GH Distribution Fit
dist-ghFit.Rd
Estimates the distrinbutional parameters for a generalized hyperbolic distribution.
Usage
ghFit(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2,
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
Arguments
- x
a numeric vector.
- alpha
first shape parameter.
- beta
second shape parameter, should in the range
(0, alpha).
- delta
scale parameter, must be zero or positive.
- mu
location parameter, by default 0.
- lambda
defines the sublclass, by default \(-1/2\).
- 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
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 liklihood 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.
Details
The meanings of the parameters correspond to the first
parameterization, see gh
for further details.
The function nlm
is used to minimize the "negative"
maximum log-likelihood function. nlm
carries out a minimization
using a Newton-type algorithm.
Examples
## ghFit -
# Simulate Random Variates:
set.seed(1953)
s = rgh(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0)
## ghFit -
# Fit Parameters:
ghFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 0 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 0 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 1.490116e-08 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 0 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 0 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1633.099
#> Parameter Estimates: 1 0 1 -0.9306297 -0.5
#>
#> Objective Function Value: -1778.891
#> Parameter Estimates: 0.8909726 -0.5885522 1.221979 -1.691269 -0.38222
#>
#> Objective Function Value: -1396.398
#> Parameter Estimates: 0.9522285 -0.2578805 1.097262 -1.263912 -0.4483934
#>
#> Objective Function Value: -1396.396
#> Parameter Estimates: 0.9522637 -0.2578805 1.097262 -1.263912 -0.4483934
#>
#> Objective Function Value: -1396.397
#> Parameter Estimates: 0.9522285 -0.2578453 1.097262 -1.263912 -0.4483934
#>
#> Objective Function Value: -1396.397
#> Parameter Estimates: 0.9522285 -0.2578805 1.097227 -1.263912 -0.4483934
#>
#> Objective Function Value: -1396.402
#> Parameter Estimates: 0.9522285 -0.2578805 1.097262 -1.263877 -0.4483934
#>
#> Objective Function Value: -1396.397
#> Parameter Estimates: 0.9522285 -0.2578805 1.097262 -1.263912 -0.4484287
#>
#> Objective Function Value: -1377.816
#> Parameter Estimates: 1.150277 -0.1235652 0.9740887 -1.589474 -0.5648356
#>
#> Objective Function Value: -1377.816
#> Parameter Estimates: 1.150273 -0.1235652 0.9740887 -1.589474 -0.5648356
#>
#> Objective Function Value: -1377.817
#> Parameter Estimates: 1.150277 -0.1235664 0.9740887 -1.589474 -0.5648356
#>
#> Objective Function Value: -1377.816
#> Parameter Estimates: 1.150277 -0.1235652 0.9740914 -1.589474 -0.5648356
#>
#> Objective Function Value: -1377.816
#> Parameter Estimates: 1.150277 -0.1235652 0.9740887 -1.589473 -0.5648356
#>
#> Objective Function Value: -1377.816
#> Parameter Estimates: 1.150277 -0.1235652 0.9740887 -1.589474 -0.5648311
#>
#> Objective Function Value: -1393.589
#> Parameter Estimates: 1.092873 0.2660124 1.148241 -1.569046 -0.4862696
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118516 0.007471271 1.017016 -1.479727 -0.5389681
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118519 0.007471271 1.017016 -1.479727 -0.5389681
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118516 0.007468453 1.017016 -1.479727 -0.5389681
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118516 0.007471271 1.017012 -1.479727 -0.5389681
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118516 0.007471271 1.017016 -1.479729 -0.5389681
#>
#> Objective Function Value: -1370.468
#> Parameter Estimates: 1.118516 0.007471271 1.017016 -1.479727 -0.538973
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085615 0.0576953 1.073831 -1.637861 -0.5090277
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085622 0.0576953 1.073831 -1.637861 -0.5090277
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085615 0.05769653 1.073831 -1.637861 -0.5090277
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085615 0.0576953 1.073825 -1.637861 -0.5090277
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085615 0.0576953 1.073831 -1.63786 -0.5090277
#>
#> Objective Function Value: -1359.095
#> Parameter Estimates: 1.085615 0.0576953 1.073831 -1.637861 -0.5090367
#>
#> Objective Function Value: -1360.175
#> Parameter Estimates: 1.015117 0.2130074 1.045539 -1.68825 -0.4915842
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068019 0.1300522 1.055076 -1.642706 -0.508582
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068014 0.1300522 1.055076 -1.642706 -0.508582
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068019 0.1300505 1.055076 -1.642706 -0.508582
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068019 0.1300522 1.05508 -1.642706 -0.508582
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068019 0.1300522 1.055076 -1.642707 -0.508582
#>
#> Objective Function Value: -1358.102
#> Parameter Estimates: 1.068019 0.1300522 1.055076 -1.642706 -0.5085764
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027971 0.1253015 1.006321 -1.686489 -0.5088187
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027964 0.1253015 1.006321 -1.686489 -0.5088187
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027971 0.1253026 1.006321 -1.686489 -0.5088187
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027971 0.1253015 1.006328 -1.686489 -0.5088187
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027971 0.1253015 1.006321 -1.686488 -0.5088187
#>
#> Objective Function Value: -1356.626
#> Parameter Estimates: 1.027971 0.1253015 1.006321 -1.686489 -0.5088091
#>
#> Objective Function Value: -1356.135
#> Parameter Estimates: 0.977486 0.155564 0.9568522 -1.685198 -0.5061335
#>
#> Objective Function Value: -1356.136
#> Parameter Estimates: 0.9774794 0.155564 0.9568522 -1.685198 -0.5061335
#>
#> Objective Function Value: -1356.135
#> Parameter Estimates: 0.977486 0.1555628 0.9568522 -1.685198 -0.5061335
#>
#> Objective Function Value: -1356.136
#> Parameter Estimates: 0.977486 0.155564 0.9568569 -1.685198 -0.5061335
#>
#> Objective Function Value: -1356.135
#> Parameter Estimates: 0.977486 0.155564 0.9568522 -1.685199 -0.5061335
#>
#> Objective Function Value: -1356.136
#> Parameter Estimates: 0.977486 0.155564 0.9568522 -1.685198 -0.5061256
#>
#> Objective Function Value: -1356.554
#> Parameter Estimates: 0.9360177 0.1885819 0.9526273 -1.740295 -0.4985723
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736088 0.1562216 0.9518937 -1.708769 -0.5075161
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736023 0.1562216 0.9518937 -1.708769 -0.5075161
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736088 0.1562229 0.9518937 -1.708769 -0.5075161
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736088 0.1562216 0.9518997 -1.708769 -0.5075161
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736088 0.1562216 0.9518937 -1.708768 -0.5075161
