Statistics Toolbox™

normcdf - Normal cumulative distribution function

Syntax

P = normcdf(X,mu,sigma)
[P,PLO,PUP] = normcdf(X,mu,sigma,pcov,alpha)

Description

P = normcdf(X,mu,sigma) computes the normal cdf at each of the values in X using the corresponding parameters in mu and sigma. X, mu, and 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.

[P,PLO,PUP] = normcdf(X,mu,sigma,pcov,alpha) produces confidence bounds for P when the input parameters mu and sigma are estimates. pcov is the covariance matrix of the estimated parameters. alpha specifies 100(1 - alpha)% confidence bounds. The default value of alpha is 0.05. PLO and PUP are arrays of the same size as P containing the lower and upper confidence bounds.

The function normdf computes confidence bounds for P using a normal approximation to the distribution of the estimate

and then transforming those bounds to the scale of the output P. The computed bounds give approximately the desired confidence level when you estimate mu, sigma, and pcov from large samples, but in smaller samples other methods of computing the confidence bounds might be more accurate.

The normal cdf is

The result, p, is the probability that a single observation from a normal distribution with parameters µ and σ will fall in the interval (-∞ x].

The standard normal distribution has µ = 0 and σ = 1.

Examples

What is the probability that an observation from a standard normal distribution will fall on the interval [-1 1]?

p = normcdf([-1 1]);
p(2)-p(1)
ans =
  0.6827

More generally, about 68% of the observations from a normal distribution fall within one standard deviation, σ, of the mean, µ.

See Also

cdf, normpdf, norminv, normstat, normfit, normlike, normrnd

nominal

normfit