TY - JOUR
T1 - Quasi-negative binomial distribution
T2 - Properties and applications
AU - Li, Shubiao
AU - Yang, Fang
AU - Famoye, Felix
AU - Lee, Carl
AU - Black, Dennis
N1 - Funding Information:
This work was completed while Felix Famoye, Central Michigan University, was on sabbatical leave at the Department of Mathematics, University of Lagos, Nigeria. Felix Famoye gratefully acknowledges the support received from the US Department of State, Bureau of Education and Cultural Affairs under the grant # 09-78737 . The authors are grateful to the anonymous referees for their valuable suggestions that improved the presentation.
PY - 2011/7/1
Y1 - 2011/7/1
N2 - In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.
AB - In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.
KW - Lagrange expansion
KW - Limiting distribution
KW - Tail property
KW - Zero-inflation
UR - http://www.scopus.com/inward/record.url?scp=79953652086&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2011.02.003
DO - 10.1016/j.csda.2011.02.003
M3 - Article
AN - SCOPUS:79953652086
VL - 55
SP - 2363
EP - 2371
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 7
ER -