pgleissberg {pastecs}

Gleissberg distribution probability

Description

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())

Usage

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

Arguments

n

the number of observations in the series

k

the number of extrema in the series, as calculated by turnpoints()

lower.tail

if lower.tail=TRUE (by default) and two.tailed=FALSE, the left-side probability is returned. If it is FALSE, the right-side probability is returned

two.tailed

if two.tailed=TRUE, the two-sided probability is returned. By default, it is FALSE and a one-sided probability is returned (left or right, depending on the value of lower.tail

Value

a value giving the probability to have k extrema in a series of n observations

Note

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

Author(s)

Frédéric Ibanez ([e-mail]), Philippe Grosjean ([e-mail])

References

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.

See Also

.gleissberg.table, turnpoints, turnogram

Examples

# 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)