skedastic (version 1.0.4)

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

Description

This function computes $P(n,k)$ as defined by Goldfeld65;textualskedastic, 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 Goldfeld65;textualskedastic. 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)

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.

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 $n\le 1000$.

References

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")