Zero inflated Poisson {countDM}

MLE of the zero inflated Poisson distribtion

Description

Evaluates the MLE of the zero inflated Poisson (ZIP) distribtion. The PMF of the ZIP is as follows:

f\left(X=x\mid\alpha,\,\theta\right)=\begin{cases} \alpha+\left(1-\alpha\right)e^{-\theta}, & x=0\\ \left(1-\alpha\right)\frac{\theta^{x}e^{-\theta}}{x!}, & x=1,2\cdots, \end{cases}

where \alpha\in(0,1) denotes the probability of extra zeros and \theta>0 is a Poisson parameter, which is also its mean and variance.

Usage

mle_zip (x, alpha, theta)

Arguments

x

A vector of (non-negative integer) discrete values.

theta

A vector of (non-negative integer) values, \theta>0.

alpha

A vector of (non-negative integer) values, \alpha\in(0,1).

Details

The function allows to estimate the unknown parameter of the ZIP distribution with standard error of the estimate and model selection measure, the Akaike information criterion (AIC).

Value

mle_zip gives the MLE along with standard error of the estimate and model selction measure AIC.

Author(s)

Muhammad Imran and M.H. Tahir.

R implementation and documentation: Muhammad Imran [e-mail] and M.H. Tahir <[e-mail]>.

References

Beckett, S., Jee, J., Ncube, T., Pompilus, S., Washington, Q., Singh, A., & Pal, N. (2014). Zero-inflated Poisson (ZIP) distribution: Parameter estimation and applications to model data from natural calamities. Involve, a Journal of Mathematics, 7(6), 751-767.

See Also

mle_zibell, mle_zibellt

Examples

x <- data_sbirth
mle_zip (x, 0.2, 1.5)