IJPAM: Volume 92, No. 3 (2014)
DISTRIBUTION WITH APPLICATIONS
Department of Statistics
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
Pages: 389 - 401
This work is licensed under the Creative Commons Attribution International License (CC BY).