Zero one inflated Poisson {countDM}

MLE of the zero one inflated Poisson distrubution

Description

Evaluates the MLE of the zero one inflated Poisson (ZOIP)distribtion.

f\left(X=x\mid\alpha,\,\beta,\,\theta\right)=\begin{cases} \alpha+\left(1-\alpha-\beta\right)e^{-\theta}, & x=0\\ \beta+\left(1-\alpha-\beta\right)\theta e^{-\theta}, & x=1\\ \left(1-\alpha-\beta\right)e^{-\theta}\frac{\theta^{x}\,}{x!}, & x=2,3,\dots \end{cases}

where \theta>0, the two parameters \alpha\in(0,1) and \beta\in(0,1), respectively denotes the unknown proportion for incorporating extra zeros and extra ones than those allowed by the traditional Poisson distribution.

Usage

mle_zoip (x, alpha, beta, theta)

Arguments

x

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

alpha

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

beta

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

theta

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

Details

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

Value

mle_zoip 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

Zhang, C., Tian, G. L., & Ng, K. W. (2016). Properties of the zero-and-one inflated Poisson distribution and likelihood-based inference methods. Statistics and its interface, 9(1), 11-32.

Tang, Y., Liu, W., & Xu, A. (2017). Statistical inference for zero-and-one-inflated Poisson models. Statistical Theory and Related Fields, 1(2), 216-226.

Alshkaki, R. S. A. (2016). On the zero-one inflated Poisson distribution. Int J Stat Distrib Appl, 2(4), 42-8.

See Also

mle_zoibell

Examples

x <- data_sbirth
mle_zoip (x, 0.2,0.1, 0.5)