Gleissberg distribution probability
pgleissberg.RdThe 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())
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) andtwo.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 oflower.tail
Value
a value giving the probability to have k extrema in a series of n observations
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.
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
See also
Examples
# Until n=50, the exact probability is returned
pgleissberg(20, 10, lower.tail=TRUE, two.tailed=FALSE)
#> [1] 0.7988259
# For higher n values, it is approximated by a normal distribution
pgleissberg(60, 33, lower.tail=TRUE, two.tailed=FALSE)
#> [1] 0.03904556