fitdistrplus (version 0.3-4)

mgedist: Maximum goodness-of-fit fit of univariate continuous distributions

Description

Fit of univariate continuous distribution by maximizing goodness-of-fit (or minimizing distance) for non censored data.

Usage

mgedist(data, distr, gof="CvM", start=NULL, fix.arg=NULL, 
    optim.method="default", lower=-Inf, upper=Inf, custom.optim=NULL, ...)

Arguments

data

A numeric vector for non censored data.

distr

A character string "name" naming a distribution for which the corresponding quantile function qname and the corresponding density distribution dname must be classically defined.

gof

A character string coding for the name of the goodness-of-fit distance used : "CvM" for Cramer-von Mises distance,"KS" for Kolmogorov-Smirnov distance, "AD" for Anderson-Darling distance, "ADR", "ADL", "AD2R", "AD2L" and "AD2" for variants of

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).

fix.arg

An optional named list giving the values of parameters of the named distribution that must kept fixed rather than estimated.

optim.method

"default" or optimization method to pass to optim.

lower

Left bounds on the parameters for the "L-BFGS-B" method (see optim).

upper

Right bounds on the parameters for the "L-BFGS-B" method (see optim).

custom.optim

a function carrying the optimization.

...

further arguments passed to the optim or custom.optim function.

Value

• mgedist returns a list with following components,
• estimate
  the parameter estimates.
• convergence
  an integer code for the convergence of optim defined as below or defined by the user in the user-supplied optimization function. 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.
• value
  the value of the statistic distance corresponding to estimate.
• hessian
  a symmetric matrix computed by optim as an estimate of the Hessian at the solution found or computed in the user-supplied optimization function.
• gof
  the code of the goodness-of-fit distance maximized.
• optim.function
  the name of the optimization function used.
• loglik
  the log-likelihood.

Details

The mgedist function numerically maximizes goodness-of-fit, or minimizes a goodness-of-fit distance coded by the argument gof. One may use one of the classical distances defined in Stephens (1986), the Cramer-von Mises distance ("CvM"), the Kolmogorov-Smirnov distance ("KS") or the Anderson-Darling distance ("AD") which gives more weight to the tails of the distribution, or one of the variants of this last distance proposed by Luceno (2006). The right-tail AD ("ADR") gives more weight only to the right tail, the left-tail AD ("ADL") gives more weight only to the left tail. Either of the tails, or both of them, can receive even larger weights by using second order Anderson-Darling Statistics (using "AD2R", "AD2L" or "AD2"). The optimization process is the same as mledist, see the 'details' section of mledist. This function is not intended to be called directly but is internally called in fitdist and bootdist. This function is intended to be used only with continuous distributions. NB: if your data are particularly low or high, a scaling may be needed before the optimization process. See example (3).

References

Luceno, A. 2006. Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics and Data Analysis, 51, 904-917. Stephens MA (1986) Tests based on edf statistics. In Goodness-of-fit techniques (D'Agostino RB and Stephens MA, eds), Marcel dekker, New York, pp. 97-194.

See Also

mmedist, mledist, qmedist, fitdist for other estimation methods.

Examples

# (1) Fit of a Weibull distribution to serving size data by maximum 
# goodness-of-fit estimation using all the distances available
# 

data(groundbeef)
serving <- groundbeef$serving
mgedist(serving,"weibull",gof="CvM")
mgedist(serving,"weibull",gof="KS")
mgedist(serving,"weibull",gof="AD")
mgedist(serving,"weibull",gof="ADR")
mgedist(serving,"weibull",gof="ADL")
mgedist(serving,"weibull",gof="AD2R")
mgedist(serving,"weibull",gof="AD2L")
mgedist(serving,"weibull",gof="AD2")

# (2) Fit of a uniform distribution using Cramer-von Mises or
# Kolmogorov-Smirnov distance
# 

u <- runif(100,min=5,max=10)
mgedist(u,"unif",gof="CvM")
mgedist(u,"unif",gof="KS")


# (3) scaling problem
#

x <- c(-0.00707717, -0.000947418, -0.00189753, 
-0.000474947, -0.00190205, -0.000476077, 0.00237812, 0.000949668, 
0.000474496, 0.00284226, -0.000473149, -0.000473373, 0, 0, 0.00283688, 
-0.0037843, -0.0047506, -0.00238379, -0.00286807, 0.000478583, 
0.000478354, -0.00143575, 0.00143575, 0.00238835, 0.0042847, 
0.00237248, -0.00142281, -0.00142484, 0, 0.00142484, 0.000948767, 
0.00378609, -0.000472478, 0.000472478, -0.0014181, 0, -0.000946522, 
-0.00284495, 0, 0.00331832, 0.00283554, 0.00141476, -0.00141476, 
-0.00188947, 0.00141743, -0.00236351, 0.00236351, 0.00235794, 
0.00235239, -0.000940292, -0.0014121, -0.00283019, 0.000472255, 
0.000472032, 0.000471809, -0.0014161, 0.0014161, -0.000943842, 
0.000472032, -0.000944287, -0.00094518, -0.00189304, -0.000473821, 
-0.000474046, 0.00331361, -0.000472701, -0.000946074, 0.00141878, 
-0.000945627, -0.00189394, -0.00189753, -0.0057143, -0.00143369, 
-0.00383326, 0.00143919, 0.000479272, -0.00191847, -0.000480192, 
0.000960154, 0.000479731, 0, 0.000479501, 0.000958313, -0.00383878, 
-0.00240674, 0.000963391, 0.000962464, -0.00192586, 0.000481812, 
-0.00241138, -0.00144963)


#only i == 0, no scaling, should not converge.
for(i in 6:0)
    cat(i, try(mgedist(x*10^i,"cauchy")$estimate, silent=TRUE), "")