Statistics Toolbox
norminv

Inverse of the normal cumulative distribution function (cdf)

Syntax

• ```X = norminv(P,MU,SIGMA)
```

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

where

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.

• ```x = norminv([0.025 0.975],0,1)
x =
-1.9600    1.9600
```

Note the interval `x` is not the only such interval, but it is the shortest.

• ```xl = norminv([0.01 0.96],0,1)
xl =
-2.3263    1.7507
```

The interval `xl` also contains 95% of the probability, but it is longer than `x`.