nlogL = logllike (params, x) returns the negative log likelihood of the data in x corresponding to the log-logistic distribution with (1) scale parameter a and (2) shape parameter b given in the two-element vector params.

[nlogL, acov] = logllike (params, x) also returns the inverse of Fisher’s information matrix, acov. If the input parameter values in params are the maximum likelihood estimates, the diagonal elements of params are their asymptotic variances.

[…] = logllike (params, x, censor) accepts a boolean vector, censor, of the same size as x with 1s for observations that are right-censored and 0s for observations that are observed exactly. By default, or if left empty, censor = zeros (size (x)).

[…] = logllike (params, x, censor, freq) accepts a frequency vector, freq, of the same size as x. freq typically contains integer frequencies for the corresponding elements in x, but it can contain any non-integer non-negative values. By default, or if left empty, freq = ones (size (x)).

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 $\mu ,\; \sigma$, i.e. mu and sigma, in analogy with the logistic distribution. Their relation to the $\alpha$ and $b$ parameters used in Wikipedia are given below:

• mu = log (a)
• sigma = 1 / a

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

Source Code: logllike