#>
#> Objective Function Value: -1356.014
#> Parameter Estimates: 0.9736088 0.1562216 0.9518937 -1.708769 -0.5075064
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826586 0.1748042 0.9646734 -1.711391 -0.507946
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826509 0.1748042 0.9646734 -1.711391 -0.507946
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826586 0.1748029 0.9646734 -1.711391 -0.507946
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826586 0.1748042 0.9646782 -1.711391 -0.507946
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826586 0.1748042 0.9646734 -1.711392 -0.507946
#>
#> Objective Function Value: -1355.907
#> Parameter Estimates: 0.9826586 0.1748042 0.9646734 -1.711391 -0.5079377
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997781 0.1724361 0.9504171 -1.710491 -0.5205651
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997777 0.1724361 0.9504171 -1.710491 -0.5205651
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997781 0.1724372 0.9504171 -1.710491 -0.5205651
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997781 0.1724361 0.9504198 -1.710491 -0.5205651
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997781 0.1724361 0.9504171 -1.71049 -0.5205651
#>
#> Objective Function Value: -1355.88
#> Parameter Estimates: 0.997781 0.1724361 0.9504171 -1.710491 -0.5205606
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007121 0.1848649 0.9657667 -1.72045 -0.5159722
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007123 0.1848649 0.9657667 -1.72045 -0.5159722
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007121 0.184863 0.9657667 -1.72045 -0.5159722
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007121 0.1848649 0.965765 -1.72045 -0.5159722
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007121 0.1848649 0.9657667 -1.720453 -0.5159722
#>
#> Objective Function Value: -1355.785
#> Parameter Estimates: 1.007121 0.1848649 0.9657667 -1.72045 -0.5159749
#>
#> Objective Function Value: -1356.04
#> Parameter Estimates: 1.000971 0.2029005 0.9544148 -1.713217 -0.5086709
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.1875923 0.9654358 -1.719619 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007153 0.1875923 0.9654358 -1.719619 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007103 0.1875923 0.9654358 -1.719619 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.18759 0.9654358 -1.719619 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.1875923 0.9654375 -1.719619 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.1875923 0.9654358 -1.719625 -0.5160411
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.1875923 0.9654358 -1.719619 -0.5160379
#>
#> Objective Function Value: -1355.781
#> Parameter Estimates: 1.007128 0.1875923 0.9654358 -1.719619 -0.5160444
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.1880382 0.9644741 -1.722252 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007519 0.1880382 0.9644741 -1.722252 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.18804 0.9644741 -1.722252 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.1880364 0.9644741 -1.722252 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.1880382 0.9644758 -1.722252 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.1880382 0.9644741 -1.722251 -0.5162199
#>
#> Objective Function Value: -1355.777
#> Parameter Estimates: 1.007521 0.1880382 0.9644741 -1.722252 -0.516217
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641427 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007723 0.1907974 0.9641427 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007715 0.1907974 0.9641427 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907962 0.9641427 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641543 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641312 -1.722277 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641427 -1.722278 -0.5155267
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641427 -1.722277 -0.5155234
#>
#> Objective Function Value: -1355.773
#> Parameter Estimates: 1.007719 0.1907974 0.9641427 -1.722277 -0.5155301
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.191497 0.9637515 -1.724439 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009213 0.191497 0.9637515 -1.724439 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.1915002 0.9637515 -1.724439 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.1914937 0.9637515 -1.724439 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.191497 0.9637532 -1.724439 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.191497 0.9637515 -1.724438 -0.5146967
#>
#> Objective Function Value: -1355.77
#> Parameter Estimates: 1.009216 0.191497 0.9637515 -1.724439 -0.5146939
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640442 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011021 0.1932954 0.9640442 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011007 0.1932954 0.9640442 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932941 0.9640442 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640613 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.964027 -1.724564 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640442 -1.724563 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640442 -1.724565 -0.5134024
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640442 -1.724564 -0.5133972
#>
#> Objective Function Value: -1355.769
#> Parameter Estimates: 1.011014 0.1932954 0.9640442 -1.724564 -0.5134077
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638913 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013001 0.1937688 0.9638913 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937746 0.9638913 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.193763 0.9638913 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638924 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638903 -1.725825 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638913 -1.725824 -0.511838
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638913 -1.725825 -0.5118357
#>
#> Objective Function Value: -1355.768
#> Parameter Estimates: 1.013004 0.1937688 0.9638913 -1.725825 -0.5118403
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634138 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014381 0.1948619 0.9634138 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014327 0.1948619 0.9634138 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948607 0.9634138 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634421 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9633855 -1.725947 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634138 -1.725946 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634138 -1.725949 -0.5096059
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634138 -1.725947 -0.5096014
#>
#> Objective Function Value: -1355.767
