# cad: Plot continuous data as cumulative age distributions In IsoplotR: Statistical Toolbox for Radiometric Geochronology

## Description

Plot a dataset as a Cumulative Age Distribution (CAD), also known as a ‘empirical cumulative distribution function’.

## Usage

 ``` 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``` ```cad(x, ...) ## Default S3 method: cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", colmap = "heat.colors", col = "black", hide = NULL, ...) ## S3 method for class 'detritals' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", colmap = "heat.colors", hide = NULL, ...) ## S3 method for class 'UPb' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", type = 4, cutoff.76 = 1100, cutoff.disc = c(-15, 5), common.Pb = 0, hide = NULL, ...) ## S3 method for class 'PbPb' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", common.Pb = 1, hide = NULL, ...) ## S3 method for class 'ArAr' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = FALSE, hide = NULL, ...) ## S3 method for class 'KCa' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = FALSE, hide = NULL, ...) ## S3 method for class 'ThU' cad(x, pch = NA, verticals = TRUE, xlab = "age [ka]", col = "black", i2i = FALSE, detritus = 0, Th02 = c(0, 0), Th02U48 = c(0, 0, 1e+06, 0, 0, 0, 0, 0, 0), hide = NULL, ...) ## S3 method for class 'ReOs' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, hide = NULL, ...) ## S3 method for class 'SmNd' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, hide = NULL, ...) ## S3 method for class 'RbSr' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, hide = NULL, ...) ## S3 method for class 'LuHf' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, hide = NULL, ...) ## S3 method for class 'UThHe' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", hide = NULL, ...) ## S3 method for class 'fissiontracks' cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", hide = NULL, ...) ```

## Arguments

 `x` a numerical vector OR an object of class `UPb`, `PbPb`, `ArAr`, `KCa`, `UThHe`, `fissiontracks`, `ReOs`, `RbSr`, `SmNd`, `LuHf`, `ThU` or `detritals` `...` optional arguments to the generic `plot` function `pch` plot character to mark the beginning of each CAD step `verticals` logical flag indicating if the horizontal lines of the CAD should be connected by vertical lines `xlab` x-axis label `colmap` an optional string with the name of one of `R`'s built-in colour palettes (e.g., `heat.colors`, `terrain.colors`, `topo.colors`, `cm.colors`), which are to be used for plotting data of class `detritals`. `col` colour to give to single sample datasets (not applicable if `x` has class `detritals`) `hide` vector with indices of aliquots that should be removed from the plot. `type` scalar indicating whether to plot the ^{207}Pb/^{235}U age (`type`=1), the ^{206}Pb/^{238}U age (`type`=2), the ^{207}Pb/^{206}Pb age (`type`=3), the ^{207}Pb/^{206}Pb-^{206}Pb/^{238}U age (`type`=4), or the (Wetherill) concordia age (`type`=5) `cutoff.76` the age (in Ma) below which the ^{206}Pb/^{238}U-age and above which the ^{207}Pb/^{206}Pb-age is used. This parameter is only used if `type=4`. `cutoff.disc` two element vector with the maximum and minimum percentage discordance allowed between the ^{207}Pb/^{235}U and ^{206}Pb/^{238}U age (if ^{206}Pb/^{238}U < cutoff.76) or between the ^{206}Pb/^{238}U and ^{207}Pb/^{206}Pb age (if ^{206}Pb/^{238}U > cutoff.76). Set `cutoff.disc=NA` if you do not want to use this filter. `common.Pb` apply a common lead correction using one of three methods: `1`: use the isochron intercept as the initial Pb-composition `2`: use the Stacey-Kramer two-stage model to infer the initial Pb-composition `3`: use the Pb-composition stored in `settings('iratio','Pb206Pb204')` and `settings('iratio','Pb207Pb204')` `i2i` ‘isochron to intercept’: calculates the initial (aka ‘inherited’, ‘excess’, or ‘common’) ^{40}Ar/^{36}Ar, ^{40}Ca/^{44}Ca, ^{207}Pb/^{204}Pb, ^{87}Sr/^{86}Sr, ^{143}Nd/^{144}Nd, ^{187}Os/^{188}Os, ^{230}Th/^{232}Th or ^{176}Hf/^{177}Hf ratio from an isochron fit. Setting `i2i` to `FALSE` uses the default values stored in `settings('iratio',...)` or zero (for the Pb-Pb method). When applied to data of class `ThU`, setting `i2i` to `TRUE` applies a detrital Th-correction. `detritus` detrital ^{230}Th correction (only applicable when `x\$format == 1` or `2`. `0`: no correction `1`: project the data along an isochron fit `2`: correct the data using an assumed initial ^{230}Th/^{232}Th-ratio for the detritus. `3`: correct the data using the measured present day ^{230}Th/^{238}U, ^{232}Th/^{238}U and ^{234}U/^{238}U-ratios in the detritus. `Th02` 2-element vector with the assumed initial ^{230}Th/^{232}Th-ratio of the detritus and its standard error. Only used if `detritus==2` `Th02U48` 9-element vector with the measured composition of the detritus, containing `X=0/8`, `sX`, `Y=2/8`, `sY`, `Z=4/8`, `sZ`, `rXY`, `rXZ`, `rYZ`. Only used if `isochron==FALSE` and `detritus==3`

## Details

Empirical cumulative distribution functions or cumulative age distributions CADs are the most straightforward way to visualise the probability distribution of multiple dates. Suppose that we have a set of n dates t_i. The the CAD is a step function that sets out the rank order of the dates against their numerical value:

where 1(\ast) = 1 if \ast is true and 1(\ast) = 0 if \ast is false. CADs have two desirable properties (Vermeesch, 2007). First, they do not require any pre-treatment or smoothing of the data. This is not the case for histograms or kernel density estimates. Second, it is easy to superimpose several CADs on the same plot. This facilitates the intercomparison of multiple samples. The interpretation of CADs is straightforward but not very intuitive. The prominence of individual age components is proportional to the steepness of the CAD. This is different from probability density estimates such as histograms, in which such components stand out as peaks.

## References

Vermeesch, P., 2007. Quantitative geomorphology of the White Mountains (California) using detrital apatite fission track thermochronology. Journal of Geophysical Research: Earth Surface, 112(F3).

`kde`, `radialplot`
 ```1 2``` ```data(examples) cad(examples\$DZ,verticals=FALSE,pch=20) ```