fitdistrplus (version 0.3-4)

bootdist: Bootstrap simulation of uncertainty for non-censored data

Description

Uses parametric or nonparametric bootstrap resampling in order to simulate uncertainty in the parameters of the distribution fitted to non-censored data.

Usage

bootdist(f, bootmethod="param", niter=1001)
## S3 method for class 'bootdist':
print(x,...)
## S3 method for class 'bootdist':
plot(x,...)
## S3 method for class 'bootdist':
summary(object,...)

Arguments

f

An object of class 'fitdist' result of the function fitdist.

bootmethod

A character string coding for the type of resampling : "param" for a parametric resampling and "nonparam" for a nonparametric resampling of data.

niter

The number of samples drawn by bootstrap.

x

an object of class 'bootdist'.

object

an object of class 'bootdist'.

...

further arguments to be passed to generic methods

Value

• bootdist returns an object of class 'bootdist', a list with 4 components,
• estim
  a data frame containing the boostrapped values of parameters.
• converg
  a vector containing the codes for convergence obtained if an iterative method is used to estimate parameters on each bootstraped data set (and 0 if a closed formula is used).
• method
  A character string coding for the type of resampling : "param" for a parametric resampling and "nonparam" for a nonparametric resampling of data.
• CI
  bootstrap medians and 95 percent confidence percentile intervals of parameters.

Details

Samples are drawn by parametric bootstrap (resampling from the distribution fitted by fitdist) or non parametric bootstrap (resampling with replacement from the data set). On each bootstrap sample the function mledist (or mmedist, qmedist or mgedist according to the component f$method of the object of class 'fitdist') is used to estimate bootstrapped values of parameters. When that function fails to converge, NA values are returned. Medians and 2.5 and 97.5 percentiles are computed by removing NA values. The medians and the 95 percent confidence intervals of parameters (2.5 and 97.5 percentiles) are printed in the summary. If inferior to the whole number of iterations, the number of iterations for which the function converges is also printed in the summary. The plot of an object of class bootdist consists in a scatterplot or a matrix of scatterplots of the bootstrapped values of parameters. It uses the function stripchart when the fitted distribution is characterized by only one parameter, and the function plot in other cases. In these last cases, it provides a representation of the joint uncertainty distribution of the fitted parameters.

References

Cullen AC and Frey HC (1999) Probabilistic techniques in exposure assessment. Plenum Press, USA, pp. 181-241.

See Also

fitdist, mledist, qmedist, mmedist, and mgedist.

Examples

# (1) basic fit of a normal distribution with maximum likelihood estimation
# followed by parametric bootstrap
#
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)
f1<-fitdist(x1,"norm",method="mle")
b1<-bootdist(f1)
print(b1)
plot(b1)
summary(b1)

# (2) non parametric bootstrap
#
b1np<-bootdist(f1,bootmethod="nonparam")
summary(b1np)

# (3) fit of a gamma distribution followed by parametric bootstrap
#
f1b<-fitdist(x1,"gamma",method="mle")
b1b<-bootdist(f1b)
summary(b1b)

# (4) fit of a gamma distribution with control of the optimization
# method, followed by parametric bootstrap
#
f1c <- fitdist(x1,"gamma",optim.method="L-BFGS-B",lower=c(0,0))
b1c <- bootdist(f1c)
summary(b1c)

# (5) estimation of the standard deviation of a normal distribution 
# by maximum likelihood with the mean fixed at 10 using the argument fix.arg
# followed by parametric bootstrap
#
f1d <-fitdist(x1,"norm",start=list(sd=5),fix.arg=list(mean=10))
b1d <- bootdist(f1d)
summary(b1d)
plot(b1d)

# (6) fit of a discrete distribution by matching moment estimation 
# (using a closed formula) followed by parametric bootstrap
#
x2<-c(rep(4,1),rep(2,3),rep(1,7),rep(0,12))
f2<-fitdist(x2,"pois",method="mme")
b2<-bootdist(f2)
plot(b2,pch=16)
summary(b2)

# (7) fit of a Weibull distribution to serving size data by maximum likelihood 
# estimation or by quantile matching estimation (in this example matching 
# first and third quartiles) followed by parametric bootstrap
#
data(groundbeef)
serving <- groundbeef$serving

fWmle <- fitdist(serving,"weibull")
bWmle <- bootdist(fWmle,niter=101)
summary(bWmle)

fWqme <- fitdist(serving,"weibull",method="qme",probs=c(0.25,0.75))
bWqme <- bootdist(fWqme,niter=101)
summary(bWqme)

# (8) Fit of a Pareto distribution by numerical moment matching estimation
# followed by parametric bootstrap
#
require(actuar)
    #simulate a sample
    x4 <- rpareto(1000, 6, 2)
    memp <- function(x, order)
        ifelse(order == 1, mean(x), sum(x^order)/length(x))

    f4 <- fitdist(x4, "pareto", "mme", order=1:2, 
        start=c(shape=10, scale=10), 
        lower=1, memp="memp", upper=50)

    b4 <- bootdist(f4, niter=101)
    summary(b4)

    b4npar <- bootdist(f4, niter=101, bootmethod="nonparam")
    summary(b4npar)

# (9) Fit of a uniform distribution using Cramer-von Mises 
# followed by parametric boostrap
# 

u <- runif(50,min=5,max=10)

fu <- fitdist(u,"unif",method="mge",gof="CvM")
bu <- bootdist(fu, bootmethod="param")
summary(bu)
plot(bu)