Function Reference: loglpdf

statistics: y = loglpdf (x, a, b)

Log-logistic probability density function (PDF).

For each element of x, compute the probability density function (PDF) of the log-logistic distribution with with scale parameter a and shape parameter b. The size of y 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, otherwise NaN is returned. x is supported in the range [0,Inf), otherwise 0 is returned.

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: loglcdf, loglinv, loglrnd, loglfit, logllike

Source Code: loglpdf

Example: 1

 

 ## Plot various PDFs from the log-logistic distribution
 x = 0:0.001:2;
 y1 = loglpdf (x, 1, 0.5);
 y2 = loglpdf (x, 1, 1);
 y3 = loglpdf (x, 1, 2);
 y4 = loglpdf (x, 1, 4);
 y5 = loglpdf (x, 1, 8);
 plot (x, y1, "-b", x, y2, "-g", x, y3, "-r", x, y4, "-c", x, y5, "-m")
 grid on
 ylim ([0,3])
 legend ({"β = 0.5", "β = 1", "β = 2", "β = 4", "β = 8"}, ...
         "location", "northeast")
 title ("Log-logistic PDF")
 xlabel ("values in x")
 ylabel ("density")
 text (0.5, 2.8, "α = 1, values of β as shown in legend")

                    
plotted figure