Description Usage Arguments Details Value Source References Examples

Computes the p-value *P(D_{n} ≥ d_{n}) \equiv P(D_{n} > d_{n})*, where *d_{n}* is the value of the KS test statistic computed based on a data sample *\{x_{1}, ..., x_{n}\}*, when *F(x)* is continuous.

1 | ```
cont_ks_test(x, y, ...)
``` |

`x` |
a numeric vector of data sample values |

`y` |
a pre-specified continuous cdf, |

`...` |
values of the parameters of the cdf, |

Given a random sample *\{X_{1}, ..., X_{n}\}* of size `n`

with an empirical cdf *F_{n}(x)*, the two-sided Kolmogorov-Smirnov goodness-of-fit statistic is defined as *D_{n} = \sup | F_{n}(x) - F(x) | *, where *F(x)* is the cdf of a prespecified theoretical distribution under the null hypothesis *H_{0}*, that *\{X_{1}, ..., X_{n}\}* comes from *F(x)*.

The function `cont_ks_test`

implements the FFT-based algorithm proposed by Moscovich and Nadler (2017) to compute the p-value *P(D_{n} ≥ d_{n})*, where *d_{n}* is the value of the KS test statistic computed based on a user provided data sample *\{x_{1}, ..., x_{n}\}*, assuming *F(x)* is continuous.
This algorithm ensures a total worst-case run-time of order *O(n^{2}log(n))* which makes it more efficient and numerically stable than the algorithm proposed by Marsaglia et al. (2003).
The latter is used by many existing packages computing the cdf of *D_{n}*, e.g., the function `ks.test`

in the package stats and the function `ks.test`

in the package dgof.
A limitation of the functions `ks.test`

is that the sample size should be less than 100, and the computation time is *O(n^{3})*.
In contrast, the function `cont_ks_test`

provides results with at least 10 correct digits after the decimal point for sample sizes *n* up to 100000 and computation time of 16 seconds on a machine with an 2.5GHz Intel Core i5 processor with 4GB RAM, running MacOS X Yosemite.
For `n`

> 100000, accurate results can still be computed with similar accuracy, but at a higher computation time.
See Dimitrova, Kaishev, Tan (2020), Appendix C for further details and examples.

A list with class "htest" containing the following components:

`statistic ` |
the value of the statistic. |

`p.value ` |
the p-value of the test. |

`alternative ` |
"two-sided". |

`data.name ` |
a character string giving the name of the data. |

Based on the C++ code available at https://github.com/mosco/crossing-probability developed by Moscovich and Nadler (2017). See also Dimitrova, Kaishev, Tan (2020) for more details.

Dimitrina S. Dimitrova, Vladimir K. Kaishev, Senren Tan. (2020) "Computing the Kolmogorov-Smirnov Distribution When the Underlying CDF is Purely Discrete, Mixed or Continuous". Journal of Statistical Software, **95**(10): 1-42. doi:10.18637/jss.v095.i10.

Moscovich A., Nadler B. (2017). "Fast Calculation of Boundary Crossing Probabilities for Poisson Processes". Statistics and Probability Letters, **123**, 177-182.

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