evoigt {voigt} | R Documentation |
Estimation of Voigt distribution parameters
Description
The function provides both point and interval estimates for the Voigt distribution parameters in a Bayesian way (see Details).
Usage
evoigt(data, hyper = NULL, init = NULL, S = 10000, burn = S/2,
thin = 10, fix.arg = NULL, chain = FALSE, ...)
Arguments
data |
A numeric vector of length at least one containing only finite values. |
hyper |
A numeric vector of length six giving the hyperparameters for |
init |
The starting values for the chain parameters. If NULL (default) all chains start at 1. If scalar it is used as the common starting value. If character it can be set either to " |
S |
The number of iterations in the Gibbs sampler. Default to |
burn |
The number of initial chain values to be discarded (burn-in period). Default to |
thin |
This parameter allows the user to specify if and how the chain should be thinned after burn-in. By default thin = 5 is used, which corresponds to keeping 1/5 of the chain values. |
fix.arg |
An optional vector of length 3 giving the values of fixed parameters of the Voigt distribution, in this order: |
chain |
logical; if TRUE the output contains also the (thinned) chains values after burn-in. The first value of the chains is set according to the |
... |
Additional arguments to be passed to functions of the package |
Details
The function runs a Gibbs sampler for estimating parameters using the following prior distributions:
\mu\sim N(\mu_0, \nu_0^2)
, \sigma\sim \Gamma(a, b)
and \gamma\sim \Gamma(c, d)
.
Value
evoigt
returns a list with the following components:
posterior mean |
the vector of posterior means |
posterior median |
the vector of posterior medians |
HPD interval |
the highest probability density intervals for the parameters |
chain |
the thinned chain values after burn-in (only if argument |
Author(s)
Massimo Cannas [aut, cre], Nicola Piras [aut]
References
Cannas, M. and Piras, N. (2025) Estimation of Voigt Distribution Parameters: A Bayesian Approach. (conference paper) https://link.springer.com/chapter/10.1007/978-3-031-96303-2_53
Cannas, M. and Piras, N. Mixture representation and parameter estimation for the Voigt profile (submitted)
See Also
See HPDinterval
for details on how the highest posterior density interval is built.
Examples
x = rvoigt(500, mu=0, sigma=1,gamma=1)
# point estimates and (default) 95% credibility intervals
evoigt(data=x)
# point estimates and 90% credibility intervals
evoigt(data=x, prob = 0.9)
# chain values
res = evoigt(data=x, prob = 0.9, chain=TRUE)
mu.chain = res$mu.chain
plot(0: (length(mu.chain)-1), type = "l", mu.chain, xlab="",ylab=c(expression(mu)) )
points(0,mu.chain[1],pch=1,col="red")
# if a parameter is known its value can be fixed using "fix.arg"
# e.g. set sigma =1:
res = evoigt(data=x, fix.arg=c(NA, 1, NA))
res["posterior mean"]
res["posterior median"]
res["HPD interval"]