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.
mle_zoip (x, alpha, beta, theta)mle_zoip gives the MLE along with standard error of the estimate and model selction measure AIC.
A vector of (non-negative integer) values, discrete values.
A vector of (non-negative integer) values, \(\alpha\in(0,1)\).
A vector of (non-negative integer) values, \(\beta\in(0,1)\).
A vector of (non-negative integer) values, \(\theta>0\).
Muhammad Imran and M.H. Tahir.
R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H. Tahir <mht@iub.edu.pk>.
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).
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.
mle_zoibell
x <- data_sbirth
mle_zoip (x, 0.2,0.1, 0.5)
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