number of observations. If length(n) > 1, the length
is taken to be the number required.
shape
shape parameter.
scale, kappa
scale parameters.
xmin
minimum x-value.
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].
Details
The Tsallis distribution with a censoring parameter is the distribution of
a Tsallis distributed random variable conditionnaly on x>xmin.
The density is defined as
f(x) = C/κ(1-(1-q)x/κ)^{1/(1-q)}
for all x>xmin where C is the appropriate constant so that the integral
of the density equals 1. That is C is the survival probability of the classic Tsallis
distribution at x=xmin.
It is convenient to introduce a re-parameterization
shape = -1/(1-q), scale = shape*κ
which makes the relationship to the Pareto clearer, and eases estimation.
If we have both shape/scale and q/kappa parameters, the latter over-ride.
Value
dtsal.tail gives the density,
ptsal.tail gives the distribution function,
qtsal.tail gives the quantile function, and
rtsal.tail generates random deviates.
The length of the result is determined by n for
rtsal.tail, and is the maximum of the lengths of the
numerical parameters for the other functions.
Author(s)
Cosma Shalizi (original R code),
Christophe Dutang (R packaging)