Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# The Loglogistic Distribution¤

The loglogistic function gives rise to probability distributions, reliability functions and hazard functions that are similar to those that can be obtained from the Weibull distribution (and the lognormal distribution) but the formulae for R(t) and h(t) are simpler. Its probability density function is:

f(t) = when > 0, > 0 and t 0.

That is if the (natural) logarithm of a variable X is distributed according to the logistic distribution, then X follows the loglogistic distribution.

The effects of changing and can be seen in these graphs of f(t), but you can click on them for an interactive version in Excel where you can experiment with different values yourself.