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matlabstatisticsnormal-distribution

Estimate the parameters of the normal distribution from which numbers are sampled

Given a vector of numbers sampled from the normal distribution, how do I estimate the parameters (i.e. the mean and variance) of the normal distribution from which those numbers were sampled?

Solution

  • The Matlab function you are looking for is normfit. If you call normfit with only one argument X, it will give you 2 outputs, an estimate of the mean and of the standard deviation:

    [muhat,sigmahat] = normfit(X)

    where the muhat is the estimate of mean and sigmahat the estimate of the standard deviation. Now if you call it with a second argument alpha it will give 4 outputs, the 2 estimates, and also the confidence intervals for each estimate:

    [muhat,sigmahat,muci,sigmaci] = normfit(X,alpha)

    muci contains are the confidence interval on the mean and sigmaci the confidence interval on the standard deviation.

    Example:

    >>a=randn(1,100);
>>[muhat,sigmahat,muci,sigmaci] = normfit(a,.01);
>>sigmaci

sigmaci =
    0.8550
    1.2360

    So P(0.8550< sigma< 1.2360) = 1-0.1.

    sigma_2 is the variance so by simply squaring sigmaci you have the confidence interval on sigma_2:

    >>sigma_2ci=sigmaci.^2
sigma_2ci =

0.7310    1.5277

    and P(0.7310< sigma_2< 1.5277) = 1-0.1.