truncdist {distributionsrd}

Truncated distribution

Description

Density, distribution function, quantile function, raw moments and random generation for a truncated distribution.

Usage

dtruncdist(
  x,
  dist = c("lnormtrunc"),
  coeff = list(meanlog = 0, sdlog = 1),
  lowertrunc = 0,
  uppertrunc = Inf,
  log = FALSE
)

ptruncdist(
  q,
  dist = c("lnormtrunc"),
  coeff = list(meanlog = 0, sdlog = 1),
  lowertrunc = 0,
  uppertrunc = Inf,
  log.p = FALSE,
  lower.tail = TRUE
)

qtruncdist(
  p,
  dist = c("lnormtrunc"),
  coeff = list(meanlog = 0, sdlog = 1),
  lowertrunc = 0,
  uppertrunc = Inf,
  lower.tail = TRUE,
  log.p = FALSE
)

mtruncdist(
  r,
  truncation = 0,
  dist = c("lnormtrunc"),
  coeff = list(meanlog = 0, sdlog = 1),
  lowertrunc = 0,
  uppertrunc = Inf,
  lower.tail = TRUE
)

rtruncdist(
  n,
  dist = c("lnormtrunc"),
  coeff = list(meanlog = 0, sdlog = 1),
  lowertrunc = 0,
  uppertrunc = Inf
)

Arguments

x, q

vector of quantiles

dist

distribution to be truncated, defaults to lnorm

coeff

list of parameters for the truncated distribution, defaults to list(meanlog=0,sdlog=1)

lowertrunc, uppertrunc

lowertrunc- and uppertrunc truncation points, defaults to 0 and Inf respectively

log, log.p

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

lower.tail

logical; if TRUE (default), probabilities (moments) are P[X \le x] (E[x^r|X \le y]), otherwise, P[X > x] (E[x^r|X > y])

p

vector of probabilities

r

rth raw moment of the distribution

truncation

lowertrunc truncation parameter, defaults to 0.

n

number of observations

Details

Probability and Cumulative Distribution Function:

f(x) = \frac{g(x)}{F(uppertrunc)-F(lowertrunc)}, \qquad F_X(x) = \frac{F(x)-F(lowertrunc)}{F(uppertrunc)-F(lowertrunc)}

Value

dtruncdist gives the density, ptruncdist gives the distribution function, qtruncdist gives the quantile function, mtruncdist gives the rth moment of the distribution and rtruncdist generates random deviates.

The length of the result is determined by n for rpareto, and is the maximum of the lengths of the numerical arguments for the other functions.

Examples

## Truncated lognormal density
plot(x = seq(0.5, 3, length.out = 100), y = dtruncdist(x = seq(0.5, 5, length.out = 100),
dist = "lnorm", coeff = list(meanlog = 0.5, sdlog = 0.5), lowertrunc = 0.5, uppertrunc = 5))
lines(x = seq(0, 6, length.out = 100), y = dlnorm(x = seq(0, 6, length.out = 100),
meanlog = 0.5, sdlog = 0.5))

# Compare quantities
dtruncdist(0.5)
dlnorm(0.5)
dtruncdist(0.5, lowertrunc = 0.5, uppertrunc = 3)

ptruncdist(2)
plnorm(2)
ptruncdist(2, lowertrunc = 0.5, uppertrunc = 3)

qtruncdist(0.25)
qlnorm(0.25)
qtruncdist(0.25, lowertrunc = 0.5, uppertrunc = 3)

mtruncdist(r = 0, truncation = 2)
mlnorm(r = 0, truncation = 2, meanlog = 0, sdlog = 1)
mtruncdist(r = 0, truncation = 2, lowertrunc = 0.5, uppertrunc = 3)

mtruncdist(r = 1, truncation = 2)
mlnorm(r = 1, truncation = 2, meanlog = 0, sdlog = 1)
mtruncdist(r = 1, truncation = 2, lowertrunc = 0.5, uppertrunc = 3)