Fit of univariate distributions by matching moments (raw or centered) for non censored data.
mmedist(data, distr, order, memp, start = NULL, fix.arg = NULL, optim.method = "default",
lower = -Inf, upper = Inf, custom.optim = NULL, weights = NULL, silent = TRUE,
gradient = NULL, checkstartfix=FALSE, ...)mmedist returns a list with following components,
the parameter estimates.
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.
the minimal value reached for the criterion to minimize.
a symmetric matrix computed by optim as an estimate of the Hessian
at the solution found or computed in the user-supplied optimization function.
(if appropriate) the name of the optimization function used for maximum likelihood.
(if appropriate) when optim is used, the name of the
algorithm used, the field method of the custom.optim function
otherwise.
the named list giving the values of parameters of the named distribution
that must kept fixed rather than estimated by maximum likelihood or NULL
if there are no such parameters.
the function used to set the value of fix.arg or NULL.
the vector of weigths used in the estimation process or NULL.
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. counts is returned by optim
or the user-supplied function or set to NULL.
A character string giving any additional information
returned by the optimizer, or NULL. To understand exactly the message,
see the source code.
the log-likelihood value.
either "closed formula" or the name of the optimization method.
the order of the moment(s) matched.
the empirical moment function.
A numeric vector for non censored data.
A character string "name" naming a distribution (see 'details').
A numeric vector for the moment order(s). The length of this vector must be equal to the number of parameters to estimate.
A function implementing empirical moments, raw or centered but has to be consistent with
distr argument (and weights argument).
See details below.
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 mledist).
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.
"default" or optimization method to pass to optim.
Left bounds on the parameters for the "L-BFGS-B" method (see optim).
Right bounds on the parameters for the "L-BFGS-B" method (see optim).
a function carrying the optimization .
an optional vector of weights to be used in the fitting process.
Should be NULL or a numeric vector with strictly positive integers
(typically the number of occurences of each observation). If non-NULL,
weighted MME is used, otherwise ordinary MME.
A logical to remove or show warnings when bootstraping.
A function to return the gradient of the squared difference for the "BFGS", "CG"
and "L-BFGS-B" methods. If it is NULL, a finite-difference approximation will be used,
see details.
A logical to test starting and fixed values. Do not change it.
further arguments passed to the optim,
constrOptim or custom.optim function.
Marie-Laure Delignette-Muller and Christophe Dutang.
The argument distr can be one of the base R distributions: "norm", "lnorm",
"exp" and "pois", "gamma", "logis",
"nbinom" , "geom", "beta" and "unif".
In that case, no other arguments than data and distr are
required, because the estimate is computed by a closed-form formula.
For distributions characterized by one parameter ("geom", "pois" and "exp"),
this parameter is simply estimated by matching theoretical and observed means, and for distributions
characterized by two parameters, these parameters are estimated by matching theoretical and observed
means and variances (Vose, 2000).
Note that for these closed-form formula, fix.arg cannot be used and start is ignored.
The argument distr can also be the distribution name
as long as a corresponding mdistr function exists, e.g. "pareto" if "mpareto" exists.
In that case arguments arguments order and memp
have to be supplied in order to carry out the matching numerically, by minimization of the
sum of squared differences between observed and theoretical moments.
Optionnally other arguments can be supplied to control optimization (see the 'details' section of
mledist for details about arguments for the control of optimization).
In that case, fix.arg can be used and start is taken into account.
For non closed-form estimators, memp must be provided to compute empirical moments.
When weights=NULL, this function must have two arguments x, order:
x the numeric vector of the data and order the order of the moment.
When weights!=NULL, this function must have three arguments x, order, weights:
x the numeric vector of the data, order the order of the moment,
weights the numeric vector of weights. See examples below.
Optionally, a vector of weights can be used in the fitting process.
By default (when weigths=NULL), ordinary MME is carried out, otherwise
the specified weights are used to compute (raw or centered) weighted moments.
For closed-form estimators, weighted mean and variance are computed by
wtd.mean and wtd.var
from the Hmisc package. When a numerical minimization
is used, weighted are expected to be computed by the memp function.
It is not yet possible to take into account weighths in functions plotdist,
plotdistcens, plot.fitdist, plot.fitdistcens, cdfcomp,
cdfcompcens, denscomp, ppcomp, qqcomp, gofstat
and descdist
(developments planned in the future).
This function is not intended to be called directly but is internally called in
fitdist and bootdist when used with the matching moments method.
Evans M, Hastings N and Peacock B (2000), Statistical distributions. John Wiley and Sons Inc.
Vose D (2000), Risk analysis, a quantitative guide. John Wiley & Sons Ltd, Chischester, England, pp. 99-143.
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
mmedist, qmedist, mgedist,
fitdist,fitdistcens,
optim, bootdistcens and bootdist.
# (1) basic fit of a normal distribution with moment matching estimation
#
set.seed(1234)
n <- 100
x1 <- rnorm(n=n)
mmedist(x1, "norm")
#weighted
w <- c(rep(1, n/2), rep(10, n/2))
mmedist(x1, "norm", weights=w)$estimate
# (2) fit a discrete distribution (Poisson)
#
set.seed(1234)
x2 <- rpois(n=30,lambda = 2)
mmedist(x2, "pois")
# (3) fit a finite-support distribution (beta)
#
set.seed(1234)
x3 <- rbeta(n=100,shape1=5, shape2=10)
mmedist(x3, "beta")
# (4) fit a Pareto distribution
#
# \donttest{
require(actuar)
#simulate a sample
x4 <- rpareto(1000, 6, 2)
#empirical raw moment
memp <- function(x, order) mean(x^order)
memp2 <- function(x, order, weights) sum(x^order * weights)/sum(weights)
#fit by MME
mmedist(x4, "pareto", order=c(1, 2), memp=memp,
start=list(shape=10, scale=10), lower=1, upper=Inf)
#fit by weighted MME
w <- rep(1, length(x4))
w[x4 < 1] <- 2
mmedist(x4, "pareto", order=c(1, 2), memp=memp2, weights=w,
start=list(shape=10, scale=10), lower=1, upper=Inf)
# }
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