distrMode {modeest}R Documentation

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 = 0)

cauchyMode(location = 0, ...)

chisqMode(df, ncp = 0)

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 = -1/2)

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

gldMode(lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8)

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(1, 2, 3, 4))

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

non-negative parameters of the Beta distribution.

shape2

non-negative parameters of the Beta distribution.

ncp

non-centrality parameter.

location

location and scale parameters.

df

degrees of freedom (non-negative, but can be non-integer).

scale

location and scale parameters.

shape1.a

shape parameters.

shape2.p

shape parameters.

df1

degrees of freedom. Inf is allowed.

df2

degrees of freedom. Inf is allowed.

shape

the location parameter a, scale parameter b, and shape parameter s.

rate

vector of rates.

mean

vector of means.

alpha

shape parameter alpha; skewness parameter beta, abs(beta) is in the range (0, alpha); scale parameter delta, delta must be zero or positive; location parameter mu, by default 0. These is the meaning of the parameters in the first parameterization pm=1 which is the default parameterization selection. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

beta

shape parameter alpha; skewness parameter beta, abs(beta) is in the range (0, alpha); scale parameter delta, delta must be zero or positive; location parameter mu, by default 0. These is the meaning of the parameters in the first parameterization pm=1 which is the default parameterization selection. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

delta

shape parameter alpha; skewness parameter beta, abs(beta) is in the range (0, alpha); scale parameter delta, delta must be zero or positive; location parameter mu, by default 0. These is the meaning of the parameters in the first parameterization pm=1 which is the default parameterization selection. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

mu

shape parameter alpha; skewness parameter beta, abs(beta) is in the range (0, alpha); scale parameter delta, delta must be zero or positive; location parameter mu, by default 0. These is the meaning of the parameters in the first parameterization pm=1 which is the default parameterization selection. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

lambda

shape parameter alpha; skewness parameter beta, abs(beta) is in the range (0, alpha); scale parameter delta, delta must be zero or positive; location parameter mu, by default 0. These is the meaning of the parameters in the first parameterization pm=1 which is the default parameterization selection. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

nu

a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.

lambda1

are numeric values where lambda1 is the location parameter, lambda2 is the location parameter, lambda3 is the first shape parameter, and lambda4 is the second shape parameter.

lambda2

are numeric values where lambda1 is the location parameter, lambda2 is the location parameter, lambda3 is the first shape parameter, and lambda4 is the second shape parameter.

lambda3

are numeric values where lambda1 is the location parameter, lambda2 is the location parameter, lambda3 is the first shape parameter, and lambda4 is the second shape parameter.

lambda4

are numeric values where lambda1 is the location parameter, lambda2 is the location parameter, lambda3 is the first shape parameter, and lambda4 is the second shape parameter.

pm

an integer value between 1 and 4 for the selection of the parameterization. The default takes the first parameterization.

meanlog

mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.

sdlog

mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.

gamma

value of the index parameter alpha in the interval= (0, 2]; skewness parameter beta, in the range [-1, 1]; scale parameter gamma; and location (or ‘shift’) parameter delta.

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

lower and upper limits of the distribution. Must be finite.

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.

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 = 2)
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)


[Package modeest version 2.4.0 Index]