Description Usage Arguments Details Value Author(s) References Examples
Density function, distribution function, quantile function, random generation.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | dtsal.tail(x, shape=1,scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale), xmin=0,
log=FALSE)
ptsal.tail(x, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale), xmin=0,
lower.tail=TRUE, log.p=FALSE)
qtsal.tail(p, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale), xmin=0,
lower.tail=TRUE, log.p=FALSE)
rtsal.tail(n, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale), xmin=0)
|
x |
vector of quantiles. |
q |
vector of quantiles or a shape parameter. |
p |
vector of probabilities. |
n |
number of observations. If |
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]. |
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.
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.
Cosma Shalizi (original R code), Christophe Dutang (R packaging)
Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions, http://bactra.org/research/tsallis-MLE/ and https://arxiv.org/abs/math/0701854.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
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