Description Usage Arguments Details Value Warning Author(s) References Examples

Compute *p*-values for a test for the null hypothesis of equal CDFs of two samples. The test
statistic is reminiscient of Kolmogorv-Smirnov's, but instead of computing it for the empirical CDFs, this function
computes it based on log-concave estimates for the CDFs.

1 2 | ```
logconTwoSample(x, y, which = c("MLE", "smooth"), M = 999,
n.grid = 500, display = TRUE, seed0 = 1977)
``` |

`x` |
First data sample. |

`y` |
Second data sample. |

`which` |
Indicate for which type of estimate the test statistic should be computed. |

`M` |
Number of permutations. |

`n.grid` |
Number of grid points in computation of maximal difference between smoothed log-concave CDFs. See |

`display` |
If |

`seed0` |
Set seed to reproduce results. |

Given two i.i.d. samples *x_1, …, x_{n_1}* and *y_1, …, y_{n_2}* this function computes a permutation
test *p*-value that provides evidence against the null hypothesis

*H_0 : F_1 = F_2*

where *F_1, F_2* are the CDFs of the samples, respectively. A test either based on the log-concave MLE or on its
smoothed version (see Duembgen and Rufibach, 2009, Section 3) are provided. Note that computation of the smoothed
version takes considerably more time.

`p.value` |
A two dimensional vector containing the |

`test.stat.orig` |
The test statistics for the original samples. |

`test.stats` |
A |

Note that the algorithm that finds the maximal difference for the smoothed estimate is of approximative nature only. It may fail for very large sample sizes.

Kaspar Rufibach, kaspar.rufibach@gmail.com,

http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,

http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

Duembgen, L. and Rufibach, K. (2009)
Maximum likelihood estimation of a log–concave density and its distribution function: basic properties and uniform consistency.
*Bernoulli*, **15(1)**, 40–68.

Duembgen, L. and Rufibach, K. (2011)
logcondens: Computations Related to Univariate Log-Concave Density Estimation.
*Journal of Statistical Software*, **39(6)**, 1–28. http://www.jstatsoft.org/v39/i06

1 2 3 4 5 6 7 8 | ```
## Not run:
n1 <- 30
n2 <- 25
x <- rgamma(n1, 2, 1)
y <- rgamma(n2, 2, 1) + 1
twosample <- logconTwoSample(x, y, which = c("MLE", "smooth")[1], M = 999)
## End(Not run)
``` |

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