ddst (version 1.6.11)

ddst.exp.test: Data Driven Smooth Test for Exponentiality

Description

Performs data driven smooth test for composite hypothesis of exponentiality. Null density is given by \(f(z;gamma) = exp(-z/gamma)\) for z >= 0 and 0 otherwise. Modelling alternatives similarly as in Kallenberg and Ledwina (1997 a,b).

Usage

ddst.exp.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=T.

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

References

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

Kallenberg, W.C.M., Ledwina, T. (1997 b). Data driven smooth tests when the hypothesis is composite. \( J. Amer. Statist. Assoc.\) 92, 1094--1104.

Examples

set.seed(7)
# H0 is true
z <- rexp(80,4)
if (FALSE) {
t <- ddst.exp.test (z, compute.p = TRUE, d.n = 10)
t
plot(t)

# H0 is false
z = rchisq(80,4)
(t = ddst.exp.test (z, compute.p = TRUE, d.n = 10))
t$p.value
plot(t)
}