Package 'nimbleCarbon' reference manual

Title:	Bayesian Analyses of Radiocarbon Dates with NIMBLE
Description:	Provides utility functions and custom probability distribution for Bayesian analyses of radiocarbon dates within the 'nimble' modelling framework. It includes various population growth models, nimbleFunction objects, as well as a suite of functions for prior and posterior predictive checks for demographic inference (Crema and Shoda (2021) <doi:10.1371/journal.pone.0251695>) and other analyses.
Authors:	Enrico Crema [aut, cre] , Robert Di Napoli [ctb]
Maintainer:	Enrico Crema <[email protected]>
License:	GPL (>= 2)
Version:	0.2.5
Built:	2025-03-09 06:32:25 UTC
Source:	https://github.com/ercrema/nimblecarbon

Calculate Agreement Indices.

Description

Computes OxCal-style (Bronk-Ramsey 1995) individual and overall agreement index for evaluating model consistency.

Usage

agreementIndex(CRA, CRAError, calCurve = "intcal20", theta, verbose = TRUE)
agreementIndex(CRA, CRAError, calCurve = "intcal20", theta, verbose = TRUE)

Arguments

`CRA`	vector of C14 ages.
`CRAError`	vector of C14 errors associated with `CRA`.
`calCurve`	character string naming a calibration curve, one between 'intcal20','intcal13','shcal20','shcal13','marine13' and 'marine20'.
`theta`	a Matrix containing the posterior samples of each date.
`verbose`	a logical variable indicating whether extra information on progress should be reported. Default is TRUE.

Value

a list containing the individual and overall agreement indices.

References

Bronk-Ramsey, C. (1995). Radiocarbon Calibration and Analysis of Stratigraphy: The OxCal Program. Radiocarbon, 37(2), 425–430.

WAIC-based model comparison

Description

Compute delta WAIC and WAIC weights for model comparison.

Usage

compare.models(...)
compare.models(...)

Arguments

...

MCMC output from either nimbleMCMC or runMCMC functions in the nimble R package. Note that in argument WAIC should be set to TRUE.

Value

A table containing WAIC, delta WAIC, and WAIC weights.

Asymmetric Laplace Distribution

Description

Density, distribution function, quantile function, and random generation for a Asymmetric Laplace Distribution.

Usage

dAsymLaplace(x, mu, sigma, tau, log)

rAsymLaplace(n, mu, sigma, tau)

pAsymLaplace(q, mu, sigma, tau, lower.tail = 1, log.p = 0)

qAsymLaplace(p, mu, sigma, tau, lower.tail = 1, log.p = 0)
dAsymLaplace(x, mu, sigma, tau, log)

rAsymLaplace(n, mu, sigma, tau)

pAsymLaplace(q, mu, sigma, tau, lower.tail = 1, log.p = 0)

qAsymLaplace(p, mu, sigma, tau, lower.tail = 1, log.p = 0)

Arguments

`x`	value to be computed.
`mu`	location parameter.
`sigma`	scale parameter.
`tau`	asymmetry parameter.
`log`, `log.p`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.
`q`	quantile to be computed.
`lower.tail`	logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
`p`	probability to be computed.

Author(s)

Enrico Crema

Double Exponential Growth Model

Description

Density and random generation of an exponential growth model distribution.

Usage

dDoubleExponentialGrowth(x, a, b, r1, r2, mu, log)

rDoubleExponentialGrowth(n, a, b, r1, r2, mu)
dDoubleExponentialGrowth(x, a, b, r1, r2, mu, log)

rDoubleExponentialGrowth(n, a, b, r1, r2, mu)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`r1`	growth rate before change point mu.
`r2`	growth rate after change point mu.
`mu`	change point (in BP).
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Value

For dDoubleExponentialGrowth: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rDoubleExponentialGrowth a simulated date in Cal BP.

Author(s)

Enrico Crema

Examples

p = list(r1=0.003,r2=-0.001,mu=5200)
modelPlot(model = dDoubleExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)
p = list(r1=0.003,r2=-0.001,mu=5200)
modelPlot(model = dDoubleExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)

Exponential Growth Model

Description

Density and random generation of an exponential growth model distribution.

Usage

dExponentialGrowth(x, a, b, r, log)

rExponentialGrowth(n, a, b, r)
dExponentialGrowth(x, a, b, r, log)

rExponentialGrowth(n, a, b, r)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`r`	intrinsic growth rate.
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Value

For dExponentialGrowth: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rExponentialGrowth a simulated date in Cal BP.

