% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrMode.R
\name{distrMode}
\alias{distrMode}
\alias{betaMode}
\alias{cauchyMode}
\alias{chisqMode}
\alias{dagumMode}
\alias{expMode}
\alias{fMode}
\alias{fiskMode}
\alias{frechetMode}
\alias{gammaMode}
\alias{normMode}
\alias{gevMode}
\alias{ghMode}
\alias{ghtMode}
\alias{gldMode}
\alias{gompertzMode}
\alias{gpdMode}
\alias{gumbelMode}
\alias{hypMode}
\alias{koenkerMode}
\alias{kumarMode}
\alias{laplaceMode}
\alias{logisMode}
\alias{lnormMode}
\alias{lomaxMode}
\alias{maxwellMode}
\alias{mvnormMode}
\alias{nakaMode}
\alias{nigMode}
\alias{paralogisticMode}
\alias{paretoMode}
\alias{rayleighMode}
\alias{stableMode}
\alias{stableMode2}
\alias{tMode}
\alias{unifMode}
\alias{weibullMode}
\alias{yulesMode}
\alias{bernMode}
\alias{binomMode}
\alias{geomMode}
\alias{hyperMode}
\alias{nbinomMode}
\alias{poisMode}
\title{Mode of some continuous and discrete distributions}
\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{
\item{x}{character. The name of the distribution to consider.}

\item{...}{Additional parameters.}

\item{shape1}{non-negative parameters of the Beta distribution.}

\item{shape2}{non-negative parameters of the Beta distribution.}

\item{ncp}{non-centrality parameter.}

\item{location}{location and scale parameters.}

\item{df}{degrees of freedom (non-negative, but can be non-integer).}

\item{scale}{location and scale parameters.}

\item{shape1.a}{shape parameters.}

\item{shape2.p}{shape parameters.}

\item{df1}{degrees of freedom.  \code{Inf} is allowed.}

\item{df2}{degrees of freedom.  \code{Inf} is allowed.}

\item{shape}{the location parameter \eqn{a},
  scale parameter \eqn{b}, and shape parameter \eqn{s}.}

\item{rate}{vector of rates.}

\item{mean}{vector of means.}

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

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

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

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

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

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

\item{lambda1}{
    are numeric values where
    \code{lambda1} is the location parameter,
    \code{lambda2} is the location parameter,
    \code{lambda3} is the first shape parameter, and
    \code{lambda4} is the second shape parameter.
  }

\item{lambda2}{
    are numeric values where
    \code{lambda1} is the location parameter,
    \code{lambda2} is the location parameter,
    \code{lambda3} is the first shape parameter, and
    \code{lambda4} is the second shape parameter.
  }

\item{lambda3}{
    are numeric values where
    \code{lambda1} is the location parameter,
    \code{lambda2} is the location parameter,
    \code{lambda3} is the first shape parameter, and
    \code{lambda4} is the second shape parameter.
  }

\item{lambda4}{
    are numeric values where
    \code{lambda1} is the location parameter,
    \code{lambda2} is the location parameter,
    \code{lambda3} is the first shape parameter, and
    \code{lambda4} is the second shape parameter.
  }

\item{pm}{
        an integer value between \code{1} and \code{4} for the 
        selection of the parameterization. The default takes the
        first parameterization.       
        }

\item{meanlog}{mean and standard deviation of the distribution
    on the log scale with default values of \code{0} and \code{1} respectively.}

\item{sdlog}{mean and standard deviation of the distribution
    on the log scale with default values of \code{0} and \code{1} respectively.}

\item{gamma}{
    value of the index parameter \code{alpha} in the interval= \eqn{(0, 2]};
    skewness parameter \code{beta}, in the range \eqn{[-1, 1]};
    scale parameter \code{gamma}; and location (or \sQuote{shift})
    parameter \code{delta}.
  }

\item{loc}{vector of (real) location parameters.}

\item{disp}{vector of (positive) dispersion parameters.}

\item{skew}{vector of skewness parameters (in [-1,1]).}

\item{tail}{vector of parameters (in [1,2]) related to the tail thickness.}

\item{min}{lower and upper limits of the distribution.  Must be finite.}

\item{max}{lower and upper limits of the distribution.  Must be finite.}

\item{prob}{Probability of success on each trial.}

\item{size}{number of trials (zero or more).}

\item{m}{the number of white balls in the urn.}

\item{n}{number of observations. If \code{length(n) > 1}, the length
    is taken to be the number required.}

\item{k}{the number of balls drawn from the urn.}
}
\value{
A numeric value is returned, the (true) mode of the distribution.
}
\description{
These functions return the mode of the main probability 
distributions implemented in R.
}
\note{
Some functions like \code{normMode} or \code{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)

}
\seealso{
\code{\link[modeest]{mlv}} for the estimation of the mode; 
the documentation of the related distributions 
\code{\link[stats]{Beta}}, \code{\link[stats]{GammaDist}}, etc.
}
\author{
\code{\link[fBasics]{ghMode}} and \code{\link[fBasics]{ghtMode}} are from 
package \pkg{fBasics}; 
\code{\link[fBasics]{hypMode}} was written by David Scott; 
\code{\link[fBasics]{gldMode}}, \code{\link[fBasics]{nigMode}} and 
\code{\link[stabledist]{stableMode}} were written by Diethelm Wuertz.
}