# Empirical cumulative distribution function with pointwise confidence intervals on probabilities or on quantiles `cdfband` plots the empirical cumulative distribution function with the bootstraped pointwise confidence intervals on probabilities of on quantiles. ```r 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, name.points = NULL, lines01 = FALSE, plotstyle = "graphics", ...) ``` ## Arguments - `b`: One `"bootdist"` object. - `CI.output`: The quantity on which (bootstraped) bootstraped confidence intervals are computed: either `"probability"` or `"quantile"`). - `CI.type`: Type of confidence intervals : either `"two.sided"` or one-sided intervals (`"less"` or `"greater"`). - `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 `NULL` corresponding to no filling. - `CI.only`: A logical whether to plot empirical and fitted distribution functions or only the confidence intervals. Default to `FALSE`. - `xlim`: The $x$-limits of the plot. - `ylim`: The $y$-limits of the plot. - `xlogscale`: If `TRUE`, uses a logarithmic scale for the $x$-axis. - `ylogscale`: If `TRUE`, uses a logarithmic scale for the $y$-axis. - `main`: A main title for the plot, see also `title`. - `xlab`: A label for the $x$-axis, defaults to a description of `x`. - `ylab`: A label for the $y$-axis, defaults to a description of `y`. - `datapch`: An integer specifying a symbol to be used in plotting data points, see also `points` (only for non censored data). - `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 `par`. - `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 `par`. - `horizontals`: If `TRUE`, draws horizontal lines for the step empirical cdf function (only for non censored data). See also `plot.stepfun`. - `verticals`: If `TRUE`, draws also vertical lines for the empirical cdf function. Only taken into account if `horizontals=TRUE` (only for non censored data). - `do.points`: logical; if `TRUE`, also draw points at the x-locations. Default is TRUE (only for non censored data). - `use.ppoints`: If `TRUE`, probability points of the empirical distribution are defined using function `ppoints` as `(1:n - a.ppoints)/(n - 2a.ppoints + 1)` (only for non censored data). If `FALSE`, probability points are simply defined as `(1:n)/n`. This argument is ignored for discrete data. - `a.ppoints`: If `use.ppoints=TRUE`, this is passed to function `ppoints` (only for non censored data). - `name.points`: Label vector for points if they are drawn i.e. if do.points = TRUE (only for non censored data). - `lines01`: A logical to plot two horizontal lines at `h=0` and `h=1` for `cdfcomp`. - `plotstyle`: `"graphics"` or `"ggplot"`. If `"graphics"`, the display is built with `graphics` functions. If `"ggplot"`, a graphic object output is created with `ggplot2` functions (the `ggplot2` package must be installed). - ``...``: Further graphical arguments passed to `matlines` or `polygon`, respectively when `CI.fill=FALSE` and `CI.fill=TRUE`. ## Details `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 `...`. ## See Also See also `cdfcomp`, `cdfcompcens`, `bootdist` and `quantile`. Please visit the [Frequently Asked Questions](https://lbbe-software.github.io/fitdistrplus/articles/FAQ.html). ## References Delignette-Muller ML and Dutang C (2015), **fitdistrplus: An R Package for Fitting Distributions**. Journal of Statistical Software, 64(4), 1-34, tools:::Rd_expr_doi("https://doi.org/10.18637/jss.v064.i04") . ## Author(s) Christophe Dutang and Marie-Laure Delignette-Muller. ## Examples ```r # 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. if (requireNamespace ("ggplot2", quietly = TRUE)) {ggplotEx <- TRUE} # (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") if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", plotstyle = "ggplot") # plot of the previous intervals as a band CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.fill = "pink", CI.col = "red") if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.fill = "pink", CI.col = "red", plotstyle = "ggplot") # 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") if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.only = TRUE, CI.fill = "pink", CI.col = "red", plotstyle = "ggplot") # same plot without contours CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.only = TRUE, CI.fill = "pink", CI.col = "pink") if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "probability", CI.only = TRUE, CI.fill = "pink", CI.col = "pink", plotstyle = "ggplot") # plot 95 percent bilateral confidence intervals on x values (quantiles) CIcdfplot(b1, CI.level= 95/100, CI.output = "quantile") if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "quantile", plotstyle = "ggplot") # 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) if (ggplotEx) CIcdfplot(b1, CI.level = 95/100, CI.output = "quant", CI.type = "less", CI.fill = "grey80", CI.col = "black", CI.lty = 1, plotstyle = "ggplot") CIcdfplot(b1, CI.level= 95/100, CI.output = "quant", CI.type = "greater", CI.fill = "grey80", CI.col = "black", CI.lty = 1) if (ggplotEx) CIcdfplot(b1, CI.level= 95/100, CI.output = "quant", CI.type = "greater", CI.fill = "grey80", CI.col = "black", CI.lty = 1, plotstyle = "ggplot") # (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) log10ATV <- log10(subset(endosulfan, group == "NonArthroInvert")$ATV) namesATV <- subset(endosulfan, group == "NonArthroInvert")$taxa 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(0,5), name.points=namesATV) if (ggplotEx) CIcdfplot(bln, CI.output = "quantile", CI.fill = "lightblue", CI.col = "blue", xlim = c(0,5), name.points=namesATV, plotstyle = "ggplot") # (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) if (ggplotEx) CIcdfplot(bln, CI.output = "quantile", CI.fill = "lightblue", CI.col = "blue", xlab = "log10(LC50)",xlim=c(0.5,2),lines01 = TRUE, plotstyle = "ggplot") # 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 if (ggplotEx) 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), plotstyle = "ggplot") + ggplot2::geom_hline(yintercept = 0.05, lty = 2) # line corresponding to a CDF of 5 percent ```

CIcdfplot function