Statistics Toolbox |

Inverse of the normal cumulative distribution function (cdf)

**Syntax**

**Description**

```
X = norminv(P,MU,SIGMA)
```

computes the inverse of the normal cdf with parameters MU and SIGMA at the corresponding probabilities in `P`

. Vector or matrix inputs for P, 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, and the values in `P`

must lie on the interval [0 1].

We define the normal inverse function in terms of the normal cdf as

The result, *x*, is the solution of the integral equation above where you supply the desired probability, *p*.

**Examples**

Find an interval that contains 95% of the values from a standard normal distribution.

Note the interval `x`

is not the only such interval, but it is the shortest.

The interval `xl`

also contains 95% of the probability, but it is longer than `x`

.

**See Also**

`icdf`

, `normfit`

, `normfit`

, `normpdf`

, `normplot`

, `normrnd`

, `normspec`

, `normstat`

normfit | normlike |