skedastic (version 1.0.0)

ppeak: Cumulative distribution function of number of peaks in an i.i.d. random sequence

Description

This function computes \(\sum_{k} P(n,k)\), i.e. the probability that a sequence of \(n\) independent and identically distributed random variables contains \(\ge k\) \((\le k)\) peaks, with peaks as defined in Goldfeld65;textualskedastic. The function may be used to compute \(p\)-values for the Goldfeld-Quandt nonparametric test for heteroskedasticity in a linear model. Computation time is very slow for \(n > 170\) if usedata is set to FALSE.

Usage

ppeak(k, n, lower.tail = FALSE, usedata = TRUE)

Arguments

k

An integer or a sequence of integers strictly incrementing by 1, with all values between 0 and n - 1 inclusive. Represents the number of peaks in the sequence.

n

A positive integer representing the number of observations in the sequence.

lower.tail

A logical. Should lower tailed cumulative probability be calculated? Defaults to FALSE due to function being designed primarily for calculating \(p\)-values for the peaks test, which is by default an upper-tailed test. Note that both upper and lower tailed cumulative probabilities are computed inclusive of k.

usedata

A logical. Should probability mass function values be read from dpeakdat rather than computing them from dpeak? This option will save significantly on computation time if \(n < 170\) but is currently only available for \(n \le 1000\).

Value

A double between 0 and 1 representing the probability of at least (at most) k peaks occurring in a sequence of \(n\) independent and identically distributed continuous random variables. The double has a names attribute with the values corresponding to the probabilities.

References

See Also

dpeak, goldfeld_quandt

Examples

# NOT RUN {
# For an independent sample of size 250, the probability of at least 10
# peaks is 0.02650008
ppeak(k = 10, n = 250, lower.tail = FALSE, usedata = TRUE)
# For an independent sample of size 10, the probability of at most 2 peaks
# is 0.7060615
ppeak(k = 2, n = 10, lower.tail = TRUE, usedata = FALSE)

# }