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]