Standardized GH distribution fit
dist-sghFit.Rd
Estimates the distributional parameters for a standardized generalized hyperbolic distribution.
Usage
sghFit(x, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE,
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
Arguments
- x
a numeric vector.
- zeta, rho, lambda
shape parameter
zeta
is positive, skewness parameterrho
is in the range (-1, 1). and index parameterlambda
, by default 1.- include.lambda
a logical flag, by default
TRUE
. Should the index parameterlambda
included in the parameter estimate?- scale
a logical flag, by default
TRUE
. Should the time series be scaled by its standard deviation to achieve a more stable optimization?- doplot
a logical flag. Should a plot be displayed?
- span
x-coordinates for the plot, by default 100 values automatically selected and ranging between the 0.001, and 0.999 quantiles. Alternatively, you can specify the range by an expression like
span=seq(min, max, times = n)
, where,min
andmax
are the left and right endpoints of the range, andn
gives the number of the intermediate points.- trace
a logical flag. Should the parameter estimation process be traced?
- title
a character string which allows for a project title.
- description
a character string which allows for a brief description.
- ...
parameters to be parsed.
Value
an object from class "fDISTFIT"
.
Slot fit
is a list with the following components:
- estimate
the point at which the maximum value of the log liklihood function is obtained.
- minimum
the value of the estimated maximum, i.e. the value of the log likelihood function.
- code
an integer indicating why the optimization process terminated.
1: relative gradient is close to zero, current iterate is probably solution;
2: successive iterates within tolerance, current iterate is probably solution;
3: last global step failed to locate a point lower thanestimate
. Eitherestimate
is an approximate local minimum of the function orsteptol
is too small;
4: iteration limit exceeded;
5: maximum step sizestepmax
exceeded five consecutive times. Either the function is unbounded below, becomes asymptotic to a finite value from above in some direction orstepmax
is too small.- gradient
the gradient at the estimated maximum.
- steps
number of function calls.
Examples
## sghFit -
# Simulate Random Variates:
set.seed(1953)
s = rsgh(n = 2000, zeta = 0.7, rho = 0.5, lambda = 0)
## sghFit -
# Fit Parameters:
sghFit(s, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE,
doplot = TRUE)
#>
#> Objective Function Value: -2647.471
#> Parameter Estimates: 1 0 1
#>
#> Objective Function Value: -2647.471
#> Parameter Estimates: 1 0 1
#>
#> Objective Function Value: -2647.471
#> Parameter Estimates: 1 1.490116e-08 1
#>
#> Objective Function Value: -2647.471
#> Parameter Estimates: 1 0 1
#>
#> Objective Function Value: -Inf
#> Parameter Estimates: 0.96663 0.9989405 0.9683076
#>
#> Objective Function Value: -2594.623
#> Parameter Estimates: 0.996663 0.09989405 0.9968308
#>
#> Objective Function Value: -2594.624
#> Parameter Estimates: 0.996711 0.09989405 0.9968308
#>
#> Objective Function Value: -2594.645
#> Parameter Estimates: 0.996663 0.09984604 0.9968308
#>
#> Objective Function Value: -2594.623
#> Parameter Estimates: 0.996663 0.09989405 0.9968788
#>
#> Objective Function Value: -2524.793
#> Parameter Estimates: 0.982503 0.2992784 0.9900936
#>
#> Objective Function Value: -2524.793
#> Parameter Estimates: 0.9825144 0.2992784 0.9900936
#>
#> Objective Function Value: -2524.793
#> Parameter Estimates: 0.982503 0.299277 0.9900936
#>
#> Objective Function Value: -2524.793
#> Parameter Estimates: 0.982503 0.2992784 0.9901305
#>
#> Objective Function Value: -2505.046
#> Parameter Estimates: 0.9247665 0.4890543 0.9645671
#>
#> Objective Function Value: -2505.046
#> Parameter Estimates: 0.9247909 0.4890543 0.9645671
#>
#> Objective Function Value: -2505.046
#> Parameter Estimates: 0.9247665 0.4890529 0.9645671
#>
#> Objective Function Value: -2505.047
#> Parameter Estimates: 0.9247665 0.4890543 0.9646077
#>
