distrMode: Mode of some continuous and discrete distributions
In modeest: Mode Estimation

Description Usage Arguments Value Note Author(s) See Also Examples

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)

`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.

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

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

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

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

## 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)