bootdist {fitdistrplus}

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, silent = TRUE, 
      parallel = c("no", "snow", "multicore"), ncpus)
## S3 method for class 'bootdist'
print(x, ...)
## S3 method for class 'bootdist'
plot(x, main = "Bootstrapped values of parameters", enhance = FALSE, 
    trueval = NULL, rampcol = NULL, nbgrid = 100, nbcol = 100, ...)
## S3 method for class 'bootdist'
summary(object, ...)

Arguments

f

An object of class "fitdist", output of the fitdist function.

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.

silent

A logical to remove or show warnings and errors when bootstraping.

parallel

The type of parallel operation to be used, "snow" or "multicore" (the second one not being available on Windows), or "no" if no parallel operation.

ncpus

Number of processes to be used in parallel operation : typically one would fix it to the number of available CPUs.

x

An object of class "bootdist".

object

An object of class "bootdist".

main

an overall title for the plot: see title, default to "Bootstrapped values of parameters".

enhance

a logical to get an enhanced plot.

trueval

when relevant, a numeric vector with the true value of parameters (for backfitting purposes).

rampcol

colors to interpolate; must be a valid argument to colorRampPalette().

nbgrid

Number of grid points in each direction. Can be scalar or a length-2 integer vector.

nbcol

an integer argument, the required number of colors

...

Further arguments to be passed to generic methods

Details

Samples are drawn by parametric bootstrap (resampling from the distribution fitted by fitdist) or nonparametric bootstrap (resampling with replacement from the data set). On each bootstrap sample the function mledist (or mmedist, qmedist, 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.

By default (when enhance=FALSE), 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, the function plot when there are two paramters and the function pairs in other cases. In these last cases, it provides a representation of the joint uncertainty distribution of the fitted parameters.

When enhance=TRUE, a personalized plot version of pairs is used where upper graphs are scatterplots and lower graphs are heatmap image using image based on a kernel based estimator for the 2D density function (using kde2d from MASS package). Arguments rampcol, nbgrid, nbcol can be used to customize the plots. Defautls values are rampcol=c("green", "yellow", "orange", "red"), nbcol=100 (see colorRampPalette()), nbgrid=100 (see kde2d). In addition, when fitting parameters on simulated datasets for backtesting purposes, an additional argument trueval can be used to plot a cross at the true value.

It is possible to accelerate the bootstrap using parallelization. We recommend you to use parallel = "multicore", or parallel = "snow" if you work on Windows, and to fix ncpus to the number of available processors.

Value

bootdist returns an object of class "bootdist", a list with 6 components,

estim

a data frame containing the bootstrapped 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.

nbboot

The number of samples drawn by bootstrap.

CI

bootstrap medians and 95 percent confidence percentile intervals of parameters.

fitpart

The object of class "fitdist" on which the bootstrap procedure was applied.

Generic functions:

print

The print of a "bootdist" object shows the bootstrap parameter estimates. If inferior to the whole number of bootstrap iterations, the number of iterations for which the estimation converges is also printed.

summary

The summary provides the median and 2.5 and 97.5 percentiles of each parameter. If inferior to the whole number of bootstrap iterations, the number of iterations for which the estimation converges is also printed in the summary.

plot

The plot shows the bootstrap estimates with stripchart function for univariate parameters and plot function for multivariate parameters.

Author(s)

Marie-Laure Delignette-Muller and Christophe Dutang.

References

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

Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.

See Also

See fitdistrplus for an overview of the package. fitdist, mledist, qmedist, mmedist, mgedist, quantile.bootdist for another generic function to calculate quantiles from the fitted distribution and its bootstrap results and CIcdfplot for adding confidence intervals on quantiles to a CDF plot of the fitted distribution.

Examples

# We choose a low number of bootstrap replicates in order to satisfy CRAN running times
# constraint.
# For practical applications, we recommend to use at least niter=501 or niter=1001.


# (1) Fit of a gamma distribution to serving size data
# using default method (maximum likelihood estimation)
# followed by parametric bootstrap
#
data(groundbeef)
x1 <- groundbeef$serving
f1 <- fitdist(x1, "gamma")
b1 <- bootdist(f1, niter=51)
print(b1)
plot(b1)
plot(b1, enhance=TRUE)
summary(b1)
quantile(b1)
CIcdfplot(b1, CI.output = "quantile")

# (2) non parametric bootstrap on the same fit
#
b1b <- bootdist(f1, bootmethod="nonparam", niter=51) 
summary(b1b)
quantile(b1b)


# (3) Fit of a normal distribution on acute toxicity values of endosulfan in log10 for
# nonarthropod invertebrates, using maximum likelihood estimation
# to estimate what is called a species sensitivity distribution 
# (SSD) in ecotoxicology, followed by estimation of the 5 percent quantile value of 
# the fitted distribution, what is called the 5 percent hazardous concentration (HC5)
# in ecotoxicology, with its two-sided 95 percent confidence interval calculated by 
# parametric bootstrap
#
data(endosulfan)
ATV <- subset(endosulfan, group == "NonArthroInvert")$ATV
log10ATV <- log10(subset(endosulfan, group == "NonArthroInvert")$ATV)
fln <- fitdist(log10ATV, "norm")
bln <- bootdist(fln, bootmethod = "param", niter=51)
quantile(bln, probs = c(0.05, 0.1, 0.2))

# (4) comparison of sequential and parallel versions of bootstrap
# to be tried with a greater number of iterations (1001 or more)
#

niter <- 1001
data(groundbeef)
x1 <- groundbeef$serving
f1 <- fitdist(x1, "gamma")

# sequential version
ptm <- proc.time()
summary(bootdist(f1, niter = niter))
proc.time() - ptm

# parallel version using snow
require(parallel)
ptm <- proc.time()
summary(bootdist(f1, niter = niter, parallel = "snow", ncpus = 2))
proc.time() - ptm

# parallel version using multicore (not available on Windows)
ptm <- proc.time()
summary(bootdist(f1, niter = niter, parallel = "multicore", ncpus = 2))
proc.time() - ptm