#> Objective Function Value: -2495.774
#> Parameter Estimates: 0.7983562 0.4267042 0.8226766
#>
#> Objective Function Value: -2482.511
#> Parameter Estimates: 0.597971 0.4268163 0.6049115
#>
#> Objective Function Value: -15525.21
#> Parameter Estimates: 1.490116e-08 0.3999997 -0.6322011
#>
#> Objective Function Value: -2482.512
#> Parameter Estimates: 0.597989 0.4268163 0.6049115
#>
#> Objective Function Value: -2482.511
#> Parameter Estimates: 0.597971 0.4268176 0.6049115
#>
#> Objective Function Value: -2482.512
#> Parameter Estimates: 0.597971 0.4268163 0.6049334
#>
#> Objective Function Value: -9543.319
#> Parameter Estimates: 1.490116e-08 0.6196524 -0.8337277
#>
#> Objective Function Value: -2484.203
#> Parameter Estimates: 0.4815999 0.5095759 0.5396964
#>
#> Objective Function Value: -2481.034
#> Parameter Estimates: 0.5545759 0.4654131 0.5768911
#>
#> Objective Function Value: -2481.035
#> Parameter Estimates: 0.5545936 0.4654131 0.5768911
#>
#> Objective Function Value: -2481.034
#> Parameter Estimates: 0.5545759 0.4654116 0.5768911
#>
#> Objective Function Value: -2481.035
#> Parameter Estimates: 0.5545759 0.4654131 0.5769016
#>
#> Objective Function Value: -2479.327
#> Parameter Estimates: 0.5153132 0.4196073 0.5541257
#>
#> Objective Function Value: -2479.327
#> Parameter Estimates: 0.5153203 0.4196073 0.5541257
#>
#> Objective Function Value: -2479.327
#> Parameter Estimates: 0.5153132 0.4196084 0.5541257
#>
#> Objective Function Value: -2479.327
#> Parameter Estimates: 0.5153132 0.4196073 0.5541456
#>
#> Objective Function Value: -2478.091
#> Parameter Estimates: 0.4611318 0.4505896 0.5379252
#>
#> Objective Function Value: -2478.091
#> Parameter Estimates: 0.4611515 0.4505896 0.5379252
#>
#> Objective Function Value: -2478.091
#> Parameter Estimates: 0.4611318 0.4505885 0.5379252
#>
#> Objective Function Value: -2478.091
#> Parameter Estimates: 0.4611318 0.4505896 0.5379346
#>
#> Objective Function Value: -2477.59
#> Parameter Estimates: 0.4127338 0.4131126 0.5176498
#>
#> Objective Function Value: -2477.59
#> Parameter Estimates: 0.4127389 0.4131126 0.5176498
#>
#> Objective Function Value: -2477.59
#> Parameter Estimates: 0.4127338 0.4131137 0.5176498
#>
#> Objective Function Value: -2477.59
#> Parameter Estimates: 0.4127338 0.4131126 0.5176733
#>
#> Objective Function Value: -2477.025
#> Parameter Estimates: 0.4277878 0.442396 0.4622076
#>
#> Objective Function Value: -2477.025
#> Parameter Estimates: 0.4277998 0.442396 0.4622076
#>
#> Objective Function Value: -2477.025
#> Parameter Estimates: 0.4277878 0.4423948 0.4622076
#>
#> Objective Function Value: -2477.025
#> Parameter Estimates: 0.4277878 0.442396 0.4622141
#>
#> Objective Function Value: -2476.739
#> Parameter Estimates: 0.4701276 0.4433887 0.4135831
#>
#> Objective Function Value: -2476.739
#> Parameter Estimates: 0.4701216 0.4433887 0.4135831
#>
#> Objective Function Value: -2476.739
#> Parameter Estimates: 0.4701276 0.4433897 0.4135831
#>
#> Objective Function Value: -2476.739
#> Parameter Estimates: 0.4701276 0.4433887 0.4135965
#>
#> Objective Function Value: -2476.498
#> Parameter Estimates: 0.4847757 0.4542832 0.3517387
#>
#> Objective Function Value: -2476.198
#> Parameter Estimates: 0.525779 0.4629315 0.2724897
#>
#> Objective Function Value: -2475.785
#> Parameter Estimates: 0.653231 0.4952472 0.002811424
#>
#> Objective Function Value: -2475.785
#> Parameter Estimates: 0.6532343 0.4952472 0.002811424
#>
#> Objective Function Value: -2475.785
#> Parameter Estimates: 0.653231 0.4952459 0.002811424
#>
#> Objective Function Value: -2475.785
#> Parameter Estimates: 0.653231 0.4952472 0.002824826
#>
#> Objective Function Value: -2478.242
#> Parameter Estimates: 0.5426647 0.4600108 -0.06066984
#>
#> Objective Function Value: -2475.663
#> Parameter Estimates: 0.6431653 0.502983 -0.0009041901
#>
#> Objective Function Value: -2475.663
#> Parameter Estimates: 0.6431685 0.502983 -0.0009041901
#>
#> Objective Function Value: -2475.663
#> Parameter Estimates: 0.6431653 0.5029816 -0.0009041901
#>
