Evaluates the MLE of the zero one inflated Bell (ZOIBELL)distribtion. $$ f\left(X=x\mid\alpha,\,\beta,\,\theta\right)=\begin{cases} \alpha+\left(1-\alpha-\beta\right)\exp\left(1-e^{\theta}\right), & x=0\\ \beta+\left(1-\alpha-\beta\right)\theta\exp\left(1-e^{\theta}\right), & x=1\\ \left(1-\alpha-\beta\right)\exp\left(1-e^{\theta}\right)\frac{\theta^{x}\,B_{x}}{x!}, & x=2,3,\dots, \end{cases} $$ 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 Bell distribution.
mle_zoibell (x, alpha, beta, theta)mle_zoibell 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, \(\theta>0\).
A vector of (non-negative integer) values, \(\alpha\in(0,1).\)
A vector of (non-negative integer) values, \(\beta\in(0,1). \)
Muhammad Imran and M.H. Tahir.
R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H. Tahir <mht@iub.edu.pk>.
Inflated models have become quite popular in the recent applied statistical literature. In many scientific studies, we often experience situations, the data consists of a large proportion of zeros and ones. Castellares et al. proposed a single-parameter discrete Bell distribution. We extended the Bell distribution into zero one inflated Bell distribution.
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_zoip
x <- data_sbirth
mle_zoibell (x, 0.1,0.2,0.2)
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