fit.ghypuv: Fitting generalized hyperbolic distributions to univariate...
In ghyp: A package on the generalized hyperbolic distribution and its special cases
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
This function performs a maximum likelihood parameter estimation for
univariate generalized hyperbolic distributions.
Usage
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fit.ghypuv(data, lambda = 1, alpha.bar = 0.5, mu = median(data),
sigma = mad(data), gamma = 0,
opt.pars = c(lambda = T, alpha.bar = T, mu = T,
sigma = T, gamma = !symmetric),
symmetric = F, standardize = F, save.data = T,
na.rm = T, silent = FALSE, ...)
fit.hypuv(data,
opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.NIGuv(data,
opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.VGuv(data, lambda = 1,
opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.tuv(data, nu = 3.5,
opt.pars = c(nu = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.gaussuv(data, na.rm = T, save.data = T)
Arguments
data
An object coercible to a vector.
lambda
Starting value for the shape parameter lambda.
alpha.bar
Starting value for the shape parameter alpha.bar.
nu
Starting value for the shape parameter nu (only used in case of a student-t distribution. It determines
the degree of freedom and is defined as -2*lambda.)
mu
Starting value for the location parameter mu.
sigma
Starting value for the dispersion parameter sigma.
gamma
Starting value for the skewness parameter gamma.
opt.pars
A named logical vector which states which parameters should be fitted.
symmetric
If TRUE the skewness parameter gamma keeps zero.
standardize
If TRUE the sample will be standardized before fitting.
Afterwards, the parameters and log-likelihood et cetera will be back-transformed.
save.data
If TRUE data will be stored within the
mle.ghyp object.
na.rm
If TRUE missing values will be removed from data.
silent
If TRUE no prompts will appear in the console.
...
Arguments passed to optim and to fit.ghypuv when
fitting special cases of the generalized hyperbolic distribution.
Details
The general-purpose optimization routine optim is used to
maximize the loglikelihood function. The default method is that of
Nelder and Mead which uses only function values. Parameters of
optim can be passed via the ... argument of the fitting
routines.
Value
An object of class mle.ghyp.
Note
The variance gamma distribution becomes singular when x - mu = 0. This singularity is catched and the reduced density
function is computed. Because the transition is not smooth in the
numerical implementation this can rarely result in nonsensical fits.
Providing both arguments, opt.pars and symmetric
respectively, can result in a conflict when opt.pars['gamma']
and symmetric are TRUE. In this case symmetric
will dominate and opt.pars['gamma'] is set to FALSE.
Author(s)
Wolfgang Breymann, David Luethi
References
ghyp-package vignette in the doc folder or on http://cran.r-project.org/web/packages/ghyp/.
See Also
fit.ghypmv, fit.hypmv, fit.NIGmv,
fit.VGmv, fit.tmv for multivariate fitting routines.
ghyp.fit.info for information regarding the fitting procedure.
Examples
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data(smi.stocks)
nig.fit <- fit.NIGuv(smi.stocks[,"SMI"], opt.pars = c(alpha.bar = FALSE),
alpha.bar = 1, control = list(abstol = 1e-8))
nig.fit
summary(nig.fit)
hist(nig.fit)
Example output
Loading required package: numDeriv
Loading required package: gplots
Attaching package: 'gplots'
The following object is masked from 'package:stats':
lowess
[1] "Llh: 5.43442381858987E+03; Pars: 5.626297E-04, 8.875123E-03, 0.000000E+00"
[1] "Llh: -9.63118912675987E+04; Pars: 4.730129E-01, 8.875123E-03, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: -1.33159421324728E+05; Pars: 5.626297E-04, 8.875123E-03, 4.724503E-01"
[1] "Llh: 5.40585124384195E+03; Pars: 2.562630E-03, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.42996237953101E+03; Pars: 1.562630E-03, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43079814576067E+03; Pars: 1.562630E-03, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.41369364563650E+03; Pars: 1.562630E-03, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43906676328363E+03; Pars: 1.562630E-03, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.42137059007665E+03; Pars: -1.437370E-03, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43772029929769E+03; Pars: -4.373703E-04, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43857178038201E+03; Pars: -4.373703E-04, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.43892892734741E+03; Pars: -4.373703E-04, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.42938207221730E+03; Pars: -4.373703E-04, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.42996237953101E+03; Pars: 1.562630E-03, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43772029929769E+03; Pars: -4.373703E-04, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.44030385848315E+03; Pars: 5.626297E-04, 1.426348E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43280955921200E+03; Pars: 5.626297E-04, 1.424923E-02, 1.000000E-03"
