MATLAB: Fitdist – How does it work

fitdist

As far as I know, there are two ways to fit the data to a distribution:

1. Using the moments.

2. Maximum likelihood estimation.

Would you please help me understand which method does Matlab uses? How does the 'fitdist' function is used to fit the data into a given distribution?

Thanks in advance.

Berk

Best Answer

The fitdist function uses maximum likelihood. The exceptions are the normal and lognormal distributions. For the normal distribution, the mle of sigma^2 is 1/n times the sum of squared deviations from the mean. But using the factor 1/(n-1) instead is very common, because it makes the variance estimate unbiased. That's what fitdist uses. It does the analogous thing for lognormal.

The mle function uses maximum likelihood even in those two cases.

Related Solutions

MATLAB: Kstest and hypothesis rejecting

When in doubt, use help()

help kstest
 kstest Single sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
    H = kstest(X) performs a Kolmogorov-Smirnov (K-S) test to determine if
    a random sample X could have come from a standard normal distribution,
    N(0,1). H indicates the result of the hypothesis test:
       H = 0 => Do not reject the null hypothesis at the 5% significance

       level. 
       H = 1 => Reject the null hypothesis at the 5% significance
       level.

The null hypothesis depends on your inputs. Again, from the documentation using doc(ktest):

Test the null hypothesis that the data comes from a normal distribution with 
a mean of 75 and a standard deviation of 10. Use these parameters to center 
and scale each element of the data vector since, by default, kstest tests for 
a standard normal distribution.
x = (test1-75)/10;
h = kstest(x)

MATLAB: Covariance terms using fitdist()

pd.ParameterCovariance(2,2) is the covariance of the variance of the estimated normal distribution.

See https://www.mathworks.com/help/stats/prob.normaldistribution.html:

Covariance matrix of the parameter estimates, specified as a p-by-p matrix, where p is the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of the ith parameter and the jth parameter. The (i,i) element is the estimated variance of the ith parameter.

Best Answer

Related Solutions

MATLAB: Kstest and hypothesis rejecting

MATLAB: Covariance terms using fitdist()

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