Author(s)

Enrico Crema

Examples

p = list(r=0.002)
modelPlot(model = dExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)
p = list(r=0.002)
modelPlot(model = dExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)

Exponential-Logistic Growth Model

Description

Density and random generation of a exponential-logistic growth model distribution.

Usage

dExponentialLogisticGrowth(x, a, b, k, r1, r2, mu, log)

rExponentialLogisticGrowth(n, a, b, k, r1, r2, mu)
dExponentialLogisticGrowth(x, a, b, k, r1, r2, mu, log)

rExponentialLogisticGrowth(n, a, b, k, r1, r2, mu)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`k`	initial proportion of the carrying capacity (must be between 0 and 1).
`r1`	growth rate of the exponential phase.
`r2`	growth rate of logistic phase.
`mu`	change point (in BP).
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Value

For dExponentialLogisticGrowth: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rExponentialLogisticGrowth a simulated date in Cal BP.

Author(s)

Enrico Crema

Examples

p = list(r1=-0.001,r2=0.01,mu=5200,k=0.2)
modelPlot(model = dExponentialLogisticGrowth,a=6000,b=4000,params=p,alpha = 1)
p = list(r1=-0.001,r2=0.01,mu=5200,k=0.2)
modelPlot(model = dExponentialLogisticGrowth,a=6000,b=4000,params=p,alpha = 1)

Logistic-Exponential Growth Model

Description

Density and random generation of a logistic-exponential growth model distribution.

Usage

dLogisticExponentialGrowth(x, a, b, r1, r2, k, mu, log)

rLogisticExponentialGrowth(n, a, b, r1, r2, k, mu)
dLogisticExponentialGrowth(x, a, b, r1, r2, k, mu, log)

rLogisticExponentialGrowth(n, a, b, r1, r2, k, mu)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`r1`	growth rate of the logistic phase.
`r2`	growth rate of exponential phase.
`k`	initial proportion of the carrying capacity (must be between 0 and 1).
`mu`	change point (in BP).
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Value

For dLogisticExponentialGrowth: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rLogisticExponentialGrowth a simulated date in Cal BP.

Author(s)

Robert DiNapoli & Enrico Crema

Examples

p = list(r1=0.01,r2=-0.001,k=0.001,mu=4500)
modelPlot(model = dLogisticExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)
p = list(r1=0.01,r2=-0.001,k=0.001,mu=4500)
modelPlot(model = dLogisticExponentialGrowth,a=6000,b=4000,params=p,alpha = 1)

Logistic Growth Model

Description

Density and random generation of a logistic growth model distribution.

Usage

dLogisticGrowth(x, a, b, k, r, log)

rLogisticGrowth(n, a, b, k, r)
dLogisticGrowth(x, a, b, k, r, log)

rLogisticGrowth(n, a, b, k, r)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`k`	initial proportion of the carrying capacity (must be between 0 and 1).
`r`	intrinsic growth rate.
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Value

For dLogisticGrowth: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rLogisticGrowth a simulated date in Cal BP.

Author(s)

Enrico Crema

Examples

p = list(k=0.01,r=0.007)
modelPlot(model = dLogisticGrowth,a=6000,b=4000,params=p,alpha = 1)
p = list(k=0.01,r=0.007)
modelPlot(model = dLogisticGrowth,a=6000,b=4000,params=p,alpha = 1)

Logistic Growth Model (parametrisation with inflection point)

Description

Density and random generation of a logistic growth model distribution with alternative parametrisation.

Usage

dLogisticGrowth2(x, a, b, m, r, log)

rLogisticGrowth2(n, a, b, m, r)
dLogisticGrowth2(x, a, b, m, r, log)

rLogisticGrowth2(n, a, b, m, r)

Arguments

`x`	vector of calendar years (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`m`	inflection point in BP (i.e. point with the highest growth rate).
`r`	intrinsic growth rate.
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Details

This is an alternative parametrisation of dLogisiticGrowth, where m is equal to log(-(k-1)/k)/r.

Value

For dLogisticGrowth2: the probability (or likelihood) or log probability of an observed date x (in Cal BP). For rLogisticGrowth2 a simulated date in Cal BP.

Author(s)

Enrico Crema

Examples

p = list(m=4500,r=0.007)
modelPlot(model = dLogisticGrowth2,a=6000,b=4000,params=p,alpha = 1)
p = list(m=4500,r=0.007)
modelPlot(model = dLogisticGrowth2,a=6000,b=4000,params=p,alpha = 1)

Trapezoidal Distribution

Description

Density and random generation of an Trapezoidal distribution.

