IJPAM: Volume 92, No. 3 (2014)

THE NEGATIVE BINOMIAL-ERLANG
DISTRIBUTION WITH APPLICATIONS

Siriporn Kongrod$^1$, Winai Bodhisuwan$^2$, Prasit Payakkapong$^3$
$^{1,2,3}$Department of Statistics
Kasetsart University
Chatuchak, Bangkok, 10900, THAILAND


Abstract. This paper introduces a new three-parameter of the mixed negative binomial distribution which is called the negative binomial-Erlang distribution. This distribution obtained by mixing the negative binomial distribution with the Erlang distribution. The negative binomial-Erlang distribution can be used to describe count data with a large number of zeros. The negative binomial-exponential is presented as special cases of the negative binomial-Erlang distribution. In addition, we present some properties of the negative binomial-Erlang distribution including factorial moments, mean, variance, skewness and kurtosis. The parameter estimation for negative binomial-Erlang distribution by the maximum likelihood estimation are provided. Applications of the the negative binomial-Erlang distribution are carried out two real count data sets. The result shown that the negative binomial-Erlang distribution is better than fit when compared the Poisson and negative binomial distributions.

Received: December 4, 2013

AMS Subject Classification: 60E05

Key Words and Phrases: mixed distribution, count data, Erlang distribution, the negative binomial-Erlang distribution, overdispersion

Download paper from here.




DOI: 10.12732/ijpam.v92i3.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 3
Pages: 389 - 401

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).