loglinv
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 , 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 , 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
## 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")
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