Re: Gaussian distribution and likelihood question

On Jan 30, 5:55 pm, "Ray Koopman" <koop...@xxxxxx> wrote:
On Jan 29, 10:06 am, "zl2k" <kdsfin...@xxxxxxxxx> wrote:



hi,
My question is: is there any method to measure how a data set fits a
Gaussian model? Suppose I have one dataset A which has N elements and
another dataset B which has M elements. From each of the dataset I can
estimate one Gaussian model, thus I have (mu1, sigma1) for A and (mu2,
sigma2) for B. How can I tell which dataset fits the Gaussian model
better? (skewness and kurtosis does not tell about fitness)
What I am thinking is from the Gaussian model I can generate the same
amount of elements and those elements should fit the model best. Then
I can compare the log-likelihood of the real dateset to the generated
dataset. But, to produce a psudo dataset from a Gaussian model is not
efficient. My next question is: is there a 1-step formula to get the
log-likelihood of the "theorically perfect Gaussian dataset" with N
elements? Basically, find the most possible log-likelihood of N
elements from Gaussian model(mu, sigma).
Thanks for your comments.
zl2k

The normal likelihood depends on the data only through the mean
and variance. All data sets with the same number of observations,
the same sample mean, and the same sample variance will have the
same likelihood, regardless of the shape of the sample distribution.

Thank you, so log-likelihood won't tell the goodness of fit of
different datasets if the Gaussian parameters are the same. I should
turn to some other ways...
zl2k

.

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