Article Sidebar

Download
PDF
Statistic
Read Counter : 672 Download : 757

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Based on the results, it is shown that the proposed distribution provides a better fit compared to the Poisson, negative binomial, and its sub-model for count data.

Keywords

Count data Over-dispersion Mixture distribution Negative binomial-new generalized Lindley distribution Maximum likelihood estimation

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

Author Biography

Sirinapa Aryuyuen, Rajamangala University of Technology Thanyaburi

Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thailand

How to Cite
Aryuyuen, S. (2022). The Negative Binomial-New Generalized Lindley Distribution for Count Data: Properties and Application. Pakistan Journal of Statistics and Operation Research, 18(1), 167-177. https://doi.org/10.18187/pjsor.v18i1.2988
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Casella, G. & R. Berger. (2002). Statistical Inference, 2nd ed. Duxbury Press, Paciï¬c Grove, CA.
  2. Elbatal, I., Merovci, F. & Elgarhy, M. (2013). A new generalized Lindley distribution. Mathematical Theory and Modeling, 3(13), 30-47.
  3. Flynn, M. & Francis, L. A. (2009). More flexible GLMs zero-inflated models and hybrid models. Casualty Actuarial Soc, 148-224.
  4. Gençtürk, Y. & Yiğiter, A. (2016). Modelling claim number using a new mixture model: negative binomial gamma distribution. Journal of Statistical Computation and Simulation, 86(10), 1829-1839.
  5. Ghitany, M. E., Atieh, B. & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and Computers in Simulation, 78(4), 493-506.
  6. Gómez-Déniz, E., Sarabia, J. M. & Calderín-Ojeda, E. (2008). Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications. Insurance: Mathematics and Economics, 42(1), 39-49.
  7. Greenwood, M. & Yule, G. U. (1920). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. Journal of the Royal Statistical Society, 83(2), 255-279.
  8. Gupta, R. D. & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
  9. Jambunathan M. B. (1954). Some properties of beta and gamma distributions. The annals of mathematical statistics. 25(2), 401-405.
  10. Johnson, N. L., Kemp, A. W. & Kotz, S. (2005). Univariate discrete distributions, 444, John Wiley & Sons.
  11. Klugman, S.A., Panjer H.H. & Willmot G.E. (2008). Loss Models: From Data to Decision. 3rd Edn., John Wiley and Sons, USA : 101-159.
  12. Lord, D. & Geedipally, S. R. (2011). The negative binomial-Lindley distribution as a tool for analyzing crash data characterized by a large amount of zeros. Accident Analysis & Prevention, 43(5), 1738-1742.
  13. Marsaglia, G., Tsang, W. W. & Wang, J. (2003), Evaluating Kolmogorov's distribution. Journal of Statistical Software, 8(18), 1-4.
  14. Panjer, H. H. & Willmot, G. E. (1981). Finite sum evaluation of the negative binomial-exponential model. ASTIN Bulletin: The Journal of the IAA, 12(2), 133-137.
  15. R Core Team. (2018). R: A language and environment for statistical computing.
  16. Rainer, W. (2000). Econometric Analysis of Count Data, 3rd edn, Springer Verlag, Berlin, Germany.
  17. Sankaran, M. (1970). The discrete Poisson-Lindley distribution, Biometrics, 26(1), 145-149.
  18. Wang, Z. (2011). One mixed negative binomial distribution with application. Journal of Statistical Planning and Inference, 141(3), 1153-1160.
  19. Zamani, H. & Ismail, N. (2010). Negative binomial-Lindley distribution and its application. Journal of Mathematics and Statistics, 6(1), 4-9.