Function Reference: loglinv

statistics: x = loglinv (p, mu, sigma)

Inverse of the log-logistic cumulative distribution function (iCDF).

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

Both parameters, mu and sigma, must be positive reals and p is supported in the range [0,1], otherwise NaN is returned.

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

OCTAVE/MATLAB use an alternative parameterization given by the pair μ, σ, i.e. mu and sigma, in analogy with the logistic distribution. Their relation to the α and b parameters used in Wikipedia are given below:

  • mu = log (a)
  • sigma = 1 / a

See also: loglcdf, loglpdf, loglrnd, loglfit, logllike, loglstat

Source Code: loglinv

Example: 1

  

 ## Plot various iCDFs from the log-logistic distribution
 p = 0.001:0.001:0.999;
 x1 = loglinv (p, log (1), 1/0.5);
 x2 = loglinv (p, log (1), 1);
 x3 = loglinv (p, log (1), 1/2);
 x4 = loglinv (p, log (1), 1/4);
 x5 = loglinv (p, log (1), 1/8);
 plot (p, x1, "-b", p, x2, "-g", p, x3, "-r", p, x4, "-c", p, x5, "-m")
 ylim ([0, 20])
 grid on
 legend ({"σ = 2 (β = 0.5)", "σ = 1 (β = 1)", "σ = 0.5 (β = 2)", ...
          "σ = 0.25 (β = 4)", "σ = 0.125 (β = 8)"}, "location", "northwest")
 title ("Log-logistic iCDF")
 xlabel ("probability")
 ylabel ("x")
 text (0.03, 12.5, "μ = 0 (α = 1), values of σ (β) as shown in legend")
plotted figure