Binomial-Discrete Lindley Distribution

Abstract

In this paper, a new discrete distribution called Binomial-Discrete Lindley (BDL) distribution is proposed by compounding the binomial and discrete Lindley distributions. Some properties of the distribution are discussed including the moment generating function, moments and hazard rate function. The estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square errors. Automobile claim data applications are also presented to see that the new distribution is useful in modelling data.

Keywords

• Binomial distribution,discrete Lindley distribution,discrete distributions,estimation

References

1. Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı I. and Sharafi, F., Uniform-geometric distribution. Journal of Statistical Computation and Simulation 86(9), (2016), 1754-1770.
2. Bakouch, H.S., Jazi, M.A. and Nadajarah, S., A new discrete distribution, Statistics: A Journal of Theoretical and Applied Statistics 48(1), (2014), 200-240.
3. Chakaraborty, S. and Chakaraborty, D., Discrete gamma distribution: Properties and Parameter Estimation. Communications in Statistics-Theory and Methods 41, (2012), 3301-3324.
4. Déniz, E.G., A new discrete distribution: Properties and applications in medical care. Journal of Applied Statistics 40(12), (2013), 2760-2770.
5. Déniz, E.G. and Ojeda, E.C., The discrete Lindley distribution: properties and applications, Journal of Statistical Computation and Simulation 81(11), (2011), 1405-1416.
6. Gupta, P.L., Gupta, R.C. and Tripathi, R.C., On the Monotonic Properties of Discrete Failure Rates, J. Statist. Plann. Inference 65, (1997), 255-268.
7. Gossiaux, A.M. and Lemaire, J. Methodes d'ajustement de distributions de sinistres. (1981). MVSV, 87-95.
8. Hu, Y., Peng, X., Li, T. and Guo, H., On the Poisson approximation to photon distribution for faint lasers. Phys. Lett 367, (2007), 173-176.

9. Khan, M.S.A., Khalique, A. and Abouammoh, A.M., On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability 38(3), (1989), 348-350.
10. Krishna, H. and Pundir, P.S., Discrete Burr and discrete Pareto distributions. Statistical Methodology 6, (2009), 177-188.
11. Mark, Y.A., Log-concave Probability Distributions: Theory and Statistical Testing, working paper, 96 - 01, Published by Center for Labour Market and Social Research, University of Aarhus and the Aarhus School of Business, Denmark, 1996.
12. Mark, B. and Bergstrom, T. Log-concave Probability and its Applications, Economic Theory 26, (2005), 445-469.
13. Nakagawa, T. and Osaki, S., Discrete Weibull distribution. IEEE Transactions on Reliability 24, (1975), 300-301.
14. Noughabi, M.S., Roknabadi, A.H.R. ve Borzadaran, G.R.M. Some discrete lifetime distributions with bathtub-shaped hazard rate functions. Quality Engineering 25, (2013), 225-236.
15. Roy, D., Discrete Rayleigh distribution. IEEE Transactions on Reliability 53(2), (2004), 255-260.
16. Roy, D., The discrete normal distribution. Communications in Statistics Theory and Methods 32(10), (2003), 1871-1883.
17. Stein, W.E. and Dattero, R., A new discrete Weibull distribution. IEEE Transactions on Reliability R-33 (1984), 196-197.
18. Steutel, F.W., Log-concave and Log-convex Distributions, Encyclopedia of Statistical Sciences (eds S. Kotz, N.L. Johnson and C. B. Read), 5, 116-117, New York: Wiley, 1985.
19. Willmot, G.E., The Poisson-inverse Gaussian distribution as an alternative to the negative binomial, Scand. Actuarial J. (1987), 113-127.