dtrunc {sads}

Left-truncation of density, probability and quantile of distributions

Description

Returns density, probability, quantile values and random generation for distribution functions left-truncated at a specified value.

Usage

dtrunc(f, x, trunc, coef, log = FALSE)
ptrunc(f, q, trunc, coef, lower.tail=TRUE, log.p=FALSE)
qtrunc(f, p, trunc, coef, lower.tail = TRUE, log.p = FALSE)
rtrunc(f, n, trunc, coef, ...)

Arguments

f

character; root name of the density or distribution function to be truncated - e.g., "lnorm" for the lognormal distribution; "geom" for the geometric distribution.

x, q

vector of quantiles.

trunc

numeric, trunc > min(x). Truncation value (see details).

p

vector of probabilities.

n

number of random values to return.

coef

numeric named list; parameters values of the density or distribution function, named accordingly (see details).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

...

in rtrunc further arguments to be passed to poweRlaw::rpldis when argument argument f = "power" and argument bissection = FALSE. The same for rpower when and argument bissection = FALSE.

Details

Given a distribution with probability distribution function (PDF) g and cumulative distribution function (CDF) G, a random variable x with these distributions left-truncated at trunc has its PDF:

g'(x) = g(x)/(1 - G(trunc)) for any x <= trunc and zero otherwise

and CDF:

G'(x) = (G(max(x,trunc)) - G(trunc)) / (1 - G(trunc))

dtrunc and ptrunc calculates the left-truncated distributions functions g'(x) and G'(x) defined above for a vector of values x from any standard distribution function available in R. This means the 'upper tail' of a continuous distribution is rescaled to integrate to one. Accordingly, for discrete distributions, the probabilities for all x>trunc are rescaled to sum one. qtrunc is the inverse function of ptrunc.

Left-truncated distributions can be used to describe the species abundance distributions (SADs), specially for continuous distributions (e.g., truncated lognormal distribution).

Value

dtrunc gives the (log) density defined by f left-truncated at trunc. ptrunc gives the (log) distribution function defined by f left-truncated at trunc. qtrunc gives the quantile of the density defined by f left-truncated at trunc. rtrunc generates a sample from the density defined by f left-truncated at trunc.

Source

Codes from Nadarajah and Kotz (2006), which provide a more generic solution for left and right truncation.

References

Nadarajah, S. and Kotz, S. 2006. R Programs for Computing Truncated Distributions. Journal of Statistical Software 16:Code Snippet 2.

See Also

Distributions for standard distributions in R; many functions in package sads have an argument trunc that allows to simulate and fit truncated distributions for species abundance distributions (e.g., fitsad rsad, radpred, octavpred. Package 'VGAM' has truncated versions of many standard functions; see Truncate-methods in package distr for general methods to build R objects of truncated distributions.

Examples

A <- dtrunc("lnorm", x = 1:5, trunc = 0.5,
       coef = list( meanlog=1, sdlog=1.5 ) )
## same as
B <- dlnorm( 1:5 , meanlog = 1, sdlog = 1.5 ) /
  ( plnorm ( 0.5 , meanlog = 1, sdlog = 1.5, lower = FALSE))
## checking
identical( A, B )

A <- ptrunc("pois", q = 1:5, trunc = 0,
       coef = list( lambda = 1.5 ) )
## same as
B <- (ppois( 1:5 , lambda = 1.5 ) -
      ppois(0 , lambda = 1.5 ) ) /
  (ppois(0 , lambda = 1.5, lower = FALSE))
## checking
identical(A,B)

# Random generation
rtrunc("ls", 100, coef=list(N=1000, alpha=50), trunc=5)