Statistics Toolbox™

logncdf - Lognormal cumulative distribution function

Syntax

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

Description

P = logncdf(X,mu,sigma) returns values at X of the lognormal cdf with distribution parameters mu and sigma. mu and sigma are the mean and standard deviation, respectively, of the associated normal distribution. X, mu, and sigma can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input for X, mu, or sigma is expanded to a constant array with the same dimensions as the other inputs.

[P,PLO,PUP] = logncdf(X,mu,sigma,pcov,alpha) returns 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.

logncdf 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 lognormal cdf is

Example

x = (0:0.2:10);
y = logncdf(x,0,1);
plot(x,y); grid;
xlabel('x'); ylabel('p');

Reference

[1] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993, pp. 102–105.

See Also

cdf, lognpdf, logninv, lognstat, lognfit, lognlike, lognrnd

linkage

lognfit