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")

                    
plotted figure