ssdtools (version 0.3.7)

burrIII3: Burr Type III Three-Parameter Distribution

Description

Density, distribution function, quantile function and random generation for the Burr Type III Three-Parameter distribution with lshape and lscale parameters.

Usage

dburrIII3(x, lshape1 = 0, lshape2 = 0, lscale = 0, log = FALSE)
qburrIII3(
  p,
  lshape1 = 0,
  lshape2 = 0,
  lscale = 0,
  lower.tail = TRUE,
  log.p = FALSE
)
pburrIII3(
  q,
  lshape1 = 0,
  lshape2 = 0,
  lscale = 0,
  lower.tail = TRUE,
  log.p = FALSE
)
rburrIII3(n, lshape1 = 0, lshape2 = 0, lscale = 0)
sburrIII3(x)

Arguments

x

The object.

lshape1

shape1 parameter on the log scale.

lshape2

shape2 parameter on the log scale.

lscale

scale parameter on the log scale.

log

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

p

vector of probabilities.

lower.tail

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

log.p

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

q

vector of quantiles.

n

number of observations.

Value

dburrIII3 gives the density, pburrIII3 gives the distribution function, qburrIII3 gives the quantile function, and rburrIII3 generates random samples.

Details

The Burr 12 distribution from the actuar package is used as a base. The Burr III distribution is the distribution of 1/x where x has the Burr Type 12 distribution. refer to https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/bu3pdf.htm for details. The shape1, shape2, and scale parameters are on the log(scale) as these must be positive.

See Also

actuar::dburr()

Examples

# NOT RUN {
x <- rburrIII3(1000)
hist(x, freq = FALSE, col = "gray", border = "white")
curve(dburrIII3(x), add = TRUE, col = "red4", lwd = 2)
# }