Statistics: loglinv

### Function Reference: `loglinv`

statistics: x = loglinv (p, a, b)

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 scale parameter a and shape parameter b. The size of x is the common size of p, 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 p is supported in the range [0,1], otherwise `NaN` 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, loglpdf, loglrnd, loglfit, logllike

Source Code: loglinv

### Example: 1

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