countDM (version 0.1.0)

Poisson: MLE of the Poisson distribution

Description

Evaluates the MLE of the Poisson distribtion. The PMF of the Poisson distribution is as follows: $$ f\left(X=x\mid\,\theta\right)=\frac{\theta^{x}e^{-\theta}}{x!};\qquad x=0,1,2,\dots, $$ where parameter \(\theta>0\) and it is equal to the expected or mean value of X and also to its variance.

Usage

mle_poisson (x, theta)

Value

mle_poisson gives the MLE along with standard error of the estimate and model selection measure AIC.

Arguments

x

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

theta

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

Author

Muhammad Imran and M.H. Tahir.

R implementation and documentation: Muhammad Imran and M.H. Tahir <[e-mail]>.

Details

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

References

Frank A. Haight (1967). Handbook of the Poisson Distribution. New York: John Wiley & Sons.

See Also

mle.bell, mle_borel

Examples

x <- data_sbirth
mle_poisson (x, 0.2)