normpdf (Statistics Toolbox)

Normal probability density function (pdf)

Syntax

```
Y = normpdf(X,MU,SIGMA)
```

Description

normpdf(X,MU,SIGMA) computes the normal pdf at each of the values in X using the corresponding parameters in MU and SIGMA. Vector or matrix inputs for X, MU, and SIGMA must all have the same size. A scalar input is expanded to a constant matrix with the same dimensions as the other inputs. The parameters in 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

normlike normplot