Statistical Sciences”, 19 (To appear).

A.M. MATHAI, H.J. HAUBOLD, (2008), Special functions of applied sciences, Springer, New York.

T. NISIDA, (1962), On the multiple exponential channel queuing system with hyper-Poisson arrivals, “Journal of the Operations Research Society”, 5, pp. 57-66.

J. RIORDAN, (1968), Combinatorial identities, Wiley, NewYork.

A. ROOHI, M. AHMAD, (2003a), Estimation of the parameter of hyper-Poisson distribution using negative moments, “Pakistan Journal of Statistics”, 19, pp. 99-105.

A. ROOHI, M. AHMAD, (2003a), Inverse ascending factorial moments of the hyper-Poisson probability distribution, “Pakistan Journal of Statistics”, 19, pp. 273-280.

P.J. STAFF, (1964), The displaced Poisson distribution, “Australian Journal of Statistics”, 6, pp. 12-20.

G.M. STIRRETT, G.BEALL, M.TIMONIN, (1937), A field experiment on the control of the European corn borer, “Pyrausta nubilalis Hubn”. by Beauveria bassiana Vuill. Scient. Agric, 17, pp. 587-591.

## Downloads

## Published

## How to Cite

*Statistica*,

*72*(3), 357–369. https://doi.org/10.6092/issn.1973-2201/3652

## Issue

## Section

## License

Copyright (c) 2012 Statistica

This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).

Authors accept to transfer their copyrights to the journal.

See also our Open Access Policy.