Main Article Content

Abstract

In this paper, a new mixed negative binomial (NB) distribution named as negative binomial-weighted Garima (NB-WG) distribution has been introduced for modeling count data. Two special cases of the formulation distribution including negative binomial- Garima (NB-G) and negative binomial-size biased Garima (NB-SBG) are obtained by setting the specified parameter. Some statistical properties such as the factorial moments, the first four moments, variance and skewness have also been derived. Parameter estimation is implemented using maximum likelihood estimation (MLE) and real data sets are discussed to demonstrate the usefulness and applicability of the proposed distribution.

Keywords

Mixed negative binomial distribution weighted Garima distribution negative binomial-weighted Garima distribution overdispersion count data

Article Details

Author Biography

Pornpop Saengthong, Institute for Research and Academic Services, Assumption University

Statistician, Institute for Research and Academic Services, Assumption University

How to Cite
Bodhisuwan, W., & Saengthong, P. (2020). The Negative Binomial – Weighted Garima Distribution: Model, Properties and Applications. Pakistan Journal of Statistics and Operation Research, 16(1), 1-10. https://doi.org/10.18187/pjsor.v16i1.3013

References

  1. Balakrishnan, N. and Nevzorov, V.B. (2003). A Primer on Statistical Distributions. John Wiley. New York.
  2. Eyob, T. and Shanker, R. (2018). A two-parameter weighted Garima distribution with properties and application. Biometrics & Biostatistics International Journal, 7, 234-242.
  3. Flynn, M. (2009). More flexible GLMs zero-inflated models and hybrid models. Casualty Actuarial Society E-Forum, Winter, 148-224.
  4. Gómez-Déniz, E., Sarabia, J. M. and Calderín-Ojeda, E. (2008). Univariate and multivariate versions of the negative binomial - inverse Gaussian distributions with applications. Insurance: Mathematics and Economics, 42, 39–49.
  5. Kongrod, S., Bodhisuwan, W. and Payakkapong, P. (2014). The negative binomial- Erlang distribution with applications. International Journal of Pure and Applied Mathematics, 92, 389–401.
  6. Lord, D. and Geedipally, S. R. (2011). The negative binomial-Lindley distribution as a tool for analysing crash data characterized by a large amount of zeros. Accident Analysis & Prevention, 43, 1738-1742.
  7. Pudprommarat, C., Bodhisuwan, W. and Zeephongsekul, P. (2012). A new mixed negative binomial distribution. Journal of Applied Sciences, 12, 1853-1858.
  8. R Core Team. (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. https://www.R-project.org/.
  9. Rainer, W. (2008). Econometric Analysis of Count Data. SpringerVerlag. Germany.
  10. Willmot, G.E. (1987). The Poisson-inverse Gaussian distribution as an alternative to the negative binomial. Scandinavian Actuarial Journal, 113-127.
  11. Yamrubboon, D., Bodhisuwan, W., Pudprommarat, C., and Saothayanun, L. (2017). The negative binomial-Sushila distribution with application in count data analysis. Thailand Statistician, 15, 69-77.
  12. Zamani, H. and Ismail, N. (2010). Negative binomial Lindley distribution and its application. Journal Mathematics and Statistics, 6, 4–9.