#> Parameter Estimates: 1.014354 0.1948619 0.9634138 -1.725947 -0.5096105
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625951 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015661 0.195163 0.9625951 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015657 0.195163 0.9625951 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195166 0.9625951 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.19516 0.9625951 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625967 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625935 -1.726725 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625951 -1.726724 -0.5073309
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625951 -1.726725 -0.507326
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.015659 0.195163 0.9625951 -1.726725 -0.5073357
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620929 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017114 0.1958253 0.9620929 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017099 0.1958253 0.9620929 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958241 0.9620929 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9621289 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620568 -1.726784 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620929 -1.72678 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620929 -1.726788 -0.5049957
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620929 -1.726784 -0.5049896
#>
#> Objective Function Value: -1355.766
#> Parameter Estimates: 1.017107 0.1958253 0.9620929 -1.726784 -0.5050017
#>
#> Objective Function Value: -1355.765
#> Parameter Estimates: 1.018516 0.1960552 0.9614033 -1.727313 -0.5026613
#>
#> Objective Function Value: -1355.765
#> Parameter Estimates: 1.019882 0.1961716 0.9607939 -1.72732 -0.5001778
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.02582 0.1966961 0.9581344 -1.727439 -0.4894186
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039966 0.1981098 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039961 0.1981098 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981124 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981072 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517114 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517058 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517086 -1.728502 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517086 -1.728503 -0.4641322
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517086 -1.728502 -0.4641142
#>
#> Objective Function Value: -1355.764
#> Parameter Estimates: 1.039964 0.1981098 0.9517086 -1.728502 -0.4641502
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338722 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051708 0.200574 0.9338722 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.2005752 0.9338722 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.2005728 0.9338722 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.933883 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338614 -1.730529 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338722 -1.730528 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338722 -1.730531 -0.4212127
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338722 -1.730529 -0.421211
#>
#> Objective Function Value: -1355.763
#> Parameter Estimates: 1.051705 0.200574 0.9338722 -1.730529 -0.4212144
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313216 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054885 0.1987621 0.9313216 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987628 0.9313216 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987614 0.9313216 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313236 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313197 -1.729026 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313216 -1.729024 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313216 -1.729028 -0.4139277
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313216 -1.729026 -0.4139257
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054887 0.1987621 0.9313216 -1.729026 -0.4139298
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317154 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054853 0.1986281 0.9317154 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054844 0.1986281 0.9317154 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986334 0.9317154 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986227 0.9317154 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.931718 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317127 -1.729022 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317154 -1.729018 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317154 -1.729026 -0.4140373
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317154 -1.729022 -0.4140327
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.054848 0.1986281 0.9317154 -1.729022 -0.4140418
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313533 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055104 0.1986509 0.9313533 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055049 0.1986509 0.9313533 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986697 0.9313533 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986321 0.9313533 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313658 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313409 -1.729031 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313533 -1.729012 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313533 -1.72905 -0.4132706
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313533 -1.729031 -0.4132453
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055076 0.1986509 0.9313533 -1.729031 -0.4132959
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055122 0.1986496 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055024 0.1986496 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.198674 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986252 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313903 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313172 -1.72903 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.729009 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.729051 -0.4132735
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.72903 -0.4132134
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.72903 -0.4133335
#>
#> Objective Function Value: -1355.762
#> Parameter Estimates: 1.055073 0.1986496 0.9313537 -1.72903 -0.4132735
#>
#> Objective Function Value: -852.99
#> Parameter Estimates: 1.744351 0.3284269 0.5633309 -1.045807 -0.4132735
#>
#> Title:
#> Generalized Hyperbolic Parameter Estimation
#>
#> Call:
#> ghFit(x = s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
#>
#> Model:
#> Generalized Hyperbolic Distribution
#>
#> Estimated Parameter(s):
#> alpha beta delta mu lambda
#> 1.7443507 0.3284269 0.5633309 -1.0458067 -0.4132735
#>