Zero inflated Bell {countDM}

MLE of the zero inflated Bell distribtion

Description

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!}.

Usage

mle_zibell (x, alpha, lambda)

Arguments

x

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

lambda

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

alpha

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

Details

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).

Value

mle_zibell 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_zibellt

Examples

x <- data_sbirth
mle_zibell (x, 0.2, 1.5)