loglpdf
              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 ,
 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 , 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
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 ## 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")
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