Description Usage Arguments Details Value Author(s) References Examples
View source: R/atkinson.exp.test.R
Performs Atkinson test for the composite hypothesis of exponentiality, see e.g. Mimoto and Zitikis (2008).
1 | atkinson.exp.test(x, p=0.99, simulate.p.value=FALSE, nrepl=2000)
|
x |
a numeric vector of data values. |
p |
a parameter of the test (see below). |
simulate.p.value |
a logical value indicating whether to compute p-values by Monte Carlo simulation. |
nrepl |
the number of replications in Monte Carlo simulation. |
The Atkinson test for exponentiality is based on the following statistic:
T_n(p) = √{n}≤ft| \frac{≤ft(n^{-1}∑_{i=1}^n{X_i^p}\right)^{1/p}}{\overline{X}} -(Γ(1+p))^{\frac{1}{p}}\right|.
The statistic is asymptotically normal: T_n(p) \to ≤ft| N(0,σ^2(p))\right|, where
σ^2(p) = ≤ft(Γ(1+p)\right)^{\frac{2}{p}}≤ft( -1 - \frac{1}{p^2} + \frac{Γ(1+2p)}{p^2Γ^2(1+p)}\right).
A list with class "htest" containing the following components:
statistic |
the value of the Atkinson statistic. |
p.value |
the p-value for the test. |
method |
the character string "Atkinson test for exponentiality". |
data.name |
a character string giving the name(s) of the data. |
Alexey Novikov and Ruslan Pusev
Mimoto, N. and Zitikis, R. (2008): The Atkinson index, the Moran statistic, and testing exponentiality. — J. Japan Statist. Soc., vol. 38, pp. 187–205.
1 2 | atkinson.exp.test(rexp(100))
atkinson.exp.test(rchisq(100,3))
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