Description Usage Arguments Details Author(s) References See Also Examples

`cdfband`

plots the empirical cumulative distribution function with the bootstraped pointwise confidence intervals on probabilities of on quantiles.

1 2 3 4 5 | ```
CIcdfplot(b, CI.output, CI.type = "two.sided", CI.level = 0.95, CI.col = "red",
CI.lty = 2, CI.fill = NULL, CI.only = FALSE, xlim, ylim, xlogscale = FALSE,
ylogscale = FALSE, main, xlab, ylab, datapch, datacol, fitlty, fitcol, fitlwd,
horizontals = TRUE, verticals = FALSE, do.points = TRUE, use.ppoints = TRUE,
a.ppoints = 0.5, lines01 = FALSE, ...)
``` |

`b` |
One |

`CI.output` |
The quantity on which (bootstraped) bootstraped confidence intervals are computed:
either |

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

`CI.level` |
The confidence level. |

`CI.col` |
the color of the confidence intervals. |

`CI.lty` |
the line type of the confidence intervals. |

`CI.fill` |
a color to fill the confidence area. Default is |

`CI.only` |
A logical whether to plot empirical and fitted distribution functions
or only the confidence intervals. Default to |

`xlim` |
The |

`ylim` |
The |

`xlogscale` |
If |

`ylogscale` |
If |

`main` |
A main title for the plot, see also |

`xlab` |
A label for the |

`ylab` |
A label for the |

`datapch` |
An integer specifying a symbol to be used in plotting data points,
see also |

`datacol` |
A specification of the color to be used in plotting data points. |

`fitcol` |
A (vector of) color(s) to plot fitted distributions. If there are fewer colors than fits they are recycled in the standard fashion. |

`fitlty` |
A (vector of) line type(s) to plot fitted distributions/densities.
If there are fewer values than fits they are recycled in the standard fashion.
See also |

`fitlwd` |
A (vector of) line size(s) to plot fitted distributions/densities.
If there are fewer values than fits they are recycled in the standard fashion.
See also |

`horizontals` |
If |

`do.points` |
logical; if |

`verticals` |
If |

`use.ppoints` |
If |

`a.ppoints` |
If |

`lines01` |
A logical to plot two horizontal lines at |

`...` |
Further graphical arguments passed to |

`CIcdfplot`

provides a plot of the empirical distribution using
`cdfcomp`

or `cdfcompcens`

,
with bootstraped pointwise confidence intervals on probabilities (y values)
or on quantiles (x values).
Each interval is computed by evaluating the quantity of interest (probability
associated to an x value or quantile associated to an y value) using all the
bootstraped values of parameters to get a bootstraped sample
of the quantity of interest and then by calculating percentiles on this sample to get a
confidence interval (classically 2.5 and 97.5 percentiles for a 95 percent
confidence level).
If `CI.fill != NULL`

, then the whole confidence area is filled by the color `CI.fill`

thanks to the function `polygon`

, otherwise only borders are drawn thanks to the function
`matline`

. Further graphical arguments can be passed to these functions using
the three dots arguments `...`

.

Christophe Dutang and Marie-Laure Delignette-Muller.

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

See also `cdfcomp`

, `cdfcompcens`

,
`bootdist`

and `quantile`

.

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 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | ```
# 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 an exponential distribution
#
set.seed(123)
s1 <- rexp(50, 1)
f1 <- fitdist(s1, "exp")
b1 <- bootdist(f1, niter= 11) #voluntarily low to decrease computation time
# plot 95 percent bilateral confidence intervals on y values (probabilities)
CIcdfplot(b1, CI.level= 95/100, CI.output = "probability")
# plot of the previous intervals as a band
CIcdfplot(b1, CI.level= 95/100, CI.output = "probability",
CI.fill = "pink", CI.col = "red")
# plot of the previous intervals as a band without empirical and fitted dist. functions
CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.only = TRUE,
CI.fill = "pink", CI.col = "red")
# same plot without contours
CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.only = TRUE,
CI.fill = "pink", CI.col = "pink")
# plot 95 percent bilateral confidence intervals on x values (quantiles)
CIcdfplot(b1, CI.level= 95/100, CI.output = "quantile")
# plot 95 percent unilateral confidence intervals on quantiles
CIcdfplot(b1, CI.level = 95/100, CI.output = "quant", CI.type = "less",
CI.fill = "grey80", CI.col = "black", CI.lty = 1)
CIcdfplot(b1, CI.level= 95/100, CI.output = "quant", CI.type = "greater",
CI.fill = "grey80", CI.col = "black", CI.lty = 1)
# (2) 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, with their
# confidence intervals, from a small number of bootstrap
# iterations to satisfy CRAN running times constraint and plot of the band
# representing pointwise confidence intervals on any quantiles (any HCx values)
# 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")
bln <- bootdist(fln, bootmethod ="param", niter=101)
quantile(bln, probs = c(0.05, 0.1, 0.2))
CIcdfplot(bln, CI.output = "quantile", CI.fill = "lightblue", CI.col = "blue",
xlim = c(1,5))
# (3) Same type of example as example (2) from ecotoxicology
# with censored data
#
data(salinity)
log10LC50 <-log10(salinity)
fln <- fitdistcens(log10LC50,"norm")
bln <- bootdistcens(fln, niter=101)
(HC5ln <- quantile(bln,probs = 0.05))
CIcdfplot(bln, CI.output = "quantile", CI.fill = "lightblue", CI.col = "blue",
xlab = "log10(LC50)",xlim=c(0.5,2),lines01 = TRUE)
# zoom around the HC5
CIcdfplot(bln, CI.output = "quantile", CI.fill = "lightblue", CI.col = "blue",
xlab = "log10(LC50)", lines01 = TRUE, xlim = c(0.8, 1.5), ylim = c(0, 0.1))
abline(h = 0.05, lty = 2) # line corresponding to a CDF of 5 percent
``` |

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