ddst (version 1.6.11)

ddst.evd.test: Data Driven Smooth Test for Extreme Value Distribution

Description

Performs data driven smooth test for composite hypothesis of extreme value distribution. Null density is given by \( f(z;\gamma)=1/\gamma_2 \exp((z-\gamma_1)/\gamma_2- \exp((z-\gamma_1)/\gamma_2))\), \(z \in R\).

Usage

ddst.evd.test(
  x,
  base = ddst.base.legendre,
  d.n = 10,
  c = 100,
  nr = 1e+05,
  compute.p = TRUE,
  alpha = 0.05,
  compute.cv = TRUE,
  ...
)

Value

An object of class htest

statistic

the value of the test statistic.

parameter

the number of choosen coordinates (k).

method

a character string indicating the parameters of performed test.

data.name

a character string giving the name(s) of the data.

p.value

the p-value for the test, computed only if compute.p=TRUE.

Arguments

x

a (non-empty) numeric vector of data values

base

a function which returns an orthonormal system, possible choice: ddst.base.legendre for the Legendre polynomials and ddst.base.cos for the cosine system

d.n

an integer specifying the maximum dimension considered, only for advanced users

c

a calibrating parameter in the penalty in the model selection rule

nr

an integer specifying the number of runs for a p-value and a critical value computation if any

compute.p

a logical value indicating whether to compute a p-value or not

alpha

a significance level

compute.cv

a logical value indicating whether to compute a critical value corresponding to the significance level alpha or not

...

further arguments

Details

We model alternatives similarly as in Kallenberg and Ledwina (1997) and Janic-Wroblewska (2004) using Legendre's polynomials or cosines. For more details see: http://www.biecek.pl/R/ddst/description.pdf.

References

Hosking, J.R.M., Wallis, J.R., Wood, E.F. (1985). Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. \( Technometrics\) 27, 251--261.

Janic-Wroblewska, A. (2004). Data-driven smooth test for extreme value distribution. \( Statistics\) 38, 413--426.

Janic, A. and Ledwina, T. (2008). Data-driven tests for a location-scale family revisited. \( J. Statist. Theory. Pract. Special issue on Modern Goodness of Fit Methods. accepted.\).

Kallenberg, W.C.M., Ledwina, T. (1997). Data driven smooth tests for composite hypotheses: Comparison of powers. \( J. Statist. Comput. Simul.\) 59, 101--121.

Examples

library(evd)
set.seed(7)

# for given vector of 19 numbers
z <- c(13.41, 6.04, 1.26, 3.67, -4.54, 2.92, 0.44, 12.93, 6.77, 10.09,
      4.10, 4.04, -1.97, 2.17, -5.38, -7.30, 4.75, 5.63, 8.84)
if (FALSE) {
t <- ddst.evd.test(z, compute.p = TRUE, d.n = 10)
t
plot(t)

# H0 is true
x <- -qgumbel(runif(100),-1,1)
t <- ddst.evd.test (x, compute.p = TRUE, d.n = 10)
t
plot(t)

# H0 is false
x <- rexp(80,4)
t <- ddst.evd.test (x, compute.p = TRUE, d.n = 10)
t
plot(t)
}