ppeak: Cumulative distribution function of number of peaks in an...

In skedastic: Handling Heteroskedasticity in the Linear Regression Model

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

Description

This function computes ∑_{k} P(n,k), i.e. the probability that a sequence of n independent and identically distributed random variables contains ≥ k (≤ k) peaks, with peaks as defined in \insertCiteGoldfeld65;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 ≤ 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

\insertAllCited

See Also

dpeak, goldfeld_quandt

Examples

# 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)

skedastic documentation built on Nov. 10, 2022, 5:43 p.m.