vcdExtra: logseries – R documentation

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logseries

The Logarithmic Series Distribution

Description

The logarithmic series distribution is a long-tailed distribution introduced by Fisher etal. (1943) in connection with data on the abundance of individuals classified by species.

These functions provide the density, distribution function, quantile function and random generation for the logarithmic series distribution with parameter prob.

Usage

dlogseries(x, prob = 0.5, log = FALSE)

plogseries(q, prob = 0.5, lower.tail = TRUE, log.p = FALSE)

qlogseries(p, prob = 0.5, lower.tail = TRUE, log.p = FALSE, max.value = 10000)

rlogseries(n, prob = 0.5)

Arguments

`x, q`	vector of quantiles representing the number of events.
`prob`	parameter for the distribution, `0 < prob < 1`
`log, log.p`	ogical; if TRUE, probabilities `p` are given as `log(p)`
`lower.tail`	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
`p`	vector of probabilities
`max.value`	maximum value returned by `qlogseries`
`n`	number of observations for `rlogseries`

Details

The logarithmic series distribution with prob = p has density

p ( x ) = α p^x / x

for x = 1, 2, …, where α= -1 / \log(1 - p) and 0 < p <1. Note that counts x==2 cannot occur.

Value

dlogseries gives the density, plogseries gives the distribution function, qlogseries gives the quantile function, and rlogseries generates random deviates.

Author(s)

Michael Friendly, using original code modified from the gmlss.dist package by Mikis Stasinopoulos.

References

https://en.wikipedia.org/wiki/Logarithmic_distribution

Fisher, R. A. and Corbet, A. S. and Williams, C. B. (1943). The relation between the number of species and the number of individuals Journal of Animal Ecology, 12, 42-58.

Examples

XL <-expand.grid(x=1:5, p=c(0.33, 0.66, 0.99))
lgs.df <- data.frame(XL, prob=dlogseries(XL[,"x"], XL[,"p"]))
lgs.df$p = factor(lgs.df$p)
str(lgs.df)

require(lattice)
mycol <- palette()[2:4]
xyplot( prob ~ x, data=lgs.df, groups=p,
	xlab=list('Number of events (k)', cex=1.25),
	ylab=list('Probability',  cex=1.25),
	type='b', pch=15:17, lwd=2, cex=1.25, col=mycol,
	key = list(
					title = 'p',
					points = list(pch=15:17, col=mycol, cex=1.25),
					lines = list(lwd=2, col=mycol),
					text = list(levels(lgs.df$p)),
					x=0.9, y=0.98, corner=c(x=1, y=1)
					)
	)


# random numbers
hist(rlogseries(200, prob=.4), xlab='x')
hist(rlogseries(200, prob=.8), xlab='x')

vcdExtra

'vcd' Extensions and Additions

v0.7-5

GPL (>= 2)

Authors

Michael Friendly [aut, cre], Heather Turner [ctb], Achim Zeileis [ctb], Duncan Murdoch [ctb], David Firth [ctb]

Initial release

2021-01-22