Zero one inflated Bell {countDM}

MLE of the zero one inflated Bell distrubution

Description

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.

Usage

mle_zoibell (x, alpha, beta, theta)

Arguments

x

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

theta

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

alpha

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

beta

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

Details

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.

Value

mle_zoibell 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

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.

See Also

mle_zoip

Examples

x <- data_sbirth
mle_zoibell (x, 0.1,0.2,0.2)