# quantile: Quantile estimation from a fitted distribution In fitdistrplus: Help to Fit of a Parametric Distribution to Non-Censored or Censored Data

## Description

Quantile estimation from a fitted distribution, optionally with confidence intervals calculated from the bootstrap result.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## S3 method for class 'fitdist' quantile(x, probs = seq(0.1, 0.9, by=0.1), ...) ## S3 method for class 'fitdistcens' quantile(x, probs = seq(0.1, 0.9, by=0.1), ...) ## S3 method for class 'bootdist' quantile(x, probs = seq(0.1, 0.9, by=0.1),CI.type = "two.sided", CI.level = 0.95, ...) ## S3 method for class 'bootdistcens' quantile(x, probs = seq(0.1, 0.9, by=0.1),CI.type = "two.sided", CI.level = 0.95, ...) ## S3 method for class 'quantile.fitdist' print(x, ...) ## S3 method for class 'quantile.fitdistcens' print(x, ...) ## S3 method for class 'quantile.bootdist' print(x, ...) ## S3 method for class 'quantile.bootdistcens' print(x, ...) ```

## Arguments

 `x` An object of class `"fitdist"`, `"fitdistcens"`, `"bootdist"`, `"bootdistcens"` or `"quantile.fitdist"`, `"quantile.fitdistcens"`, `"quantile.bootdist"`, `"quantile.bootdistcens"` for the `print` generic function. `probs` A numeric vector of probabilities with values in [0, 1] at which quantiles must be calculated. `CI.type` Type of confidence intervals : either `"two.sided"` or one-sided intervals (`"less"` or `"greater"`). `CI.level` The confidence level. `...` Further arguments to be passed to generic functions.

## Details

Quantiles of the parametric distribution are calculated for each probability specified in `probs`, using the estimated parameters. When used with an object of class `"bootdist"` or `"bootdistcens"`, percentile confidence intervals and medians etimates are also calculated from the bootstrap result. If `CI.type` is `two.sided`, the `CI.level` two-sided confidence intervals of quantiles are calculated. If `CI.type` is `less` or `greater`, the `CI.level` one-sided confidence intervals of quantiles are calculated. The print functions show the estimated quantiles with percentile confidence intervals and median estimates when a bootstrap resampling has been done previously, and the number of bootstrap iterations for which the estimation converges if it is inferior to the whole number of bootstrap iterations.

## Value

`quantile` returns a list with 2 components (the first two described below) when called with an object of class `"fitdist"` or `"fitdistcens"` and 8 components (described below) when called with an object of class `"bootdist"` or `"bootdistcens"` :

 `quantiles` a dataframe containing the estimated quantiles for each probability value specified in the argument `probs` (one row, and as many columns as values in `probs`). `probs` the numeric vector of probabilities at which quantiles are calculated. `bootquant ` A data frame containing the bootstraped values for each quantile (many rows, as specified in the call to `bootdist` in the argument `niter`, and as many columns as values in `probs`) `quantCI` If `CI.type` is `two.sided`, the two bounds of the `CI.level` percent two.sided confidence interval for each quantile (two rows and as many columns as values in `probs`). If `CI.type` is `less`, right bound of the `CI.level` percent one.sided confidence interval for each quantile (one row). If `CI.type` is `greater`, left bound of the `CI.level` percent one.sided confidence interval for each quantile (one row). `quantmedian` Median of bootstrap estimates (per probability). `CI.type` Type of confidence interval: either `"two.sided"` or one-sided intervals (`"less"` or `"greater"`). `CI.level` The confidence level. `nbboot` The number of samples drawn by bootstrap. `nbconverg` The number of iterations for which the optimization algorithm converges.

## Author(s)

Marie-Laure Delignette-Muller and Christophe Dutang.

## References

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

`fitdist`, `bootdist`, `fitdistcens`, `bootdistcens` and `CIcdfplot`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52``` ```# (1) Fit of a normal distribution on acute toxicity log-transformed values of # endosulfan 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, 10 and 20 percent quantile # values of the fitted distribution, which are called the 5, 10, 20 percent hazardous # concentrations (HC5, HC10, HC20) in ecotoxicology, followed with calculations of their # confidence intervals with various definitions, from a small number of bootstrap # iterations to satisfy CRAN running times constraint. # For practical applications, we recommend to use at least niter=501 or niter=1001. # data(endosulfan) ATV <- subset(endosulfan, group == "NonArthroInvert")\$ATV log10ATV <- log10(subset(endosulfan, group == "NonArthroInvert")\$ATV) fln <- fitdist(log10ATV, "norm") quantile(fln, probs = c(0.05, 0.1, 0.2)) bln <- bootdist(fln, bootmethod="param", niter=101) quantile(bln, probs = c(0.05, 0.1, 0.2)) quantile(bln, probs = c(0.05, 0.1, 0.2), CI.type = "greater") quantile(bln, probs = c(0.05, 0.1, 0.2), CI.level = 0.9) # (2) Draw of 95 percent confidence intervals on quantiles of the # previously fitted distribution # cdfcomp(fln) q1 <- quantile(bln, probs = seq(0,1,length=101)) points(q1\$quantCI[1,],q1\$probs,type="l") points(q1\$quantCI[2,],q1\$probs,type="l") # (2b) Draw of 95 percent confidence intervals on quantiles of the # previously fitted distribution # using the NEW function CIcdfplot # CIcdfplot(bln, CI.output = "quantile", CI.fill = "pink") # (3) Fit of a distribution on acute salinity log-transformed tolerance # for riverine macro-invertebrates, using maximum likelihood estimation # to estimate what is called a species sensitivity distribution # (SSD) in ecotoxicology, followed by estimation of the 5, 10 and 20 percent quantile # values of the fitted distribution, which are called the 5, 10, 20 percent hazardous # concentrations (HC5, HC10, HC20) in ecotoxicology, followed with calculations of # their confidence intervals with various definitions. # from a small number of bootstrap iterations to satisfy CRAN running times constraint. # For practical applications, we recommend to use at least niter=501 or niter=1001. # data(salinity) log10LC50 <-log10(salinity) flncens <- fitdistcens(log10LC50,"norm") quantile(flncens, probs = c(0.05, 0.1, 0.2)) blncens <- bootdistcens(flncens, niter = 101) quantile(blncens, probs = c(0.05, 0.1, 0.2)) quantile(blncens, probs = c(0.05, 0.1, 0.2), CI.type = "greater") quantile(blncens, probs = c(0.05, 0.1, 0.2), CI.level = 0.9) ```