normpdf (Statistics Toolbox)

Normal probability density function (pdf).

Syntax

Y = normpdf(X,MU,SIGMA)

Description

normpdf(X,MU,SIGMA) computes the normal pdf with parameters mu and SIGMA at the values in X. The arguments X, MU and SIGMA must all be the same size except that scalar arguments function as constant matrices of the common size of the other arguments.

The parameter SIGMA must be positive.

The normal pdf is:

The likelihood function is the pdf viewed as a function of the parameters. Maximum likelihood estimators (MLEs) are the values of the parameters that maximize the likelihood function for a fixed value of x.

The standard normal distribution has µ = 0 and

= 1.

If x is standard normal, then x

+ µ is also normal with mean µ and standard deviation

. Conversely, if y is normal with mean µ and standard deviation

, then x = (y -µ)/

is standard normal.

Examples

mu = [0:0.1:2];
[y i] = max(normpdf(1.5,mu,1));
MLE = mu(i)

MLE =

    1.5000

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