Description Arguments Details Value Note Author(s) References See Also
Density, distribution function, hazards, quantile function and random generation for the log-logistic distribution.
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
shape, scale |
vector of shape and scale parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P(X <= x), otherwise, P(X > x). |
The log-logistic distribution with shape
parameter
a>0 and scale
parameter b>0 has probability
density function
f(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)^2
and hazard
h(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)
for x>0. The hazard is decreasing for shape a <= 1, and unimodal for a > 1.
The probability distribution function is
F(x | a, b) = 1 - 1 / (1 + (x/b)^a)
If a > 1, the mean is b c / sin(c), and if a > 2 the variance is b^2 * (2*c/sin(2*c) - c^2/sin(c)^2), where c = π/a, otherwise these are undefined.
dllogis
gives the density, pllogis
gives the
distribution function, qllogis
gives the quantile function,
hllogis
gives the hazard function, Hllogis
gives the
cumulative hazard function, and rllogis
generates random
deviates.
Various different parameterisations of this distribution are
used. In the one used here, the interpretation of the parameters
is the same as in the standard Weibull distribution
(dweibull
). Like the Weibull, the survivor function
is a transformation of (x/b)^a from the non-negative real line to [0,1],
but with a different link function. Covariates on b
represent time acceleration factors, or ratios of expected
survival.
The same parameterisation is also used in
eha::dllogis
in the eha package.
Christopher Jackson <chris.jackson@mrc-bsu.cam.ac.uk>
Stata Press (2007) Stata release 10 manual: Survival analysis and epidemiological tables.
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