Advertisement

Journal of Statistical Theory and Practice

, Volume 7, Issue 3, pp 544–557 | Cite as

On Intervened Stuttering Poisson Distribution and Its Applications

  • C. Satheesh Kumar
  • D. S. Shibu
Article
First Online:
Received:
Accepted:

Abstract

Intervened Poisson distribution (IPD) has been found suitable for dealing with intervention problems in medical situations where positive Poisson distribution fails. Kumar and Shibu (2011a) introduced a modified version of IPD, namely, MIPD, to deal situations of two interventions. Through this article we propose an extended form of this modified version, namely, the intervened stuttering Poisson distribution (ISPD), appropriate for situations of more than two interventions. An important characteristic of ISPD over IPD and MIPD is that it is both underdispersed and overdispersed for particular values of its parameters and hence more suitable for practical situations. Here, we study some important properties of ISPD and discuss the estimation of its parameters by method of factorial moments and maximum likelihood. Some real-life data sets are given to illustrate that ISPD gives the best fit compared to the existing models.

Keywords

Factorial moments Maximum likelihood estimation Positive Poisson distribution Probability generating function stuttering Poisson distribution 

AMS (2000) subject classification

Primary 60E05 60E10 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aki, S. 1985. Discrete distributions of order k on a binary sequence. Ann. Inst. Stat. Math., 37, 205–224.MathSciNetCrossRefGoogle Scholar
  2. Cohen, A. C. 1960. Estimating parameters in a conditional Poisson distribution. Biometrics, 16, 203–211.MathSciNetCrossRefGoogle Scholar
  3. Consul, P. C. 1989. Generalized Poisson distribution: Properties and applications. New York, Marcel Dekker.zbMATHGoogle Scholar
  4. Consul, P. C., and F. Famoye. 1989. The truncated generalized Poisson distribution and its estimation. Commun. Stat. Theory Methods, 18, 3635–3648.MathSciNetCrossRefGoogle Scholar
  5. Galliher, H. P., P. M. Morse, and M. Simmond. 1959. Dynamics of two classes of continuous review inventory systems. Operations Res., 7, 372–394.MathSciNetCrossRefGoogle Scholar
  6. Huang, M., and K.Y. Fung. 1989. Intervened truncated Poisson distribution. Sankhya, 51, 302–310.MathSciNetzbMATHGoogle Scholar
  7. Jani, P. N., and S. M. Shah. 1979. On fitting of the generalized logarithmic series distribution. J. Indian Soc. Agric. Stat., 30, 1–10.Google Scholar
  8. Karian, Z. A., and E. J. Deudewicz. 1999. Modern statistical systems and GPSS simulations, 2nd ed. Boca Raton, FL, CRC Press.Google Scholar
  9. Kendall, M. G., 1961. Natural law in science. J. R. Stat. Soc. Ser. A, 124, 1–18.MathSciNetCrossRefGoogle Scholar
  10. Kumar, C. S. 2009. A class of discrete distributions of order k. J. Stat. Theory Pract., 3, 795–803.MathSciNetCrossRefGoogle Scholar
  11. Kumar, C. S. 2010. Binomial Poisson distribution revisited. Econ. Quality Control, 25, 183–188.MathSciNetCrossRefGoogle Scholar
  12. Kumar, C. S., and D. S. Shibu. 2011a. Modified intervened Poisson distribution. Statistica, 71, 489–499.Google Scholar
  13. Kumar, C. S., and D. S. Shibu. 2011b. Estimation of the parameters of a finite mixture of intervened Poisson distribution. In Statistical methods in interdisciplinary studies, ed. S. Santhosh, 93–103. Department of Statistics, Maharajahs College, Cochin, India.Google Scholar
  14. Kumar, C. S., and D. S. Shibu. 2012. An alternative to intervened Poisson distribution. J. Stat. Appl., 5, 131–141.Google Scholar
  15. Moothathu, T. S. K., and C. S. Kumar. 1995. Some properties of the stuttering Poisson distribution. Calcutta Stat. Assoc. Bull., 45, 125–130.MathSciNetCrossRefGoogle Scholar
  16. Patel, Y. C. 1976. Estimation of parameters of the triple and quadruple stuttering Poisson distribution. Technometrics, 18, 67–73.MathSciNetCrossRefGoogle Scholar
  17. Puig, P. 2003. Characterizing additively closed discrete models by a property of their MLEs, with an application to generalized Hermite distributions. J. Am. Stat. Assoc., 98, 687–692.CrossRefGoogle Scholar
  18. Scollnik, D. P. M. 2006. On the intervened generalized Poisson distribution. Commun. Stat. Theory Methods, 35, 953–963.MathSciNetCrossRefGoogle Scholar
  19. Shanmugam, R. 1985. An intervened Poisson distribution and its medical application. Biometrics, 41, 1025–1029.MathSciNetCrossRefGoogle Scholar
  20. Shanmugam, R. 1992. An inferential procedure for the Poisson intervention parameter. Biometrics, 48, 559–565.CrossRefGoogle Scholar
  21. Singh, J. 1978. A characterization of positive Poisson distribution and its applications. SIAMJ. Appl. Math., 34, 545–548.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of KeralaTrivandrumIndia

Personalised recommendations

Cite article

Buy options