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 15 16 17 | dtsal(x, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale),
log=FALSE)
ptsal(x, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale),
lower.tail=TRUE, log.p=FALSE)
qtsal(p, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale),
lower.tail=TRUE, log.p=FALSE)
rtsal(n, shape=1, scale=1, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale))
tsal.mean(shape, scale, q=tsal.q.from.shape(shape),
kappa=tsal.kappa.from.ss(shape,scale))
|
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. |
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 is defined by the following density
f(x) = 1/κ(1-(1-q)x/κ)^{1/(1-q)}
for all x. 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
gives the density,
ptsal
gives the distribution function,
qtsal
gives the quantile function, and
rtsal
generates random deviates.
tsal.mean
computes the expected value.
The length of the result is determined by n
for
rtsal
, 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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