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)
Value
mle_borel gives the MLE along with standard error of the estimate and model selction measure AIC.
Arguments
x
A vector of (non-negative integer) discrete values.
alpha
A vector of (non-negative integer) values, \(\alpha\in(0,1)\).
Author
Muhammad Imran and M.H. Tahir.
R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H. Tahir <mht@iub.edu.pk>.
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).
References
Tanner, J. C. (1961). A derivation of the Borel distribution. Biometrika, 48(1/2), 222-224.