Borel {countDM}

MLE of the Borel distribution

Description

Evaluates the MLE of the Borel distribution. It is defined by the following PMF:

f(X=x\mid \alpha)=\frac{\left(\alpha x\right)^{x-1}e^{-\alpha x}}{x!};\qquad x=1,2,\dots,

where the parameter \alpha\in(0,1).

Usage

mle_borel (x, alpha)

Arguments

x

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

alpha

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

Details

The function allows to estimate the unknown parameter of the Borel distribution with standard error of the estimate and model selection measure, the Akaike information criterion (AIC).

Value

mle_borel 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

Tanner, J. C. (1961). A derivation of the Borel distribution. Biometrika, 48(1/2), 222-224.

See Also

mle.bell, mle_poisson

Examples

x <- c(rep(1,48), rep(2,20), rep(3,7), rep(4,5),rep(5,2),rep(6,6))
mle_borel (x, 0.8)