EWGoF (version 2.2.2)

MLEst: Maximum Likelihood Estimators of the two parameters of the Weibull distribution

Description

This function computes the Maximum Likelihood Estimators (MLEs) of the shape and scale parameters of the Weibull distribution from an i.i.d sample x. It also gives the sample \(\hat{y}\) after using the logarithmic transformation (\(\hat{y}=(\hat{shape})\ln(x/\hat{scale})\), where \(\hat{shape}\) and \(\hat{scale}\) are the estimated shape and scale parameters).

Usage

MLEst(x)

Arguments

x

a numeric vector of data values.

Value

A list containing the following elements:

eta

the maximum likelihood estimator of the scale parameter of the Weibull distribution (\(\hat{scale}\)).

beta

the maximum likelihood estimator of the shape parameter of the Weibull distribution (\(\hat{shape}\)).

y

the pseudo-observations \(\hat{y}\) after using the logarithmic transformation and the MLEs.

Details

The elements of the numeric vector should be positive. The support of the Weibull distribution is R+*.

References

D'Agostino R.B. and Stephens M.A., Goodness-of-fit techniques, Marcel Dekker, 1986.

Krit M., Gaudoin O., Xie M. and Remy E., Simplified likelihood goodness-of-fit tests for the Weibull distribution, Communications in Statistics - Simulation and Computation.

Examples

# NOT RUN {
x <- rweibull(50,2,3)

Est <- MLEst(x)

#Value of the maximum likelihood estimator of the scale parameter
Est$eta

#Value of the maximum likelihood estimator of the shape parameter
Est$beta
# }