Poisson {countDM}

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)

Arguments

x

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

theta

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

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).

Value

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

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)