R: Computing the Mode of Some Distributions

distribMode {modeest} | R Documentation

## Computing the Mode of Some Distributions

### Description

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

### Usage

      ## Continuous distributions

      # Beta
      betaMode(shape1, shape2, ncp = 0)

      # Cauchy
      cauchyMode(location = 0, ...)

      # Chisquare
      chisqMode(df, ncp = 0)

      # Exponentiel
      expMode(...)

      # F
      fMode(df1, df2)

      # Fisk (package 'VGAM')
      fiskMode(shape1.a, scale = 1)

      # Frechet (package 'evd')
      frechetMode(loc = 0, scale = 1, shape = 1, ...)

      # Gamma
      gammaMode(shape, rate = 1, scale = 1/rate)

      # Normal (Gaussian)
      normMode(mean = 0, ...)

      # Generalised Extreme Value (package 'evd')
      gevMode(loc = 0, scale = 1, shape = 0, ...)

      # Generalised Hyperbolic (package 'fBasics')
      ghMode(alpha = 1, beta = 0, delta = 1, mu = 0,
             lambda = -1/2, ...)

      # Gompertz (package 'VGAM')
      gompertzMode(shape, scale = 1)

      # Generalised Pareto (package 'evd')
      gpdMode(loc = 0, scale = 1, shape = 0, ...)

      # Gumbel (package 'evd')
      gumbelMode(loc = 0, ...)

      # Hyperbolic (package 'fBasics')
      hypMode(alpha = 1, beta = 0, delta = 1, mu = 0,
              pm = c(1, 2, 3, 4))

      # Koenker (package 'VGAM')
      koenkerMode(location = 0, ...)

      # Kumaraswamy (package 'VGAM')
      kumarMode(shape1, shape2)

      # Laplace (package 'VGAM')
      laplaceMode(location = 0, ...)

      # Logistic
      logisMode(location = 0, ...)

      # Lognormal
      lnormMode(meanlog = 0, sdlog = 1)

      # Normal Inverse Gaussian (package 'fBasics')
      nigMode(alpha = 1, beta = 0, delta = 1, mu = 0, ...)

      # Stable (package 'stabledist')
      stableMode(alpha, beta, gamma = 1, delta = 0, pm = 0, ...)

      # Negative Weibull (package 'evd')
      rweibullMode(loc = 0, scale = 1, shape = 1, ...)

      # Paralogistic (package 'VGAM')
      paralogisticMode(shape1.a, scale = 1)

      # Pareto (package 'VGAM')
      paretoMode(location, ...)

      # Rayleigh (package 'VGAM')
      rayleighMode(scale = 1)

      # T (Student)
      tMode(df, ncp = 0)

      # Uniform
      unifMode(min = 0, max = 1)

      # Weibull
      weibullMode(shape, scale = 1, ...)

      ## Discrete distributions

      # Bernoulli
      bernMode(prob)

      # Binomial
      binomMode(size, prob)

      # Geometric
      geomMode(...)

      # Hypergeometric
      hyperMode(m, n, k, ...)

      # Negative Binomial
      nbinomMode(size, prob, mu)

      # Poisson
      poisMode(lambda)

### Arguments

`shape1` | First positive parameter of the Beta and Kumaraswamy distributions. See the package VGAM for more details.
`shape2` | Second positive parameter of the Beta and Kumaraswamy distributions. See the package VGAM for more details.
`shape1.a` | Shape parameter of the Fisk and Paralogistic distributions. See the package VGAM for more details.
`ncp` | Non-centrality parameter of the Beta, Chisquare, and Student distributions.
`location` | Location parameter of the Cauchy, Koenker, Laplace, Logistic, and Pareto distributions. See the package VGAM for more details.
`df` | Degree of freedom of the Chisquare and Student distributions.
`df1` | First degree of freedom of the F distribution.
`df2` | Second degree of freedom of the F distribution.
`loc` | Location parameter of the Fr\'echet, Generalized Extreme Value, Generalized Pareto, Gumbel, and Negative Weibull distributions.
`scale` | Scale parameter of the Fisk, Fr\'echet, Gamma, Generalized Extreme Value, Gompertz, Generalized Pareto, Negative Weibull, Paralogistic, Rayleigh, and Weibull distributions. See the packages evd and VGAM for more details.
`shape` | Shape parameter of the Fr\'echet, Gamma, Generalized Extreme Value, Gompertz, Generalized Pareto, Negative Weibull, and Weibull distributions. See the packages evd and VGAM for more details.
`rate` | An alternative way to specify the scale of the Gamma distribution.
`mean` | Mean of the Normal distribution.
`alpha` | Parameter of the Hyperbolic, Generalised Hyperbolic, Stable, and Normal Inverse Gaussian distributions. See the packages fBasics and stabledist for more details.
`beta` | Parameter of the Hyperbolic, Generalised Hyperbolic, Stable, and Normal Inverse Gaussian distributions. See the packages fBasics and stabledist for more details.
`delta` | Parameter of the Hyperbolic, Generalised Hyperbolic, Stable, and Normal Inverse Gaussian distributions. See the packages fBasics and stabledist for more details.
`mu` | Parameter of the Hyperbolic, Generalised Hyperbolic, Normal Inverse Gaussian, and Negative binomial distributions. See the package fBasics for more details.
`lambda` | Vector of (non-negative) means of the Poisson distribution.
`pm` | Integer value for the selection of the parameterization of the Hyperbolic and Stable distributions. See the packages fBasics and stabledist for more details.
`meanlog` | Mean of the Lognormal distribution on the log scale.
`sdlog` | Standard deviation of the Lognormal distribution on the log scale.
`gamma` | Scale parameter of the Stable distribution. See the package stabledist for more details.
`min` | Lower limit of the Uniform distribution. Must be finite.
`max` | Upper limit of the Uniform distribution. Must be finite.
`prob` | Probability of success on each trial (between 0 and 1), used in the Bernoulli, Binomial and Negative Binomial distributions.
`size` | Number of trials (zero or more), used in the Binomial and Negative Binomial distributions.
`m` | Number of white balls in the urn for the Hypergeometric distribution.
`n` | Number of black balls in the urn for the Hypergeometric distribution.
`k` | Number of balls drawn from the urn for the Hypergeometric distribution.
`...` | Further arguments, which will be ignored.

### Value

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

### Note

Some functions like `normMode` or `cauchyMode`, which are related to symmetric distributions, are trivial, but are implemented for exhaustivity.

### Author(s)

P. Poncet, except for `hypMode` written by David Scott, `nigMode` and `stableMode` written by Diethelm Wuertz; see packages fBasics and stabledist.

### See Also

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

### Examples

    layout(mat = matrix(1:2,1,2))

    ## 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(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)

    ## Poisson distribution
    poisMode(lambda = 6)
    poisMode(lambda = 6.1)
    mlv("poisson", lambda = 6.1)

    layout(mat = matrix(1,1,1))

[Package modeest version 2.1 Index]