Normal inverse cumulative distribution function
X = norminv(P)
X = norminv(P,mu,sigma)
[X,XLO,XUP] = norminv(P,mu,sigma,pcov,alpha)
X = norminv(P) computes the inverse of the standard normal cdf. The
standard normal distribution has parameters
mu = 0 and
P can be a vector, matrix, or multidimensional array, and
the values in
P must lie in the interval [0 1].
X = norminv(P,mu,sigma) computes the inverse of the
normal cdf using the corresponding mean
mu and standard deviation
sigma at the corresponding probabilities in
sigma can be vectors,
matrices, or multidimensional arrays that all have the same size. A scalar input is expanded
to a constant array with the same dimensions as the other inputs. The parameters in
sigma must be positive, and the values in
P must lie
in the interval [0 1].
[X,XLO,XUP] = norminv(P,mu,sigma,pcov,alpha) produces confidence
X when the input parameters
sigma are estimates.
pcov is the covariance matrix of
the estimated parameters.
alpha specifies 100(1 -
alpha)% confidence bounds. The default value of
XUP are arrays of the
same size as
X containing the lower and upper confidence bounds.
norminv computes confidence bounds for
P using a normal approximation to the distribution of the estimate
where q is the
Pth quantile from a normal
distribution with mean 0 and standard deviation 1. The computed bounds give approximately the
desired confidence level when you estimate
pcov from large samples, but in smaller samples other methods of
computing the confidence bounds may be more accurate.
The normal inverse function is defined 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.
Find an interval that contains 95% of the values from a standard normal distribution.
x = norminv([0.025 0.975]) x = -1.9600 1.9600
Note that the interval
x is not the only
such interval, but it is the shortest.
xl = norminv([0.01 0.96]) xl = -2.3263 1.7507
xl also contains 95% of the
probability, but it is longer than