dpeak {skedastic}

Probability mass function of number of peaks in an i.i.d. random sequence

Description

This function computes P(n,k) as defined by Goldfeld and Quandt (1965), i.e. the probability that a sequence of n independent and identically distributed random variables contains exactly k peaks, with peaks also as defined by Goldfeld and Quandt (1965). The function is used in ppeak to compute p-values for the Goldfeld-Quandt nonparametric test for heteroskedasticity in a linear model.

Usage

dpeak(k, n, usedata = FALSE)

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.

usedata

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

Value

A double between 0 and 1 representing the probability of exactly 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. Computation time is very slow for n > 170 (if usedata is FALSE) and for n > 1000 regardless of usedata value.

References

Goldfeld SM, Quandt RE (1965). “Some Tests for Homoscedasticity.” Journal of the American Statistical Association, 60(310), 539–547.

See Also

ppeak, goldfeld_quandt

Examples

dpeak(0:9, 10)
plot(0:9, dpeak(0:9, 10), type = "p", pch = 20, xlab = "Number of Peaks",
         ylab = "Probability")

# This would be extremely slow if usedata were set to FALSE:
prob <- dpeak(0:199, 200, usedata = TRUE)
plot(0:199, prob, type = "l", xlab = "Number of Peaks", ylab = "Probability")

# `dpeakdat` is a dataset containing probabilities generated from `dpeak`
utils::data(dpeakdat)
expval <- unlist(lapply(dpeakdat,
                 function(p) sum(p * 0:(length(p) - 1))))
plot(1:1000, expval[1:1000], type = "l", xlab = parse(text = "n"),
     ylab = "Expected Number of Peaks")