norminv (Statistics Toolbox)

Inverse of the normal cumulative distribution function (cdf).

Syntax

X = norminv(P,MU,SIGMA)

Description

norminv(P,MU,SIGMA) computes the inverse of the normal cdf with parameters MU and SIGMA at the values in P. The arguments P, 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 and P must lie on [0 1].

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

The result, x, is the solution of the integral equation above with the parameters µ and

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.

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