Description Usage Arguments Value Note Author(s) References See Also Examples

The Gleissberg distribution gives the probability to have k extrema in a series of n observations. This distribution is used in the turnogram to determine if monotony indices are significant (see `turnogram()`

)

1 | ```
pgleissberg(n, k, lower.tail=TRUE, two.tailed=FALSE)
``` |

`n` |
the number of observations in the series |

`k` |
the number of extrema in the series, as calculated by |

`lower.tail` |
if |

`two.tailed` |
if |

a value giving the probability to have `k`

extrema in a series of `n`

observations

The Gleissberg distribution is asymptotically normal. For `n`

> 50, the distribution is approximated by a Gaussian curve. For lower `n`

values, the exact probability is returned (using data in the variable `.gleissberg.table`

Frédéric Ibanez (ibanez@obs-vlfr.fr), Philippe Grosjean (phgrosjean@sciviews.org)

Dallot, S. & M. Etienne, 1990. *Une méthode non paramétrique d'analyse des séries en océanographie biologique: les tournogrammes.* Biométrie et océanographie - Société de biométrie, 6, Lille, 26-28 mai 1986. IFREMER, Actes de colloques, 10:13-31.

Johnson, N.L. & Kotz, S., 1969. *Discrete distributions.* J. Wiley & sons, New York, 328 pp.

`.gleissberg.table`

, `turnpoints`

, `turnogram`

1 2 3 4 | ```
# Until n=50, the exact probability is returned
pgleissberg(20, 10, lower.tail=TRUE, two.tailed=FALSE)
# For higher n values, it is approximated by a normal distribution
pgleissberg(60, 33, lower.tail=TRUE, two.tailed=FALSE)
``` |

```
Loading required package: boot
[1] 0.2011741
[1] 0.03904556
```

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