Fit of destruction rate models
Description
Fit of univariate distributions to destruction rate data by maximum likelihood (mle),
moment matching (mme), quantile matching (qme) or
maximizing goodnessoffit estimation (mge).
The latter is also known as minimizing distance estimation.
Generic methods are print
, plot
,
summary
, quantile
, logLik
, vcov
and coef
.
Usage
1 2 
Arguments
x 
A numeric vector. 
dist 
A character string 
method 
A character string coding for the fitting method:

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

optim.method 

... 
Further arguments to be passed to 
Details
The fitted distribution (dist
) has its d, p, q, r functions defined in the
man page: oiunif
, oistpareto
, oibeta
,
oigbeta
, mbbefd
, MBBEFD
.
The two possible fitting methods are described below:
 When
method="mle"

Maximum likelihood estimation consists in maximizing the loglikelihood. A numerical optimization is carried out in
mledist
viaoptim
to find the best values (seemledist
for details). For oneinflated distributions, the probability parameter is estimated by a closedform formula and other parameters use a twooptimization procedures.  When
method="tlmme"

Total loss and moment matching estimation consists in equalizing theoretical and empirical total loss as well as theoretical and empirical moments. The theoretical and the empirical moments are matched numerically, by minimization of the sum of squared differences between observed and theoretical quantities (see
mmedist
for details).
For oneinflated distributions,
by default, direct optimization of the loglikelihood (or other criteria depending
of the chosen method) is performed using optim
,
with the "LBFGSB" method for distributions characterized by more than
one parameter and the "Brent" method for distributions characterized by only
one parameter. Note that when errors are raised by optim
, it's a good
idea to start by adding traces during the optimization process by adding
control=list(trace=1, REPORT=1)
.
For the MBBEFD distribution, constrOptim.nl
is used.
A prefitting process is carried out for the following distributions
"mbbefd"
, "MBBEFD"
and "oigbeta"
before
the main optimization.
The estimation process is carried out via fitdist
from the
fitdistrplus
package and the output object will inherit from the
"fitdist"
class.
Therefore, the following generic methods are available print
, plot
,
summary
, quantile
, logLik
, vcov
and coef
.
Value
fitDR
returns an object of class "fitDR"
inheriting
from the "fitdist"
class. That is a list with the following components:
estimate 
the parameter estimates. 
method 
the character string coding for the fitting method :

sd 
the estimated standard errors, 
cor 
the estimated correlation matrix, 
vcov 
the estimated variancecovariance matrix, 
loglik 
the loglikelihood. 
aic 
the Akaike information criterion. 
bic 
the the socalled BIC or SBC (Schwarz Bayesian criterion). 
n 
the length of the data set. 
data 
the data set. 
distname 
the name of the distribution. 
fix.arg 
the named list giving the values of parameters of the named distribution
that must be kept fixed rather than estimated by maximum likelihood or 
fix.arg.fun 
the function used to set the value of 
discrete 
the input argument or the automatic definition by the function to be passed
to functions 
dots 
the list of further arguments passed in ... to be used in 
weights 
the vector of weigths used in the estimation process or 
Generic functions:
print

The print of a
"fitDR"
object shows few traces about the fitting method and the fitted distribution. summary

The summary provides the parameter estimates of the fitted distribution, the loglikelihood, AIC and BIC statistics and when the maximum likelihood is used, the standard errors of the parameter estimates and the correlation matrix between parameter estimates.
plot

The plot of an object of class "fitDR" returned by
fitdist
uses the functionplotdist
. An object of class "fitdist" or a list of objects of class "fitDR" corresponding to various fits using the same data set may also be plotted using a cdf plot (functioncdfcomp
), a density plot(functiondenscomp
), a density QQ plot (functionqqcomp
), or a PP plot (functionppcomp
). logLik
Extracts the estimated loglikelihood from the
"fitDR"
object.vcov
Extracts the estimated varcovariance matrix from the
"fitDR"
object (only available whenmethod = "mle"
).coef
Extracts the fitted coefficients from the
"fitDR"
object.
Author(s)
Christophe Dutang.
References
Cullen AC and Frey HC (1999), Probabilistic techniques in exposure assessment. Plenum Press, USA, pp. 81155.
Venables WN and Ripley BD (2002), Modern applied statistics with S. Springer, New York, pp. 435446.
Vose D (2000), Risk analysis, a quantitative guide. John Wiley & Sons Ltd, Chischester, England, pp. 99143.
DelignetteMuller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 134.
See Also
See mledist
, mmedist
,
for details on parameter estimation.
See gofstat
for goodnessoffit statistics.
See plotdist
,
graphcomp
for graphs.
See bootDR
for bootstrap procedures
See optim
for base R optimization procedures.
See quantile.fitdist
, another generic function, which calculates
quantiles from the fitted distribution.
See quantile
for base R quantile computation.
Examples
1 2 3 4 5 6 7 8 9 10 