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 distri- bution. In addition, we present some properties of the negative binomial-Erlang distribution including factorial moments, mean, variance, skewness and kurto- sis. The parameter estimation for negative binomial-Erlang distribution by the maximum likelihood estimation are provided. Applications of the the nega- tive 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.
Highlights
The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time, since data in multiple research fields often achieve the Poisson distribution
Let X be a random variable of the negative binomial (NB)-EL (r, k, c) distribution, when the NB distribution have parameters r > 0 and p = exp(−λ), where λ is distributed as the EL distribution with positive parameters k and c, i.e., X|λ ∼ NB(r, p = exp(−λ)) and λ ∼ EL(k, c)
We introduce a new three-parameter negative binomial-Erlang distribution, NB-EL(r, k, c)
Summary
The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time, since data in multiple research fields often achieve the Poisson distribution. In this paper we introduce a new mixed negative binomial distribution, which is called the negative binomial-Erlang (NB-EL) distribution. The NBEL distribution can be used to describe count data distribution with a large number of zeros in Poisson distribution. The Erlang (EL) distribution was introduced by Agner Erlang [1] was the first author to extend the exponential distribution with his method of stages. He defined a non-negative random variable as the time taken to move through a fixed number of stages, spending an exponential amount of time with a fixed rate in each one.
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