quantile | R Documentation |

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

```
## 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, ...)
```

`x` |
An object of class |

`probs` |
A numeric vector of probabilities with values in [0, 1] at which quantiles must be calculated. |

`CI.type` |
Type of confidence intervals : either |

`CI.level` |
The confidence level. |

`...` |
Further arguments to be passed to generic functions. |

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.

`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` |
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 |

`quantCI` |
If |

`quantmedian` |
Median of bootstrap estimates (per probability). |

`CI.type` |
Type of confidence interval: either |

`CI.level` |
The confidence level. |

`nbboot` |
The number of samples drawn by bootstrap. |

`nbconverg` |
The number of iterations for which the optimization algorithm converges. |

Marie-Laure Delignette-Muller and Christophe Dutang.

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) 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)
```

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