Usage

dTrapezoidal(x, a, m1, m2, b, log)

rTrapezoidal(n, a, m1, m2, b)
dTrapezoidal(x, a, m1, m2, b, log)

rTrapezoidal(n, a, m1, m2, b)

Arguments

`x`	A calendar year (in BP).
`a`	lower (earliest) limit of the distribution (in BP).
`m1`	lower mode (in BP)
`m2`	upper mode (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`n`	number of random draws. Currently only n = 1 is supported, but the argument exists for standardization of "r" functions.

Author(s)

Enrico Crema

Examples

a=7000
b=6700
c=4000
d=3000
x=5400
modelPlot(dTrapezoidal,a=7000,b=5000,params=c(m1=6000,m2=5300),alpha=1,col=1)

a=7000
b=6700
c=4000
d=3000
x=5400
modelPlot(dTrapezoidal,a=7000,b=5000,params=c(m1=6000,m2=5300),alpha=1,col=1)

IntCal20 radiocarbon age calibration curve for the Northern hemisphere.

Description

IntCal20 radiocarbon age calibration curve for the Northern hemisphere.

Usage

intcal20
intcal20

Format

A data.frame with the following fields:

CalBP: ID of each radiocarbon date
C14Age: Radiocarbon age in 14C years BP
C14Age.sigma: Radiocarbon age error
Delta14C: Labcode of the radiocarbon date
Delta14C.sigma: Material of the dated sample

Source

https://intcal.org/curves/intcal20.14c

References

Reimer, P. J., Austin, W. E. N., Bard, E., Bayliss, A., Blackwell, P. G., Ramsey, C. B., et al. (2020). The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP). Radiocarbon, 62(4), 725–757. https://doi.org/10.1017/RDC.2020.41

Linear interpolation function

Description

A nimbleFunction emulating BUGS/JAGS's interp.lin.

Usage

interpLin(z, x, y)
interpLin(z, x, y)

Arguments

`z`	value where the interpolation take place
`x`	numeric vector giving the coordinates of the points to be interpolated.
`y`	numeric vector giving the coordinates of the points to be interpolated.

Value

interpolated value

Examples

data(intcal20)
interpLin(4500,intcal20$CalBP,intcal20$C14Age)
# equivalent to:
approx(x=intcal20$CalBP,y=intcal20$C14Age,xout=4500)$y
data(intcal20)
interpLin(4500,intcal20$CalBP,intcal20$C14Age)
# equivalent to:
approx(x=intcal20$CalBP,y=intcal20$C14Age,xout=4500)$y

Marine20 radiocarbon age calibration curve.

Description

Marine20 radiocarbon age calibration curve.

Usage

marine20
marine20

Format

A data.frame with the following fields:

CalBP: ID of each radiocarbon date
C14Age: Radiocarbon age in 14C years BP
C14Age.sigma: Radiocarbon age error
Delta14C: Labcode of the radiocarbon date
Delta14C.sigma: Material of the dated sample

Source

https://intcal.org/curves/marine20.14c

References

Heaton, T. J., Köhler, P., Butzin, M., Bard, E., Reimer, R. W., Austin, W. E. N., et al. (2020). Marine20—The Marine Radiocarbon Age Calibration Curve (0–55,000 cal BP). Radiocarbon, 62(4), 779–820. https://doi.org/10.1017/RDC.2020.68

Plot Growth Models

Description

Plots growth models based on user provided parameters for prior and posterior predictive checks.

Usage

modelPlot(
  model,
  a,
  b,
  params,
  type = c("spaghetti"),
  nsample = NULL,
  interval = 0.9,
  calendar = "BP",
  col = "lightgrey",
  alpha = 0.1,
  ylim = NULL,
  xlim = NULL,
  xlab = NULL,
  ylab = NULL,
  add = FALSE,
  lwd = 1,
  ...
)
modelPlot(
  model,
  a,
  b,
  params,
  type = c("spaghetti"),
  nsample = NULL,
  interval = 0.9,
  calendar = "BP",
  col = "lightgrey",
  alpha = 0.1,
  ylim = NULL,
  xlim = NULL,
  xlab = NULL,
  ylab = NULL,
  add = FALSE,
  lwd = 1,
  ...
)

