Plot continuous data as cumulative age distributions
Plot a dataset as a Cumulative Age Distribution (CAD), also known as a ‘empirical cumulative distribution function’.
cad(x, ...) ## Default S3 method: cad( x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", hide = NULL, ... ) ## S3 method for class 'detritals' cad( x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "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 = discfilter(), 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 'ThPb' cad( x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, hide = NULL, ... ) ## S3 method for class 'ThU' cad( x, pch = NA, verticals = TRUE, xlab = "age [ka]", col = "black", i2i = FALSE, detritus = 0, hide = NULL, ... ) ## S3 method for class 'ThPb' cad( x, pch = NA, verticals = TRUE, xlab = "age [Ma]", col = "black", i2i = TRUE, 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, ... )
x |
a numerical vector OR an object of class |
... |
optional arguments to the generic |
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 |
col |
either the name of one of |
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 ( |
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 |
cutoff.disc |
discordance cutoff filter. This is an object of
class |
common.Pb |
common lead correction:
|
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, ^{176}Hf/^{177}Hf or
^{204}Pb/^{208}Pb ratio from an isochron
fit. Setting |
detritus |
detrital ^{230}Th correction (only applicable
when
|
Empirical cumulative distribution functions or cumulative age distributions 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 CAD is a step function that sets out the rank order of the dates against their numerical value:
CAD(t) = ∑_i 1(t<t_i)/n
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.
Vermeesch, P., 2007. Quantitative geomorphology of the White Mountains (California) using detrital apatite fission track thermochronology. Journal of Geophysical Research: Earth Surface, 112(F3).
data(examples) cad(examples$DZ,verticals=FALSE,pch=20)
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