Description

Density function, distribution function, quantile function, random generation, raw moments and limited moments for the Loglogistic distribution with parameters shape and scale.

Usage

Arguments

Details

The loglogistic distribution with parameters shape = a and scale = s has density:

f(x) = a (x/s)^a / (x [1 + (x/s)^a]^2)

for x > 0, a > 0 and b > 0.

The kth raw moment of the random variable X is E[X^k], -shape < k < shape.

The kth limited moment at some limit d is E[min(X, d)^k], k > -shape and 1 - k/shape not a negative integer.

Value

dllogis gives the density, pllogis gives the distribution function, qllogis gives the quantile function, rllogis generates random deviates, mllogis gives the kth raw moment, and levllogis gives the kth moment of the limited loss variable.

Invalid arguments will result in return value NaN, with a warning.

Note

levllogis computes the limited expected value using betaint.

Also known as the Fisk distribution. See also Kleiber and Kotz (2003) for alternative names and parametrizations.

The "distributions" package vignette provides the interrelations between the continuous size distributions in actuar and the complete formulas underlying the above functions.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

References

Kleiber, C. and Kotz, S. (2003), Statistical Size Distributions in Economics and Actuarial Sciences, Wiley.

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

See Also

dpareto3 for an equivalent distribution with a location parameter.

Examples