### 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")