fitdistrplus (version 0.2-2)

qmedist: Quantile matching fit of univariate distributions

Description

Fit of univariate distribution by matching quantiles for non censored data.

Usage

qmedist(data, distr, probs, start=NULL, fix.arg=NULL, qtype=7, 
    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.

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. 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.

qtype

The quantile type used by the R quantile function to compute the empirical quantiles, (default 7 corresponds to the default quantile method in R).

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

• qmedist 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.
• probs
  the probability vector on which quantiles are matched.
• optim.function
  the name of the optimization function used.
• loglik
  the log-likelihood.

Details

The qmedist function carries out the quantile matching numerically, by minimization of the sum of squared differences between observed and theoretical quantiles. 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.

References

Klugman et al. (2004) Loss Models: From Data to Decisions, 2nd edition. Wiley Series in Probability and Statistics, p. 331.

See Also

mmedist, mledist, fitdist for other estimation methods and quantile for empirical quantile estimation in R.

Examples

# (1) basic fit of a normal distribution 
#

x1<-c(6.4,13.3,4.1,1.3,14.1,10.6,9.9,9.6,15.3,22.1,13.4,
13.2,8.4,6.3,8.9,5.2,10.9,14.4)
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)
#

x2<-c(rep(4,1),rep(2,3),rep(1,7),rep(0,12))
qmedist(x2, "pois", probs=1/2)
qmedist(x2, "nbinom", probs=c(1/3, 2/3))

# (4) fit a finite-support distribution (beta)
#

x3<-c(0.80,0.72,0.88,0.84,0.38,0.64,0.69,0.48,0.73,0.58,0.81,
0.83,0.71,0.75,0.59)
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))