[1] "Llh: 5.44070688002371E+03; Pars: 5.626297E-04, 1.424923E-02, -1.000000E-03"
[1] "Llh: 5.43079814576067E+03; Pars: 1.562630E-03, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.43857178038201E+03; Pars: -4.373703E-04, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.44203031551468E+03; Pars: 5.626297E-04, 1.420654E-02, 0.000000E+00"
[1] "Llh: 5.43363797827799E+03; Pars: 5.626297E-04, 1.422076E-02, 1.000000E-03"
[1] "Llh: 5.44156695163584E+03; Pars: 5.626297E-04, 1.422076E-02, -1.000000E-03"
[1] "Llh: 5.41369364563650E+03; Pars: 1.562630E-03, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43892892734741E+03; Pars: -4.373703E-04, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43280955921200E+03; Pars: 5.626297E-04, 1.424923E-02, 1.000000E-03"
[1] "Llh: 5.43363797827799E+03; Pars: 5.626297E-04, 1.422076E-02, 1.000000E-03"
[1] "Llh: 5.41734544414001E+03; Pars: 5.626297E-04, 1.423498E-02, 2.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43906676328363E+03; Pars: 1.562630E-03, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.42938207221730E+03; Pars: -4.373703E-04, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.44070688002371E+03; Pars: 5.626297E-04, 1.424923E-02, -1.000000E-03"
[1] "Llh: 5.44156695163584E+03; Pars: 5.626297E-04, 1.422076E-02, -1.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43317170665703E+03; Pars: 5.626297E-04, 1.423498E-02, -2.000000E-03"
Symmetric Normal Inverse Gaussian Distribution:
Parameters:
alpha.bar mu sigma gamma
1.0000000000 0.0005626297 0.0142349834 0.0000000000
log-likelihood:
5441.17
Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE), alpha.bar = 1, control = list(abstol = 1e-08))
Symmetric Normal Inverse Gaussian Distribution:
Parameters:
alpha.bar mu sigma gamma
1.0000000000 0.0005626297 0.0142349834 0.0000000000
Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE), alpha.bar = 1, control = list(abstol = 1e-08))
Optimization information:
log-Likelihood: 5441.17
AIC: -10876.34
Fitted parameters: mu, sigma, gamma; (Number: 3)
Number of iterations: 4
Converged: TRUE
ghyp documentation built on May 2, 2019, 6:09 p.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
This function performs a maximum likelihood parameter estimation for univariate generalized hyperbolic distributions.
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 | fit.ghypuv(data, lambda = 1, alpha.bar = 0.5, mu = median(data),
sigma = mad(data), gamma = 0,
opt.pars = c(lambda = T, alpha.bar = T, mu = T,
sigma = T, gamma = !symmetric),
symmetric = F, standardize = F, save.data = T,
na.rm = T, silent = FALSE, ...)
fit.hypuv(data,
opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.NIGuv(data,
opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.VGuv(data, lambda = 1,
opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.tuv(data, nu = 3.5,
opt.pars = c(nu = T, mu = T, sigma = T, gamma = !symmetric),
symmetric = F, ...)
fit.gaussuv(data, na.rm = T, save.data = T)
|
Arguments
data |
An object coercible to a |
lambda |
Starting value for the shape parameter |
alpha.bar |
Starting value for the shape parameter |
nu |
Starting value for the shape parameter |
mu |
Starting value for the location parameter |
sigma |
Starting value for the dispersion parameter |
gamma |
Starting value for the skewness parameter |
opt.pars |
A named logical |
symmetric |
If |
standardize |
If |
save.data |
If |
na.rm |
If |
silent |
If |
... |
Arguments passed to |
Details
The general-purpose optimization routine optim is used to
maximize the loglikelihood function. The default method is that of
Nelder and Mead which uses only function values. Parameters of
optim can be passed via the ... argument of the fitting
routines.
Value
An object of class mle.ghyp.
Note
The variance gamma distribution becomes singular when x - mu = 0. This singularity is catched and the reduced density function is computed. Because the transition is not smooth in the numerical implementation this can rarely result in nonsensical fits.
Providing both arguments, opt.pars and symmetric
respectively, can result in a conflict when opt.pars['gamma']
and symmetric are TRUE. In this case symmetric
will dominate and opt.pars['gamma'] is set to FALSE.
Author(s)
Wolfgang Breymann, David Luethi
References
ghyp-package vignette in the doc folder or on http://cran.r-project.org/web/packages/ghyp/.
See Also
fit.ghypmv, fit.hypmv, fit.NIGmv,
fit.VGmv, fit.tmv for multivariate fitting routines.
ghyp.fit.info for information regarding the fitting procedure.
