You can calculate GOF using AIC (from my PhD):

AIC represents a measure of the ‘goodness of fit’ of an estimated statistical model:

AIC = −2loge L (θ | data) + 2K = −2MLL + 2K

where K is the number of estimable parameters in the approximating model .

AIC provides a measure of model fit, accounting for the sample size and the number of parameters estimated in the model, with smaller values of AIC indicating a better-fitting model. Delta (Δ) AIC is the difference in AIC between a model and the best-fitting ‘final’ model, which has ΔAIC of 0. Models with ΔAIC ≤ 2 have substantial support, those with 4 ≤ ΔAIC ≤ 7 have weaker support, and those with ΔAIC > 10 have virtually no support. Where multiple models have ΔAIC ≤ 2, the model with the lowest AIC value is the ‘final’ model.

For a fixed set of data and underlying probability model, MLL ‘picks’ the values of the model parameters that make the data ‘more likely’ than any other values of the parameters would make them.

MLL = loge L (θ | data)

where loge L (θ | data) is the value of maximized log-likelihood over unknown parameters (θ), given the data and the model.

I hope this helps :-)

You can also try gofstat function

Andrew,thank you

The suggested test is already calculated by the R function fitdistrplus package tests GOF tests like:

Goodness-of-fit statistics:

• Kolmogorov-Smirnov
• Cramer-von Mises
• Anderson-Darling

Goodness-of-fit criteria

• Aikake's
• bayesian

I'm trying to use this test> gofstat

Greetings.

Hello, Anderson

Exactly this gofstat function I'm trying to use.

The program performs parameter estimates by maximum likelihood and then performs GOF test statistics. I'm trying to enter my estimates for GOF testing.

Here's what the program does:

X my data

> dist.wbl dist.wbl

Fitting of the distribution ' weibull ' by maximum likelihood 

Parameters:

estimate Std. Error

shape 1.488095 0.1699613

scale 46072.261690 4377.2569648

> gofstat(dist.wbl)

Goodness-of-fit statistics

1-mle-weibull

Kolmogorov-Smirnov statistic 0.09208698

Cramer-von Mises statistic 0.04004545

Anderson-Darling statistic 0.25809205

Goodness-of-fit criteria

1-mle-weibull

Aikake's Information Criterion 1134.867

Bayesian Information Criterion 1138.651

See that all the results use the estimation by maximum likelihood. I want to perform these tests with the values of the parameters estimated by my method.

Greetings.

Hola Joelton,

Here's another route using another package

install.packages("fitdistrplus")

library(fitdistrplus)

xw xw

Fitting of the distribution ' weibull ' by maximum likelihood

Parameters:

estimate Std. Error

shape 1.488095 0.1699613

scale 46072.261690 4377.2569648

> summary(xw)

Fitting of the distribution ' weibull ' by maximum likelihood

Parameters :

estimate Std. Error

shape 1.488095 0.1699613

scale 46072.261690 4377.2569648

Loglikelihood: -565.4336 AIC: 1134.867 BIC: 1138.651

Correlation matrix:

shape scale

shape 1.0000000 0.2860867

scale 0.2860867 1.0000000

plot(xw) # plots attached

Reference

file:///C:/Users/Faye/Downloads/v64i04.pdf

The plot gives you 4 tests of GOF.

Suerte!