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 *s*th 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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