Function Reference: logncdf

statistics: p = logncdf (x)
statistics: p = logncdf (x, mu)
statistics: p = logncdf (x, mu, sigma)
statistics: p = logncdf (…, "upper")
statistics: [p, plo, pup] = logncdf (x, mu, sigma, pcov)
statistics: [p, plo, pup] = logncdf (x, mu, sigma, pcov, alpha)
statistics: [p, plo, pup] = logncdf (…, "upper")

Log-normal cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the log-normal distribution with mean mu and standard deviation sigma corresponding to the associated normal distribution. The size of p is the common size of x, mu and sigma. A scalar input functions as a constant matrix of the same size as the other inputs.

If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma.

Default parameter values are mu = 0 and sigma = 1. Both parameters must be reals and sigma > 0. For sigma <= 0, NaN is returned.

When called with three output arguments, i.e. [p, plo, pup], logncdf computes the confidence bounds for p when the input parameters mu and sigma are estimates. In such case, pcov, a 2×2 matrix containing the covariance matrix of the estimated parameters, is necessary. Optionally, alpha, which has a default value of 0.05, specifies the 100 * (1 - alpha) percent confidence bounds. plo and pup are arrays of the same size as p containing the lower and upper confidence bounds.

[…] = logncdf (…, "upper") computes the upper tail probability of the log-normal distribution with parameters mu and sigma, at the values in x.

Further information about the log-normal distribution can be found at https://en.wikipedia.org/wiki/Log-normal_distribution

See also: logninv, lognpdf, lognrnd, lognfit, lognlike, lognstat

Source Code: logncdf

Example: 1

 

 ## Plot various CDFs from the log-normal distribution
 x = 0:0.01:3;
 p1 = logncdf (x, 0, 1);
 p2 = logncdf (x, 0, 0.5);
 p3 = logncdf (x, 0, 0.25);
 plot (x, p1, "-b", x, p2, "-g", x, p3, "-r")
 grid on
 legend ({"μ = 0, σ = 1", "μ = 0, σ = 0.5", "μ = 0, σ = 0.25"}, ...
         "location", "southeast")
 title ("Log-normal CDF")
 xlabel ("values in x")
 ylabel ("probability")

                    
plotted figure