tsal.test {tsallisqexp}

Test Tsallis Distributions

Description

Test functions.

Usage

test.tsal.quantile.transform(from=0, to=1e6, shape=1, scale=1,
    q=tsal.q.from.shape(shape), kappa=tsal.kappa.from.ss(shape,scale),
    n=1e5, lwd=0.01, xmin=0, ...)

test.tsal.LR.distribution(n=100, reps=100, shape=1, scale=1,
    q=tsal.q.from.shape(shape), kappa=tsal.kappa.from.ss(shape,scale),
    xmin=0,method="mle.equation",...)

Arguments

from

lower limit for x.

to

upper limit for x.

shape, q

shape parameters.

scale, kappa

scale parameters. If we have both shape/scale and q/kappa parameters, the latter over-ride.

n

number of points at which to evaluate the function over the domain or number of sample points.

lwd

line width.

xmin

minimum x-value (left-censoring threshold).

...

further arguments to be passed to curve or plot, except xlim for test.tsal.LR.distribution.

reps

number of replicates.

method

estimation method, see tsal.fit.

Details

plot.tsal.quantile.transform check the accuracy of quantile/inverse quantile transformations For all parameter values and all x, qtsal(ptsal(x)) should = x. This function displays the relative error in the transformation, which is due to numerical imprecision. This indicates roughly how far off random variates generated by the transformation method will be. If everything is going according to plan, the curve plotted should oscillate extremely rapidly between positive and negative limits which, while growing, stay quite small in absolute terms, e.g., on the order of 1e-5 when x is on the order of 1e9.

plot.tsal.LR.distribution checks likelihood ratio estimation accuracy : 2*[(Likelihood at estimated parameters) - (likelihood at true parameters)] should have a chi square distribution with 2 degrees of freedom, at least asymptotically for large samples.

Value

plot.tsal.quantile.transform plots the relative error in the transformation.

plot.tsal.LR.distribution plots the likelihood ratio against a chi-square distribution and returns the result of Kolmgorov-Smirnov test against theoretical distribution.

Author(s)

Cosma Shalizi (original R code), Christophe Dutang (R packaging)

References

Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions, http://bactra.org/research/tsallis-MLE/ and https://arxiv.org/abs/math/0701854.

Examples

#####
# (1) fit
x <- rtsal(20, 1/2, 1/4)
tsal.loglik(x, 1/2, 1/4)

tsal.fit(x, method="mle.equation")
tsal.fit(x, method="mle.direct")
tsal.fit(x, method="leastsquares")