idist: General inverse distribution

In nisone: Inference for Samples of Size at Least One

General inverse distribution

Description

Let X come from some location-scale family

f(x) = \frac{1}{\sigma}\rho\left(\frac{X - \mu}{\sigma}\right),

for some standard distribution \rho(). You provide \rho(), \mu and \sigma and these functions will provide the density, distribution, quantile, and random generation for Z = 1/X. Convenience arguments for the normal, Cauchy, and uniform are provided.

Usage

didist(
  x,
  center = 0,
  scale = 1,
  fam = c("normal", "cauchy", "uniform"),
  ddist = NULL,
  log = FALSE,
  ...
)

pidist(
  q,
  center = 0,
  scale = 1,
  fam = c("normal", "cauchy", "uniform"),
  pdist = NULL,
  lower.tail = TRUE,
  log.p = FALSE,
  ...
)

qidist(
  p,
  center = 0,
  scale = 1,
  fam = c("normal", "cauchy", "uniform"),
  qdist = NULL,
  pdist = NULL,
  ...
)

ridist(
  n,
  center = 0,
  scale = 1,
  fam = c("normal", "cauchy", "uniform"),
  rdist = NULL,
  ...
)

Arguments

x, q	vector of quantiles
center	The center parameter \mu.
scale	The scale parameter \sigma.
fam	One of "normal", "cauchy", or "uniform". If ddist, pdist, qdist, or rdist are specified then this argument is ignored.
ddist	Density function of standard distribution \rho(). Should have a log argument.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
...	Additional arguments for ddist, pdist, qdist, and rdist.
pdist	Cumulative distribution function of standard distribution.
lower.tail	logical; if TRUE (default), probabilities are P(X<=x) otherwise, P(X>x).
p	vector of probabilities
qdist	Quantile function of standard distribution.
n	sample size
rdist	Random generation of standard distribution.

Value

Either a random sample (ridist), the density (didist), the tail probability (pidist), or the quantile (qidist) of the inverse distribution.

Functions

• didist(): Density function.

• pidist(): Distribution function.

• qidist(): Quantile function.

• ridist(): Random generation.

Author(s)

David Gerard

Examples

didist(1, fam = "normal")
didist(1, center = 3, scale = 2, ddist = dt, df = 1)

pidist(1, fam = "normal")
pidist(1, center = 3, scale = 2, pdist = pt, df = 1)

qidist(0.1, fam = "normal")
qidist(0.1, center = 3, scale = 2, qdist = qt, pdist = pt, df = 1)

nisone documentation built on Sept. 8, 2026, 5:08 p.m.