Examples
1 2 3 4 5 6 7 8 9 | data(smi.stocks)
nig.fit <- fit.NIGuv(smi.stocks[,"SMI"], opt.pars = c(alpha.bar = FALSE),
alpha.bar = 1, control = list(abstol = 1e-8))
nig.fit
summary(nig.fit)
hist(nig.fit)
|
Example output
Loading required package: numDeriv
Loading required package: gplots
Attaching package: 'gplots'
The following object is masked from 'package:stats':
lowess
[1] "Llh: 5.43442381858987E+03; Pars: 5.626297E-04, 8.875123E-03, 0.000000E+00"
[1] "Llh: -9.63118912675987E+04; Pars: 4.730129E-01, 8.875123E-03, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: -1.33159421324728E+05; Pars: 5.626297E-04, 8.875123E-03, 4.724503E-01"
[1] "Llh: 5.40585124384195E+03; Pars: 2.562630E-03, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.42996237953101E+03; Pars: 1.562630E-03, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43079814576067E+03; Pars: 1.562630E-03, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.41369364563650E+03; Pars: 1.562630E-03, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43906676328363E+03; Pars: 1.562630E-03, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.42137059007665E+03; Pars: -1.437370E-03, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43772029929769E+03; Pars: -4.373703E-04, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43857178038201E+03; Pars: -4.373703E-04, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.43892892734741E+03; Pars: -4.373703E-04, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.42938207221730E+03; Pars: -4.373703E-04, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.42996237953101E+03; Pars: 1.562630E-03, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.43772029929769E+03; Pars: -4.373703E-04, 1.424923E-02, 0.000000E+00"
[1] "Llh: 5.44030385848315E+03; Pars: 5.626297E-04, 1.426348E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43280955921200E+03; Pars: 5.626297E-04, 1.424923E-02, 1.000000E-03"
[1] "Llh: 5.44070688002371E+03; Pars: 5.626297E-04, 1.424923E-02, -1.000000E-03"
[1] "Llh: 5.43079814576067E+03; Pars: 1.562630E-03, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.43857178038201E+03; Pars: -4.373703E-04, 1.422076E-02, 0.000000E+00"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.44203031551468E+03; Pars: 5.626297E-04, 1.420654E-02, 0.000000E+00"
[1] "Llh: 5.43363797827799E+03; Pars: 5.626297E-04, 1.422076E-02, 1.000000E-03"
[1] "Llh: 5.44156695163584E+03; Pars: 5.626297E-04, 1.422076E-02, -1.000000E-03"
[1] "Llh: 5.41369364563650E+03; Pars: 1.562630E-03, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43892892734741E+03; Pars: -4.373703E-04, 1.423498E-02, 1.000000E-03"
[1] "Llh: 5.43280955921200E+03; Pars: 5.626297E-04, 1.424923E-02, 1.000000E-03"
[1] "Llh: 5.43363797827799E+03; Pars: 5.626297E-04, 1.422076E-02, 1.000000E-03"
[1] "Llh: 5.41734544414001E+03; Pars: 5.626297E-04, 1.423498E-02, 2.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43906676328363E+03; Pars: 1.562630E-03, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.42938207221730E+03; Pars: -4.373703E-04, 1.423498E-02, -1.000000E-03"
[1] "Llh: 5.44070688002371E+03; Pars: 5.626297E-04, 1.424923E-02, -1.000000E-03"
[1] "Llh: 5.44156695163584E+03; Pars: 5.626297E-04, 1.422076E-02, -1.000000E-03"
[1] "Llh: 5.44117035692981E+03; Pars: 5.626297E-04, 1.423498E-02, 0.000000E+00"
[1] "Llh: 5.43317170665703E+03; Pars: 5.626297E-04, 1.423498E-02, -2.000000E-03"
Symmetric Normal Inverse Gaussian Distribution:
Parameters:
alpha.bar mu sigma gamma
1.0000000000 0.0005626297 0.0142349834 0.0000000000
log-likelihood:
5441.17
Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE), alpha.bar = 1, control = list(abstol = 1e-08))
Symmetric Normal Inverse Gaussian Distribution:
Parameters:
alpha.bar mu sigma gamma
1.0000000000 0.0005626297 0.0142349834 0.0000000000
Call:
fit.NIGuv(data = smi.stocks[, "SMI"], opt.pars = c(alpha.bar = FALSE), alpha.bar = 1, control = list(abstol = 1e-08))
Optimization information:
log-Likelihood: 5441.17
AIC: -10876.34
Fitted parameters: mu, sigma, gamma; (Number: 3)
Number of iterations: 4
Converged: TRUE
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