Description Usage Arguments Details Value Author(s) References Examples
View source: R/rossberg.exp.test.R
Performs test for the composite hypothesis of exponentiality based on the Rossberg characterization, see Volkova (2010).
1 |
x |
a numeric vector of data values. |
The test is based on the following statistic:
S_n=\int_0^∞(H_n(t)-G_n(t))dF_n(t),
where F_n is the empirical distribution function,
H_n(t) = (C_n^3)^{-1}∑_{1≤q i<j<k≤q n}1\{X_{2,\{i,j,k\}}-X_{1,\{i,j,k\}}<t\}, \quad t≥q 0,
G_n(t) =(C_n^2)^{-1}∑_{1≤q i<j≤q n}1\{\min (X_i,X_j)<t\}, \quad t≥q 0.
Here X_{s,\{i,j,k\}}, s=1,2, denotes the sth order statistic of X_i,X_j,X_k. The p-value is computed from the limit null distribution. Under exponentiality, one has
√{n}S_n\stackrel{d}{\rightarrow}\mathcal N≤ft(0,\frac{52}{1125}\right)
(see, Volkova (2010)).
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value for the test. |
method |
the character string "Test for exponentiality based on Rossberg characterization". |
data.name |
a character string giving the name(s) of the data. |
Ruslan Pusev and Maxim Yakovlev
Volkova, K.Yu. (2010): On asymptotic efficiency of exponentiality tests based on Rossberg characterization. — J. Math. Sci., vol. 167, No. 4, pp. 486–494.
1 2 | rossberg.exp.test(rexp(25))
rossberg.exp.test(runif(25, min = 50, max = 100))
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