Evaluates the MLE of the zero inflated Bell (ZIBELL) distribtion. The PMF of the ZIBELL distribution is as follows: $$ f\left(X=x\mid\alpha,\,\lambda\right)=\begin{cases} \alpha+\left(1-\alpha\right)\exp\left\{ \theta\left[1-e^{\lambda}\right]\right\} , & x=0\\ \left(1-\alpha\right)\exp\left\{ \theta\left[1-e^{\lambda}\right]\right\} \frac{\lambda^{x}\,B_{x}}{x!}, & x=1,2\cdots, \end{cases} $$ where \(\alpha\in(0,1)\), \(\lambda>0\) and \(B_{x}\) are the Bell numbers and it is given by $$B_{n}=\frac{1}{e}\sum_{k=0}^{\infty}\frac{k^{n}}{k!}.$$
mle_zibell (x, alpha, lambda)mle_zibell 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, \(\lambda>0\).
A vector of (non-negative integer) values, \(\alpha\in(0,1)\).
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 ZIBELL distribution with standard error of the estimate and model selection measure, the Akaike information criterion (AIC).
Castellares, F., Ferrari, S. L., & Lemonte, A. J. (2018). On the Bell distribution and its associated regression model for count data. Applied Mathematical Modelling, 56, 172-185.
mle_zibellt
x <- data_sbirth
mle_zibell (x, 0.2, 1.5)
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