distrMode function

Mode of some continuous and discrete distributions

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

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.

Returns

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.

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)

See Also

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

Author(s)

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