Cumulative Distribution Function

Calculates the cumulative probability for a given truncated distribution

Usage

ptrunc(q, family, ..., lower.tail = TRUE, log.p = FALSE)

ptruncnorm(
  q,
  mean = 0,
  sd = 1,
  a = -Inf,
  b = Inf,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncbeta(
  q,
  shape1,
  shape2,
  a = 0,
  b = 1,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncbinom(
  q,
  size,
  prob,
  a = 0,
  b = size,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncpois(q, lambda, a = 0, b = Inf, ..., lower.tail = TRUE, log.p = FALSE)

ptruncchisq(q, df, a = 0, b = Inf, ..., lower.tail = TRUE, log.p = FALSE)

ptrunccontbern(q, lambda, a = 0, b = 1, ...)

ptruncexp(q, rate = 1, a = 0, b = Inf, ..., lower.tail = TRUE, log.p = FALSE)

ptruncgamma(
  q,
  shape,
  rate = 1,
  scale = 1/rate,
  a = 0,
  b = Inf,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncinvgamma(
  q,
  shape,
  rate = 1,
  scale = 1/rate,
  a = 0,
  b = Inf,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncinvgauss(q, m, s, a = 0, b = Inf, ...)

ptrunclnorm(
  q,
  meanlog = 0,
  sdlog = 1,
  a = 0,
  b = Inf,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

ptruncnbinom(
  q,
  size,
  prob,
  mu,
  a = 0,
  b = Inf,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

q

vector of quantiles

family

distribution family to use

...

named distribution parameters and/or truncation limits (a, b)

lower.tail

logical; if TRUE, probabilities are \(P(X <= x)\) otherwise, \(P(X > x)\)

log.p

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

mean

mean of parent distribution

sd

standard deviation is parent distribution

a

point of left truncation. For discrete distributions, a will be included in the support of the truncated distribution.

b

point of right truncation

shape1

positive shape parameter alpha

shape2

positive shape parameter beta

size

target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.

prob

probability of success on each trial

lambda

mean and var of "parent" distribution

df

degrees of freedom for "parent" distribution

rate

inverse gamma rate parameter

shape

inverse gamma shape parameter

scale

inverse gamma scale parameter

m

vector of means

s

vector of dispersion parameters

meanlog

mean of untruncated distribution

sdlog

standard deviation of untruncated distribution

mu

alternative parametrization via mean

Value

The cumulative probability of y.

Examples

ptrunc(0)
#> [1] 0.5
ptrunc(6, family = "gaussian", mean = 5, sd = 10, b = 7)
#> [1] 0.9319271
pnorm(6, mean = 5, sd = 10) # for comparison
#> [1] 0.5398278