Evaluating goodness of fit of a probability distribution at a certain interval

Hi all,

I fitted probability distributions to some data and would like to evaluate their goodness of fit with

kstest
adtest
chi2gof

However, I am only interested in the lower tail of the distribution, and would therefore like to weight the tail higher, or restrain the evaluation to the lower half of the probability distribution object. So far I tried to use

truncate

, but then the pd rescales, so that the integral of the pdf would still be 1. Does anyone know how to avoid this or a different approach?

Cheers,

Darragh

[Torsten]

Shouldn't this "weighting" already be applied during the fitting process ?

[Darragh Kenny]

Yes, that would be even better! Not sure how to implement it though

[Jeff Miller]

Could you say a bit more about why truncate isn't satisfactory? It seems to me that if you truncate both the pd and the observations in the dataset at the same truncation point, then you are automatically weighting only the tail in the fitting process and also automatically evaluating only the fit of the tail with kstest, etc.

[Darragh Kenny]

pd=makedist('normal','mu',1,'sigma',1);
pd_trunc=truncate(pd,0,mean(asdf))
plot(-5:.1:5,pdf(pd,-5:.1:5))
hold on;
plot(-5:.1:5,pdf(pd_trunc,-5:.1:5))

Inside the truncation interval, the pdf of pd_trunc is not equal to the pdf of pd, because it is divided by the probability assigned to that interval by pd. Therefore, in this example pd_trunc will be larger than pd in the truncation interval. pd_trunc is scaled so that its integral is still 1.

Answer 1

[Jeff Miller]

Do you want to rescale the pdf back like this?

pd=makedist('normal','mu',1,'sigma',1);
pd_trunc=truncate(pd,0,mean(asdf))
plot(-5:.1:5,pdf(pd,-5:.1:5))
frac = cdf(pd,mean(asdf)) - cdf(pd,0)
hold on;
plot(-5:.1:5,pdf(pd_trunc,-5:.1:5)*frac)