### 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"`)

Lognormal cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the lognormal distribution with mean parameter mu and standard deviation parameter sigma, each 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 lognormal 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")