Quantile matching fit of univariate distributions
Fit of univariate distribution by matching quantiles for non censored data.
qmedist(data, distr, probs, start = NULL, fix.arg = NULL, qtype = 7,
optim.method = "default", lower = -Inf, upper = Inf,
custom.optim = NULL, weights = NULL, silent = TRUE, gradient = NULL,
checkstartfix=FALSE, ...)data |
A numeric vector for non censored data. |
distr |
A character string |
probs |
A numeric vector of the probabilities for which the quantile matching is done. The length of this vector must be equal to the number of parameters to estimate. |
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. |
qtype |
The quantile type used by the R |
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. |
weights |
an optional vector of weights to be used in the fitting process.
Should be |
silent |
A logical to remove or show warnings when bootstraping. |
gradient |
A function to return the gradient of the squared difference for the |
checkstartfix |
A logical to test starting and fixed values. Do not change it. |
... |
further arguments passed to the |
The qmedist function carries out the quantile matching numerically, by minimization of the
sum of squared differences between observed and theoretical quantiles.
Note that for discrete distribution, the sum of squared differences is a step function and
consequently, the optimum is not unique, see the FAQ.
The optimization process is the same as mledist, see the 'details' section
of that function.
Optionally, a vector of weights can be used in the fitting process.
By default (when weigths=NULL), ordinary QME is carried out, otherwise
the specified weights are used to compute weighted quantiles used in the squared differences.
Weigthed quantiles are computed by wtd.quantile from the Hmisc package.
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).
qmedist 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. |
probs |
the probability vector on which quantiles are matched. |
Christophe Dutang and Marie Laure Delignette-Muller.
Klugman SA, Panjer HH and Willmot GE (2012), Loss Models: From Data to Decissions, 4th edition. Wiley Series in Statistics for Finance, Business and Economics, p. 253.
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
# (1) basic fit of a normal distribution # set.seed(1234) x1 <- rnorm(n=100) qmedist(x1, "norm", probs=c(1/3, 2/3)) # (2) defining your own distribution functions, here for the Gumbel # distribution for other distributions, see the CRAN task view dedicated # to probability distributions dgumbel <- function(x, a, b) 1/b*exp((a-x)/b)*exp(-exp((a-x)/b)) qgumbel <- function(p, a, b) a - b*log(-log(p)) qmedist(x1, "gumbel", probs=c(1/3, 2/3), start=list(a=10,b=5)) # (3) fit a discrete distribution (Poisson) # set.seed(1234) x2 <- rpois(n=30,lambda = 2) qmedist(x2, "pois", probs=1/2) # (4) fit a finite-support distribution (beta) # set.seed(1234) x3 <- rbeta(n=100,shape1=5, shape2=10) qmedist(x3, "beta", probs=c(1/3, 2/3)) # (5) fit frequency distributions on USArrests dataset. # x4 <- USArrests$Assault qmedist(x4, "pois", probs=1/2) qmedist(x4, "nbinom", probs=c(1/3, 2/3))
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