central  R Documentation 
Computes the logratio mean composition of a continuous mixture of fission track or UThHe data and returns the corresponding age and fitting parameters. Only propagates the systematic uncertainty associated with decay constants and calibration factors after computing the weighted mean isotopic composition. Does not propagate the uncertainty of any initial daughter correction, because this is neither a purely random or purely systematic uncertainty.
central(x, ...)
## Default S3 method:
central(x, ...)
## S3 method for class 'UThHe'
central(x, compositional = FALSE, model = 1, ...)
## S3 method for class 'fissiontracks'
central(x, exterr = FALSE, ...)
x 
an object of class 
... 
optional arguments 
compositional 
logical. If 
model 
only relevant if

exterr 
include the zeta or decay constant uncertainty into the error propagation for the central age? 
The central age assumes that the observed age distribution is the combination of two sources of scatter: analytical uncertainty and true geological dispersion.
For fission track data, the analytical uncertainty is assumed to obey Binomial counting statistics and the geological dispersion is assumed to follow a lognormal distribution.
For UThHe data, the UTh(Sm)He compositions and uncertainties are assumed to follow a logistic normal distribution.
For all other data types, both the analytical uncertainties and the true ages are assumed to follow lognormal distributions.
The difference between the central age and the weighted mean age is usually small unless the data are imprecise and/or strongly overdispersed.
The uncertainty budget of the central age does not include the
uncertainty of the initial daughter correction (if any), for the
same reasons as discussed under the weightedmean
function.
If x
has class UThHe
and compositional
is TRUE
, returns a list containing the following items:
(if the input data table contains Sm) or uv (if it does not): the mean log[U/He], log[Th/He] (, and log[Sm/He]) composition.
the covariance matrix of uvw
or uv
.
the reduced Chisquare statistic of data concordance,
i.e. mswd=SS/df
, where SS
is the sum of squares of the
log[U/He]log[Th/He] compositions.
the fitting model.
the degrees of freedom (2n2
) of the fit (only
reported if model=1
).
the pvalue of a Chisquare test with df
degrees of freedom (only reported if model=1
.)
a two or threeelement vector with:
t
: the 'barycentric' age, i.e. the age corresponding to uvw
.
s[t]
: the standard error of t
.
disp[t]
: the standard error of t
enhanced by a
factor of \sqrt{mswd}
(only reported if model=1
).
the geological overdispersion term. If model=3
,
this is a twoelement vector with the standard deviation of the
(assumedly) Normal dispersion and its standard error. w=0
if
model<3
.
OR, otherwise:
a twoelement vector with the central age and its standard error.
a twoelement vector with the overdispersion (standard deviation) of the excess scatter, and its standard error.
the reduced Chisquare statistic of data concordance,
i.e. mswd=X^2/df
, where X^2
is a Chisquare statistic
of the EDM data or ages
the degrees of freedom (n2
)
the pvalue of a Chisquare test with df
degrees of freedom
Galbraith, R.F. and Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements, 21(4), pp.459470.
Vermeesch, P., 2008. Three new ways to calculate average (UTh)/He ages. Chemical Geology, 249(3), pp.339347.
weightedmean
, radialplot
,
helioplot
attach(examples)
print(central(UThHe)$age)
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