fitdistrplus (version 0.1-1)

mledist: Maximum likelihood fitting of univariate distributions

Description

Fits a univariate distribution by maximum likelihood using the optimization function optim.

Usage

mledist(data, distr, start)

Arguments

data

A numeric vector.

distr

A character string "name" naming a distribution for which the corresponding density function dname must be defined, or directly the density function.

start

A named list giving the initial values of parameters of the named distribution. This argument may be omitted for some distributions for which reasonable starting values are computed (see details).

Value

• mledist returns a list with 4 components,
• estimate
  the parameter estimates
• convergence
  an integer code for the convergence of optim. 0 indicates successful convergence. 1 indicates that the iteration limit of optim has been reached. 10 indicates degeneracy of the Nealder-Mead simplex. 100 indicates that optim encountered an internal error.
• loglik
  the log-likelihood
• hessian
  a symmetric matrix computed by optim as an estimate of the Hessian at the solution found. It is used in fitdist to estimate standard errors.

Details

Maximum likelihood estimations of the distribution parameters are computed. Direct optimization of the log-likelihood is performed using optim, with its default method "Nelder-Mead" for distributions characterized by more than one parameter and the method "BFGS" for distributions characterized by only one parameter. For the following named distributions, reasonable starting values will be computed if start is omitted : "norm", "lnorm", "exp" and "pois", "cauchy", "gamma", "logis", "nbinom" (parametrized by mu and size), "geom", "beta" and "weibull". Note that these starting values may not be good enough if the fit is poor. The function is not able to fit a uniform distribution. This function is not intended to be called directly but is internally called in fitdist and bootdist when used with the maximum likelihood method.

References

Venables WN and Ripley BD (2002) Modern applied statistics with S. Springer, New York, pp. 435-446.

See Also

momdist, fitdist, optim and bootdist.

Examples

x1<-c(6.4,13.3,4.1,1.3,14.1,10.6,9.9,9.6,15.3,22.1,13.4,
13.2,8.4,6.3,8.9,5.2,10.9,14.4)
mledist(x1,"norm")

dgumbel<-function(x,a,b) 1/b*exp((a-x)/b)*exp(-exp((a-x)/b))
mledist(x1,"gumbel",start=list(a=10,b=5))

x2<-c(rep(4,1),rep(2,3),rep(1,7),rep(0,12))
mledist(x2,"pois")
mledist(x2,"nbinom")

x3<-c(0.80,0.72,0.88,0.84,0.38,0.64,0.69,0.48,0.73,0.58,0.81,
0.83,0.71,0.75,0.59)
mledist(x3,"beta")