Maximum goodness-of-fit fit of univariate continuous distributions
Fit of univariate continuous distribution by maximizing goodness-of-fit (or minimizing distance) for non censored data.
mgedist(data, distr, gof = "CvM", start = NULL, fix.arg = NULL, optim.method = "default", lower = -Inf, upper = Inf, custom.optim = NULL, silent = TRUE, gradient = NULL, checkstartfix=FALSE, ...)
data |
A numeric vector for non censored data. |
distr |
A character string |
gof |
A character string coding for the name of the goodness-of-fit distance used :
|
start |
A named list giving the initial values of parameters of the named distribution
or a function of data computing initial values and returning a named list.
This argument may be omitted (default) for some distributions for which reasonable
starting values are computed (see the 'details' section of |
fix.arg |
An optional named list giving the values of fixed parameters of the named distribution or a function of data computing (fixed) parameter values and returning a named list. Parameters with fixed value are thus NOT estimated. |
optim.method |
|
lower |
Left bounds on the parameters for the |
upper |
Right bounds on the parameters for the |
custom.optim |
a function carrying the optimization. |
silent |
A logical to remove or show warnings when bootstraping. |
gradient |
A function to return the gradient of the gof distance for the |
checkstartfix |
A logical to test starting and fixed values. Do not change it. |
... |
further arguments passed to the |
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 that function.
This function is intended to be used only with continuous distributions and weighted maximum goodness-of-fit estimation is not allowed.
NB: if your data values are particularly small or large, a scaling may be needed before the optimization process. See example (4).
mgedist returns a list with following components,
estimate |
the parameter estimates. |
convergence |
an integer code for the convergence of |
value |
the minimal value reached for the criterion to minimize. |
hessian |
a symmetric matrix computed by |
optim.function |
the name of the optimization function used for maximum likelihood. |
optim.method |
when |
fix.arg |
the named list giving the values of parameters of the named distribution
that must kept fixed rather than estimated by maximum likelihood or |
fix.arg.fun |
the function used to set the value of |
weights |
the vector of weigths used in the estimation process or |
counts |
A two-element integer vector giving the number of calls
to the log-likelihood function and its gradient respectively.
This excludes those calls needed to compute the Hessian, if requested,
and any calls to log-likelihood function to compute a finite-difference
approximation to the gradient. |
optim.message |
A character string giving any additional information
returned by the optimizer, or |
loglik |
the log-likelihood value. |
gof |
the code of the goodness-of-fit distance maximized. |
Marie-Laure Delignette-Muller and Christophe Dutang.
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.
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
# (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$serving
mgedist(serving, "weibull", gof="CvM")
mgedist(serving, "weibull", gof="KS")
mgedist(serving, "weibull", gof="AD")
mgedist(serving, "weibull", gof="ADR")
mgedist(serving, "weibull", gof="ADL")
mgedist(serving, "weibull", gof="AD2R")
mgedist(serving, "weibull", gof="AD2L")
mgedist(serving, "weibull", gof="AD2")
# (2) Fit of a uniform distribution using Cramer-von Mises or
# Kolmogorov-Smirnov distance
#
set.seed(1234)
u <- runif(100,min=5,max=10)
mgedist(u,"unif",gof="CvM")
mgedist(u,"unif",gof="KS")
# (3) Fit of a triangular distribution using Cramer-von Mises or
# Kolmogorov-Smirnov distance
#
## Not run:
require(mc2d)
set.seed(1234)
t <- rtriang(100,min=5,mode=6,max=10)
mgedist(t,"triang",start = list(min=4, mode=6,max=9),gof="CvM")
mgedist(t,"triang",start = list(min=4, mode=6,max=9),gof="KS")
## End(Not run)
# (4) scaling problem
# the simulated dataset (below) has particularly small values, hence without scaling (10^0),
# the optimization raises an error. The for loop shows how scaling by 10^i
# for i=1,...,6 makes the fitting procedure work correctly.
set.seed(1234)
x2 <- rnorm(100, 1e-4, 2e-4)
for(i in 6:0)
cat(i, try(mgedist(x*10^i,"cauchy")$estimate, silent=TRUE), "\n")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.