R: Quantile estimation from a fitted distribution

quantiles {fitdistrplus} | R Documentation

## Quantile estimation from a fitted distribution

### Description

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

### Usage

    ## 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.

### See Also

`fitdist`, `bootdist`, `fitdistcens`, `bootdistcens` and `CIcdfplot`.

### Examples

    # (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)

[Package fitdistrplus version 1.0-9 Index]