Statistics: logncdf

### 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 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 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")