distrMode: Mode of some continuous and discrete distributions

In modeest: Mode Estimation

Mode of some continuous and discrete distributions

Description

These functions return the mode of the main probability distributions implemented in R.

Usage

distrMode(x, ...)

betaMode(shape1, shape2, ncp = 0L)

cauchyMode(location = 0, ...)

chisqMode(df, ncp = 0L)

dagumMode(scale = 1, shape1.a, shape2.p)

expMode(...)

fMode(df1, df2)

fiskMode(scale = 1, shape1.a)

frechetMode(location = 0, scale = 1, shape = 1, ...)

gammaMode(shape, rate = 1, scale = 1/rate)

normMode(mean = 0, ...)

gevMode(location = 0, scale = 1, shape = 0, ...)

ghMode(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -0.5)

ghtMode(beta = 0.1, delta = 1, mu = 0, nu = 10)

gldMode(lambda1 = 0, lambda2 = -1, lambda3 = -0.125, lambda4 = -0.125)

gompertzMode(scale = 1, shape)

gpdMode(location = 0, scale = 1, shape = 0)

gumbelMode(location = 0, ...)

hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = c(1L, 2L, 3L, 4L))

koenkerMode(location = 0, ...)

kumarMode(shape1, shape2)

laplaceMode(location = 0, ...)

logisMode(location = 0, ...)

lnormMode(meanlog = 0, sdlog = 1)

lomaxMode(...)

maxwellMode(rate)

mvnormMode(mean, ...)

nakaMode(scale = 1, shape)

nigMode(alpha = 1, beta = 0, delta = 1, mu = 0)

paralogisticMode(scale = 1, shape1.a)

paretoMode(scale = 1, ...)

rayleighMode(scale = 1)

stableMode(alpha, beta, gamma = 1, delta = 0, pm = 0, ...)

stableMode2(loc, disp, skew, tail)

tMode(df, ncp)

unifMode(min = 0, max = 1)

weibullMode(shape, scale = 1)

yulesMode(...)

bernMode(prob)

binomMode(size, prob)

geomMode(...)

hyperMode(m, n, k, ...)

nbinomMode(size, prob, mu)

poisMode(lambda)

Arguments

x	character. The name of the distribution to consider.
...	Additional parameters.
shape1, shape2	non-negative parameters of the Beta distribution.
ncp	non-centrality parameter.
location, scale	location and scale parameters.
df	degrees of freedom (non-negative, but can be non-integer).
shape1.a, shape2.p	shape parameters.
df1, df2	degrees of freedom. Inf is allowed.
shape	the shape parameter \xi.
rate	vector of rates.
mean	vector of means.
alpha	first shape parameter.
beta	second shape parameter, should in the range (0, alpha).
delta	scale parameter, must be zero or positive.
mu	location parameter, by default 0.
lambda	defines the sublclass, by default -1/2.
nu	a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.
lambda1	location parameter.
lambda2	scale parameter.
lambda3	first shape parameter.
lambda4	second shape parameter.
pm	an integer value between 1 and 4 for the selection of the parameterization. The default takes the first parameterization.
meanlog, sdlog	mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.
gamma	scale parameter.
loc	vector of (real) location parameters.
disp	vector of (positive) dispersion parameters.
skew	vector of skewness parameters (in [-1,1]).
tail	vector of parameters (in [1,2]) related to the tail thickness.
min, max	lower and upper limits of the distribution. Must be finite.
prob	Probability of success on each trial.
size	number of trials (zero or more).
m	the number of white balls in the urn.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
k	the number of balls drawn from the urn, hence must be in 0,1,\dots, m+n.

Value

A numeric value is returned, the (true) mode of the distribution.

Note

Some functions like normMode or cauchyMode, which relate to symmetric distributions, are trivial, but are implemented for the sake of exhaustivity.

Author(s)

ghMode and ghtMode are from package fBasics; hypMode was written by David Scott; gldMode, nigMode and stableMode were written by Diethelm Wuertz.

See Also

mlv for the estimation of the mode; the documentation of the related distributions Beta, GammaDist, etc.

Examples

## Beta distribution
curve(dbeta(x, shape1 = 2., shape2 = 3.1),
      xlim = c(0., 1.), ylab = "Beta density")
M <- betaMode(shape1 = 2., shape2 = 3.1)
abline(v = M, col = 2L)
mlv("beta", shape1 = 2., shape2 = 3.1)

## Lognormal distribution
curve(stats::dlnorm(x, meanlog = 3, sdlog = 1.1),
      xlim = c(0, 10), ylab = "Lognormal density")
M <- lnormMode(meanlog = 3, sdlog = 1.1)
abline(v = M, col = 2)
mlv("lnorm", meanlog = 3, sdlog = 1.1)


curve(VGAM::dpareto(x, scale = 1, shape = 1), xlim = c(0, 10))
abline(v = paretoMode(scale = 1), col = 2)

## Poisson distribution
poisMode(lambda = 6.)
poisMode(lambda = 6.1)
mlv("poisson", lambda = 6.1)

modeest documentation built on Sept. 21, 2026, 1:06 a.m.