Lognormal cumulative distribution function
p = logncdf(x,mu,sigma)
[p,plo,pup] = logncdf(x,mu,sigma,pcov,alpha)
[p,plo,pup] = logncdf(___,'upper')
p = logncdf(x,mu,sigma) returns
x of the lognormal cdf with distribution
the mean and standard deviation, respectively, of the associated normal
be vectors, matrices, or multidimensional arrays that all have the
same size. A scalar input for
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
pcov is the covariance matrix of the
confidence bounds. The default value of
pup are arrays
of the same size as
p containing the lower and
upper confidence bounds.
[p,plo,pup] = logncdf(___,'upper') returns
the complement of the lognormal cdf at each value in
using an algorithm that more accurately computes the extreme upper
tail probabilities. You can use
'upper' with any
of the previous syntaxes.
logncdf computes confidence bounds for
a normal approximation to the distribution of the estimate
and then transforming those bounds to the scale of the output
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 might be more accurate.
The lognormal cdf is
Compute the cdf of a lognormal distribution with
mu = 0 and
sigma = 1.
x = (0:0.2:10); y = logncdf(x,0,1);
Plot the cdf.
plot(x,y); grid; xlabel('x'); ylabel('p');
 Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993, pp. 102–105.