distrMode: 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)

Value

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

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
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 \(0,1,\dots, m+n\).

Author

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

Examples

Run this code

## 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)

if (FALSE) { # requireNamespace("VGAM")
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)