Arguments

`model`	growth model.
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`params`	a list of vectors containing model parameters. The names attribute of each vector should match growth model parameters.
`type`	either a 'spaghetti' plot or a quantile based 'envelope' plot. Default is 'spaghetti'.
`nsample`	number of samples to be used. Default is the length of the parameter vectors supplied in the argument `params`.
`interval`	quantile interval used for the envelope plot. Ignored when type is set to 'spaghetti'.
`calendar`	either `'BP'` or `'BCAD'`. Indicate whether the calibrated date should be displayed in BP or BC/AD. Default is `'BP'`.
`col`	fill color for the quantile envelope (when `type=='envelope'`) or line colour (when `type=='spaghetti'`).
`alpha`	transparency value for each line in the spaghetti plot or the fill color in the 'envelope' plot. Default is 1.
`ylim`	the y limits of the plot.
`xlim`	the x limits of the plot (in Cal BP).
`xlab`	a label for the x axis. Default is 'Years cal BP','Years BC/AD','Years BC', or 'Years AD' depending on data range and settings of `calendar`.
`ylab`	a label for the y axis. Default is 'Probability'.
`add`	whether or not the new graphic should be added to an existing plot.
`lwd`	line width. Default is 1.
`...`	additional arguments affecting the plot

Value

None.

Examples


params = list(k=runif(100,0.01,0.02),r=runif(100,0.003,0.004))
modelPlot(model=dLogisticGrowth,a=5000,b=2000,params=params,type=c('spaghetti'),alpha=0.5)

params = list(k=runif(100,0.01,0.02),r=runif(100,0.003,0.004))
modelPlot(model=dLogisticGrowth,a=5000,b=2000,params=params,type=c('spaghetti'),alpha=0.5)

Plot SPD-based Posterior Predictive Check

Description

Plots spdppc class object for SPD-based Posterior Predictive Check.

Usage

## S3 method for class 'spdppc'
plot(
  x,
  type = "envelope",
  nsample = NULL,
  interval = 0.9,
  obs.lwd = 1.5,
  obs.col = "black",
  sim.col = "lightgrey",
  alpha = 1,
  envelope.col = "lightgrey",
  positive.col = "red",
  negative.col = "blue",
  calendar = "BP",
  xlab = NULL,
  ylab = NULL,
  ...
)
## S3 method for class 'spdppc'
plot(
  x,
  type = "envelope",
  nsample = NULL,
  interval = 0.9,
  obs.lwd = 1.5,
  obs.col = "black",
  sim.col = "lightgrey",
  alpha = 1,
  envelope.col = "lightgrey",
  positive.col = "red",
  negative.col = "blue",
  calendar = "BP",
  xlab = NULL,
  ylab = NULL,
  ...
)

Arguments

`x`	An `spdppc` class object.
`type`	Either a 'spaghetti' plot or a quantile based envelope plot. Default is 'envelope'.
`nsample`	Number of samples to be displayed in the 'spaghetti' plot. Default is the total number of simulations supplied in the 'spdppc' class object, ignored when `type` is set to 'envelope'.
`interval`	Quantile interval used for the envelope plot. Ignored when `type` is set to 'spaghetti'. Default is 0.90.
`obs.lwd`	Line width of the observed SPD. Default is 1.5.
`obs.col`	Line colour of the observed SPD. Default is 'black'.
`sim.col`	Line colour of simulated SPDs. Default is 'lightgrey', ignored when `type` is set to 'envelope'.
`alpha`	Transparency value for each line in the spaghetti plot. Default is 1, ignored when `type` is set to 'envelope'.
`envelope.col`	Fill colour of the simulation envelope. Default is 'lightgrey', ignored when `type` is set to 'envelope.'spaghetti'.
`positive.col`	Fill colour for the area with positive deviation from the simulation envelope. Default is 'red', ignored when `type` is set to 'spaghetti'.
`negative.col`	Fill colour for the area with positive deviation from the simulation envelope. Default is 'blue', ignored when `type` is set to 'spaghetti'.
`calendar`	Either `'BP'` or `'BCAD'`. Indicate whether the calibrated date should be displayed in BP or BC/AD. Default is `'BP'`.
`xlab`	a label for the x axis. Default is 'Years cal BP','Years BC/AD','Years BC', or 'Years AD' depending on data range and settings of `calendar`.
`ylab`	a label for the y axis. Default is 'Probability'.
`...`	Additional arguments affecting the plot

Value

None.

Plot Marginal Posterior Distribution

Description

Plot marginal posterior distribution highlighting user-defined higher posterior density interval.

