The purpose of this study is to compare a negative binomial distribution with a negative binomial—Lindley by using stochastic orders. We characterize the comparisons in usual stochastic order, likelihood ratio order, convex order, expectation order and uniformly more variable order based on theorem and some numerical example of comparisons between negative binomial random variable and negative binomial—Lindley random variable.
References
[1]
W. Rainer, “Econometric Analysis of Count Data,” 3rd Edition, Springer-Verlag, Berlin, 2000.
[2]
H. Zamani and N. Ismail, “Negative Binomial—Lindley Distribution and Its Application,” Journal of Mathematics and Statistics, Vol. 6, No. 1, 2010, pp. 4-9.
doi:10.3844/jmssp.2010.4.9
[3]
M. Shaked and J. G. Shanthikumar, “Stochastic Orders,” Academic Press, New York, 2006.
[4]
S. M. Ross, “Stochastic Processes,” Wiley, New York, 1983.
[5]
N. Misra, H. Singh and E. J. Harner, “Stochastic Comparisons of Poisson and Binomial Random Variables with Their Mixtures,” Statistics and Probability Letters, Vol. 65, No. 4, 2003, pp. 279-290.
doi:10.1016/j.spl.2003.07.002
[6]
M. Shaked, “On Mixtures from Exponential Families,” Journal of the Royal Statistical Society: Series B, Vol. 42, No. 2, 1980, pp. 192-198.
[7]
M. Shaked and J. G. Shanthikumar, “Stochastic Orders and Their Applications,” Academic Press, New York, 1994.
[8]
H. Singh, “On Partial Orderings of Life Distributions,” Naval Research Logistics, Vol. 36, No. 1, 1989, pp. 103- 110.
doi:10.1002/1520-6750(198902)36:1<103::AID-NAV3220360108>3.0.CO;2-7
