Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming a von Mises-Fisher distribution.

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`x` |
A matrix with the dataset in Eulcidean coordinates, i.e. unit vectors. |

`ina` |
A variable indicating the groupings. |

`fraction` |
The fraction of data to be used as test set. |

`R` |
The number of repetitions. |

`seed` |
If seed is TRUE, the results will always be the same. |

A repeated cross validation procedure is performed to estimate the rate of correct classification.

A list including:

`percent` |
The estimated percent of correct classification and two estimated standard deviations. The one is the standard devation of the rates and the other is assuming a binomial distribution. |

`ci` |
Three types of confidence intervals, the standard one, another one based on the binomial distribution and the third one is the empirical one, which calcualtes the upper and lower 2.5% of the rates. |

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

Morris, J. E., & Laycock, P. J. (1974). Discriminant analysis of directional data. Biometrika, 61(2): 335-341.

```
vmfda.pred, mix.vmf, vmf, dirknn
```

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