#> Objective Function Value: -2475.663
#> Parameter Estimates: 0.6431653 0.502983 -0.0008909593
#>
#> Objective Function Value: -2475.617
#> Parameter Estimates: 0.6322473 0.4994268 -0.007470356
#>
#> Objective Function Value: -2475.617
#> Parameter Estimates: 0.6322518 0.4994268 -0.007470356
#>
#> Objective Function Value: -2475.617
#> Parameter Estimates: 0.6322473 0.499428 -0.007470356
#>
#> Objective Function Value: -2475.617
#> Parameter Estimates: 0.6322473 0.4994268 -0.007458999
#>
#> Objective Function Value: -2475.595
#> Parameter Estimates: 0.6330886 0.5041055 -0.01981401
#>
#> Objective Function Value: -2475.595
#> Parameter Estimates: 0.633092 0.5041055 -0.01981401
#>
#> Objective Function Value: -2475.595
#> Parameter Estimates: 0.6330886 0.5041043 -0.01981401
#>
#> Objective Function Value: -2475.595
#> Parameter Estimates: 0.6330886 0.5041055 -0.01980751
#>
#> Objective Function Value: -2475.58
#> Parameter Estimates: 0.6356588 0.5048162 -0.03276981
#>
#> Objective Function Value: -2475.55
#> Parameter Estimates: 0.6464089 0.5111394 -0.07053396
#>
#> Objective Function Value: -2475.519
#> Parameter Estimates: 0.6633998 0.5201116 -0.1352302
#>
#> Objective Function Value: -2475.519
#> Parameter Estimates: 0.6634028 0.5201116 -0.1352302
#>
#> Objective Function Value: -2475.519
#> Parameter Estimates: 0.6633998 0.5201127 -0.1352302
#>
#> Objective Function Value: -2475.519
#> Parameter Estimates: 0.6633998 0.5201116 -0.1352239
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6689899 0.5250719 -0.1705175
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.668993 0.5250719 -0.1705175
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6689899 0.5250735 -0.1705175
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6689899 0.5250703 -0.1705175
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6689899 0.5250719 -0.1705108
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699212 0.526159 -0.1761966
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699245 0.526159 -0.1761966
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699178 0.526159 -0.1761966
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699212 0.52616 -0.1761966
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699212 0.5261579 -0.1761966
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699212 0.526159 -0.1760518
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699212 0.526159 -0.1763414
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700252 0.5262556 -0.1767013
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700657 0.5262556 -0.1767013
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6699847 0.5262556 -0.1767013
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700252 0.5262668 -0.1767013
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700252 0.5262443 -0.1767013
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700252 0.5262556 -0.1765645
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700252 0.5262556 -0.176838
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.526254 -0.1766919
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.670086 0.526254 -0.1766919
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.669949 0.526254 -0.1766919
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.5262782 -0.1766919
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.5262298 -0.1766919
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.526254 -0.1765471
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.526254 -0.1768368
#>
#> Objective Function Value: -2475.512
#> Parameter Estimates: 0.6700175 0.526254 -0.1766919
#>
#> Standardized Parameters:
#> zeta rho lambda
#> 0.6700175 0.5262540 -0.1766919
#>
#> 1st Parameterization:
#> alpha beta delta mu
#> 1.3633157 0.7174504 0.5779677 -0.4887948
#>
#> Title:
#> SGH Parameter Estimation
#>
#> Call:
#> sghFit(x = s, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE,
#> doplot = TRUE)
#>
#> Model:
#> Standarized GH Distribution
#>
#> Estimated Parameter(s):
#> zeta rho lambda
#> 0.6700175 0.5262540 -0.1766919
#>