HDR: Highest density region (HDR)

Description

HDR.xxxx returns the highest density region (HDR) for a chosen distribution.

Usage

HDR.norm(
  cover.prob,
  mean = 0,
  sd = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.lnorm(
  cover.prob,
  meanlog = 0,
  sdlog = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.t(cover.prob, df, ncp = 0, gradtol = 1e-10, steptol = 1e-10, iterlim = 100)
HDR.cauchy(
  cover.prob,
  location = 0,
  scale = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.f(
  cover.prob,
  df1,
  df2,
  ncp = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.beta(
  cover.prob,
  shape1,
  shape2,
  ncp = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.chisq(
  cover.prob,
  df,
  ncp = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.gamma(
  cover.prob,
  shape,
  rate = 1,
  scale = 1/rate,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.weibull(
  cover.prob,
  shape,
  scale = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.exp(cover.prob, rate, gradtol = 1e-10, steptol = 1e-10, iterlim = 100)
HDR.unif(
  cover.prob,
  min = 0,
  max = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.hyper(cover.prob, m, n, k, gradtol = 1e-10, steptol = 1e-10, iterlim = 100)
HDR.geom(cover.prob, prob, gradtol = 1e-10, steptol = 1e-10, iterlim = 100)
HDR.binom(
  cover.prob,
  size,
  prob,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.pois(cover.prob, lambda, gradtol = 1e-10, steptol = 1e-10, iterlim = 100)
HDR.nbinom(
  cover.prob,
  size,
  prob,
  mu,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.arcsine(
  cover.prob,
  min = 0,
  max = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.matching(cover.prob, size, trials = 1, prob = 0, approx = (trials > 100))
HDR.betapr(
  cover.prob,
  shape1,
  shape2,
  scale = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.fatigue(
  cover.prob,
  alpha,
  beta = 1,
  mu = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.gompertz(
  cover.prob,
  shape = 1,
  scale = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.gpd(
  cover.prob,
  mu = 0,
  sigma = 1,
  xi = 0,
  location = mu,
  scale = sigma,
  shape = xi,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.huber(
  cover.prob,
  mu,
  sigma,
  epsilon,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.kumar(
  cover.prob,
  a = 1,
  b = 1,
  shape1 = a,
  shape2 = b,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.tnorm(
  cover.prob,
  mean = 0,
  sd = 1,
  a = -Inf,
  b = Inf,
  min = a,
  max = b,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.invchisq(
  cover.prob,
  df,
  ncp = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.invexp(
  cover.prob,
  rate = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.invgamma(
  cover.prob,
  shape,
  rate = 1,
  scale = 1/rate,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.benini(
  cover.prob,
  shape,
  y0,
  scale = y0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.frechet(
  cover.prob,
  shape,
  scale = 1,
  location = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.gengamma(
  cover.prob,
  d,
  k,
  shape1 = d,
  shape2 = k,
  rate = 1,
  scale = 1/rate,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.gumbelII(
  cover.prob,
  shape,
  scale = 1,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)
HDR.lgamma(
  cover.prob,
  shape = 1,
  scale = 1,
  location = 0,
  gradtol = 1e-10,
  steptol = 1e-10,
  iterlim = 100
)

Arguments

cover.prob

The probability coverage for the HDR (scalar between zero and one). The significance level for the HDR i is 1-cover.prob.

gradtol

Parameter for the nlm optimisation - a positive scalar giving the tolerance at which the scaled gradient is considered close enough to zero to terminate the algorithm (see [nlm doccumentation](https://stat.ethz.ch/R-manual/R-patched/library/stats/html/nlm.html)).

steptol

Parameter for the nlm optimisation - a positive scalar providing the minimum allowable relative step length (see [nlm doccumentation](https://stat.ethz.ch/R-manual/R-patched/library/stats/html/nlm.html)).

iterlim

Parameter for the nlm optimisation - a positive integer specifying the maximum number of iterations to be performed before the program is terminated (see [nlm doccumentation](https://stat.ethz.ch/R-manual/R-patched/library/stats/html/nlm.html)).

shape1, shape2, ncp, location, scale, df, rate, df1, df2, meanlog, sdlog, mean, sd, min, max, shape, size, prob, m, n, k, mu, lambda, alpha, beta, sigma, xi, epsilon, a, b, y0, d, trials, approx

Distribution parameters.

Value

An interval object with classes hdr and interval containing the highest density region and related information.

Details

This function computes the highest density region (HDR) for a univariate distribution in the stats package. The functions for the HDR for different distributions are named in the form HDR.xxxx where the xxxx refers to the distribution (e.g., HDR.chisq, HDR.gamma, HDR.norm, etc.). The user can use any univariate distribution in the stats package, and the function accepts parameters from the specified distribution (see table below). The output of the function is an interval of classes hdr and interval giving the highest density region and some related information pertaining to the distribution and the computation of the HDR (for information on intervals, see the sets package). If the input distribution is continuous then the HDR is a real interval, and if the input distribution discrete then the HDR is a discrete interval. For non-trivial cases the computation is done by optimisation using the nlm function.

Using `stats`	Continuous
HDR.arcsine	min	max
HDR.beta	shape1	shape2	ncp
HDR.cauchy	location	scale
HDR.chisq	df	ncp
HDR.exp	rate
HDR.f	df1	df2	ncp
HDR.gamma	shape	rate	scale
HDR.lnorm	meanlog	sdlog
HDR.norm	mean	sd
HDR.t	df	ncp
HDR.unif	min	max
HDR.weibull	shape	scale

Using `stats`	Discrete
HDR.binom	size	prob
HDR.geom	prob
HDR.hyper	m	n	k
HDR.nbinom	size	prob	mu
HDR.pois	lambda

Using `extraDistr`
HDR.betapr	shape1	shape2	scale
HDR.fatigue	alpha	beta	mu
HDR.gompertz	shape	scale
HDR.gpd	mu,location	sigma, scale	shape, xi
HDR.huber	mu	sigma	epsilon
HDR.kumar	a,shape1	b,shape2
HDR.tnorm	mean	sd	a, b, min, max

Using `invgamma`
HDR.invchisq	df	ncp
HDR.invexp	rate
HDR.invgamma	shape	rate	scale

Using `VGAM`
HDR.benini	shape	y0	scale
HDR.frechet	shape	scale	location
HDR.gengamma	d, shape1	k, shape2	rate, scale
HDR.gumbelII	shape	scale
HDR.lgamma	shape	scale	location
HDR.matching	size	prob	trials & approx

The table above shows the parameters in each of the distributions. Some have default values, but most need to be specified. (For the gamma distribution you should specify either the rate or scale but not both.)

Examples

Run this code

# NOT RUN {
HDR.norm(.95)
# }

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