Skip to main content
SpringerLink
Log in

The exponential COM-Poisson distribution

  • Regular Paper
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35–42, 1998) and Kuş (Comput Stat Data Anal 51:4497–4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adamidis K, Loukas S (1998) A lifetime distribution with decreasing failure rate. Stat Prob Lett 39: 35–42

    Article  MathSciNet  MATH  Google Scholar 

  • Chahkandi M, Ganjali M (2009) On some lifetime distributions with decreasing failure rate. Comput Stat Data Anal 53: 4433–4440

    Article  MathSciNet  MATH  Google Scholar 

  • Chen GM, Balakrishnan N (1995) A general-purpose approximate goodness-of-fit test. J Qual Technol 27: 154–161

    Google Scholar 

  • Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen & Co. Ltd, London

    MATH  Google Scholar 

  • de Gusmão FRS, Ortega EMM, Cordeiro GM (2009) The generalized inverse Weibull distribution. Stat Papers. doi:10.1007/s00362-009-0271-3

  • Dunn J (2008) Compoisson: Conway-Maxwell-Poisson distribution. R package version 0.3

  • Gradshteyn IS, Ryzhik IM (2000) Table of integrals, series, and products, 6th edn. Academic Press, San Diego, CA

    MATH  Google Scholar 

  • Kim C, Jung J, Chung Y (2009) Bayesian estimation for the exponentiated Weibull model under type II progressive censoring, Stat Papers. doi:10.1007/s00362-009-0203-2

  • Kuş C (2007) A new lifetime distribution. Comput Stat Data Anal 51: 4497–4509

    Article  MATH  Google Scholar 

  • Lord D, Guikema SD, Geedipally SR (2008) Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes. Accid Anal Prev 40: 1123–1134

    Article  Google Scholar 

  • Minka TP, Shmueli G, Kadane JB, Borle S, Boatwright P (2003) Computing with the COM-Poisson distribution. Technical report 776, Department of Statistics, Carnegie Mellon University. from http://www.stat.cmu.edu/tr/tr776/tr776.html

  • Proschan F (1963) Theoretical explanation of observed decreasing failure rate. Technometrics 5: 375–383

    Google Scholar 

  • R Development Core Team (2010) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Rigby RA, Stasinopoulos DM (2005) Generalized additive models for location, scale and shape (with discussion). Appl Stat 54: 507–554

    Article  MathSciNet  MATH  Google Scholar 

  • Rodrigues J, de Castro M, Cancho VG, Balakrishnan N (2009) COM–Poisson cure rate survival models and an application to a cutaneous melanoma data. J Stat Plann Inference 139: 3605–3611

    Article  MATH  Google Scholar 

  • Sellers KF, Shmueli G (2010) A flexible regression model for count data. Ann Appl Stat 4: 943–961

    Article  MathSciNet  MATH  Google Scholar 

  • Shmueli G, Minka TP, Kadane JB, Borle S, Boatwright P (2005) A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Appl Stat 54: 127–142

    Article  MathSciNet  MATH  Google Scholar 

  • Stasinopoulos DM, Rigby RA (2007) Generalized additive models for location scale and shape (GAMLSS) in R. J Stat Softw 23: 1–46

    Google Scholar 

  • Tahmasbi R, Rezaei S (2008) A two-parameter lifetime distribution with decreasing failure rate. Comput Stat Data Anal 52: 3889–3901

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Recife, PE, Brazil

    Gauss M. Cordeiro

  2. Departamento de Estatística, Universidade Federal de São Carlos, São Carlos, SP, Brazil

    Josemar Rodrigues

  3. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil

    Mário de Castro

Authors
  1. Gauss M. Cordeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Josemar Rodrigues
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mário de Castro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gauss M. Cordeiro.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cordeiro, G.M., Rodrigues, J. & de Castro, M. The exponential COM-Poisson distribution. Stat Papers 53, 653–664 (2012). https://doi.org/10.1007/s00362-011-0370-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-011-0370-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation