Statistics: loglcdf

### Function Reference: `loglcdf`

statistics: p = loglcdf (x, a, b)
statistics: p = loglcdf (x, a, b, `"upper"`)

Log-logistic cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the log-logistic distribution with scale parameter a and shape parameter b. The size of p is the common size of x, a, and b. A scalar input functions as a constant matrix of the same size as the other inputs.

Both parameters, a and b, must be positive reals and x is supported in the range [0,inf), otherwise `NaN` is returned.

`p = loglcdf (x, a, b, "upper")` computes the upper tail probability of the log-logistic distribution with parameters a and b, at the values in x.

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

MATLAB compatibility: MATLAB uses an alternative parameterization given by the pair μ, s, i.e. mu and s, in analogy with the logistic distribution. Their relation to the a and b parameters is given below:

- `a = exp (mu)`
- `b = 1 / s`

See also: loglinv, loglpdf, loglrnd, loglfit, logllike

Source Code: loglcdf

### Example: 1

     ## Plot various CDFs from the log-logistic distribution
     x = 0:0.001:2;
     p1 = loglcdf (x, 1, 0.5);
     p2 = loglcdf (x, 1, 1);
     p3 = loglcdf (x, 1, 2);
     p4 = loglcdf (x, 1, 4);
     p5 = loglcdf (x, 1, 8);
     plot (x, p1, "-b", x, p2, "-g", x, p3, "-r", x, p4, "-c", x, p5, "-m")
     legend ({"β = 0.5", "β = 1", "β = 2", "β = 4", "β = 8"}, ...
             "location", "northwest")
     grid on
     title ("Log-logistic CDF")
     xlabel ("values in x")
     ylabel ("probability")
     text (0.05, 0.64, "α = 1, values of β as shown in legend")