Usage

postHPDplot(
  x,
  prob = 0.9,
  bw = "SJ",
  hpd.col = "lightblue",
  line.col = "darkgrey",
  rnd = 3,
  HPD = TRUE,
  show.hpd.val = TRUE,
  ...
)
postHPDplot(
  x,
  prob = 0.9,
  bw = "SJ",
  hpd.col = "lightblue",
  line.col = "darkgrey",
  rnd = 3,
  HPD = TRUE,
  show.hpd.val = TRUE,
  ...
)

Arguments

`x`	Posterior samples
`prob`	Highest posterior density interval. Default is 0.9.
`bw`	The smoothing bandwidth to be used. See `density` for details. Default is "SJ".
`hpd.col`	Fill colour for the highest density interval. Default is 'lightblue'. Ignored when `HPD` is set to FALSE.
`line.col`	Line color for the density plot. Default is 'darkgrey'.
`rnd`	Integer indicating the number of decimal places to be used in the reporting of the highest posterior density interval.
`HPD`	Whether the highest posterior density interval is highlighted or not. Default is TRUE.
`show.hpd.val`	Whether the highest posterior density interval is displayed as subtitle. Default is TRUE.
`...`	other graphical parameters.

Value

None.

Calculates correlation between observed and posterior generated SPD.

Description

Computes the correlation between observed SPDs and posterior generated SPD from the output of postPredSPD() function as an heuristic of the goodness-of-fit of the model.

Usage

postPredCor(x, method = "pearson")
postPredCor(x, method = "pearson")

Arguments

`x`	An object of class `spdppc`.
`method`	a character string indicating which correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman": can be abbreviated.

Value

A vector of correlation values.

SPD-based Posterior Predictive Check

Description

Generates SPDs from posterior samples.

Usage

postPredSPD(
  x,
  errors,
  calCurve,
  model,
  a,
  b,
  params,
  nsim,
  method = NULL,
  spdnormalised = TRUE,
  datenormalised = TRUE,
  ncores = 1,
  verbose = TRUE
)
postPredSPD(
  x,
  errors,
  calCurve,
  model,
  a,
  b,
  params,
  nsim,
  method = NULL,
  spdnormalised = TRUE,
  datenormalised = TRUE,
  ncores = 1,
  verbose = TRUE
)

Arguments

`x`	a vector of observed uncalibrated radiocarbon ages.
`errors`	a vector of standard deviations corresponding to each estimated radiocarbon age.
`calCurve`	character string naming a calibration curve already provided with the rcarbon package (currently 'intcal20','intcal13','intcal13nhpine16','shcal20','shcal13','shcal13shkauri16',”marine13','marine20').
`model`	growth model
`a`	lower (earliest) limit of the distribution (in BP).
`b`	upper (latest) limit of the distribution (in BP).
`params`	list of vectors containing model parameters. The names attribute of each vector should match growth model parameters.
`nsim`	number of SPDs to be generated. Default is the length of the parameter vectors supplied in the argument `params`.
`method`	method for the creation of random dates from the fitted model. Either 'uncalsample' or 'calsample'.
`spdnormalised`	a logical variable indicating whether the total probability mass of the SPD is normalised to sum to unity for both observed and simulated data. Default is TRUE.
`datenormalised`	a logical variable indicating whether dates should be normalised to sum to unity or not. Default is TRUE.
`ncores`	number of cores used for for parallel execution. Default is 1.
`verbose`	a logical variable indicating whether extra information on progress should be reported. Default is TRUE.

Value

An object of class spdppc with the following elements

obs A data.frame containing the years (in Cal BP) and the corresponding summed probability in the observed data.
spdmat A matrix containing the summed probability distribution of the simulated data.

IntCal20 radiocarbon age calibration curve for the Southern hemisphere.

Description

IntCal20 radiocarbon age calibration curve for the Southern hemisphere.

Usage

shcal20
shcal20

Format

A data.frame with the following fields:

CalBP: ID of each radiocarbon date
C14Age: Radiocarbon age in 14C years BP
C14Age.sigma: Radiocarbon age error
Delta14C: Labcode of the radiocarbon date
Delta14C.sigma: Material of the dated sample

Source

https://intcal.org/curves/shcal20.14c

Package 'nimbleCarbon'

Help Index

Calculate Agreement Indices.

Description

Usage

Arguments

Value

References

WAIC-based model comparison

Description

Usage

Arguments

Value

Asymmetric Laplace Distribution

Description

Usage

Arguments

Author(s)

Double Exponential Growth Model

Description

Usage

Arguments

Value

Author(s)

Examples

Exponential Growth Model

Description

Usage

Arguments

Value

Author(s)

Examples

Exponential-Logistic Growth Model

Description

Usage

Arguments

Value

Author(s)

Examples

Logistic-Exponential Growth Model

Description

Usage

Arguments

Value

Author(s)

Examples

Logistic Growth Model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Logistic Growth Model (parametrisation with inflection point)

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Trapezoidal Distribution

Description

Usage

Arguments

Author(s)

Examples

IntCal20 radiocarbon age calibration curve for the Northern hemisphere.

Description

Usage

Format

Source

References

Linear interpolation function

Description

Usage

Arguments

Value

Examples