Fit of a Normal Inverse Gaussian Distribution
dist-nigFit.Rd
Estimates the parameters of a normal inverse Gaussian distribution.
Usage
nigFit(x, alpha = 1, beta = 0, delta = 1, mu = 0,
method = c("mle", "gmm", "mps", "vmps"), scale = TRUE, doplot = TRUE,
span = "auto", trace = TRUE, title = NULL, description = NULL, ...)
Arguments
- alpha, beta, delta, mu
The parameters are
alpha
,beta
,delta
, andmu
:
shape parameteralpha
; skewness parameterbeta
,abs(beta)
is in the range (0, alpha); scale parameterdelta
,delta
must be zero or positive; location parametermu
, by default 0. These is the meaning of the parameters in the first parameterizationpm=1
which is the default parameterization selection. In the second parameterization,pm=2
alpha
andbeta
take the meaning of the shape parameters (usually named)zeta
andrho
. In the third parameterization,pm=3
alpha
andbeta
take the meaning of the shape parameters (usually named)xi
andchi
. In the fourth parameterization,pm=4
alpha
andbeta
take the meaning of the shape parameters (usually named)a.bar
andb.bar
.- description
a character string which allows for a brief description.
- doplot
a logical flag. Should a plot be displayed?
- method
a character string. Either
"mle"
, Maximum Likelihood Estimation, the default,"gmm"
Gemeralized Method of Moments Estimation,"mps"
Maximum Product Spacings Estimation, or"vmps"
Minimum Variance Product Spacings Estimation.- scale
a logical flag, by default
TRUE
. Should the time series be scaled by its standard deviation to achieve a more stable optimization?- 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.- title
a character string which allows for a project title.
- trace
a logical flag. Should the parameter estimation process be traced?
- x
a numeric vector.
- ...
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 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.
Examples
## nigFit -
# Simulate Random Variates:
set.seed(1953)
s = rnig(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0)
## nigFit -
# Fit Parameters:
nigFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
#>
#> Objective Function Value: -1646.542
#> Parameter Estimates: 1 0 1 -0.9230541
#>
#> Objective Function Value: -1646.542
#> Parameter Estimates: 1 0 1 -0.9230541
#>
#> Objective Function Value: -1646.542
#> Parameter Estimates: 1 1.490116e-08 1 -0.9230541
#>
#> Objective Function Value: -1646.542
#> Parameter Estimates: 1 0 1 -0.9230541
#>
#> Objective Function Value: -1646.542
#> Parameter Estimates: 1 0 1 -0.9230541
#>
#> Objective Function Value: -1739.817
#> Parameter Estimates: 0.8878693 -0.590966 1.226999 -1.68899
#>
#> Objective Function Value: -1393.208
#> Parameter Estimates: 0.9484807 -0.2715238 1.104297 -1.274969
#>
#> Objective Function Value: -1393.206
#> Parameter Estimates: 0.9485159 -0.2715238 1.104297 -1.274969
#>
#> Objective Function Value: -1393.206
#> Parameter Estimates: 0.9484807 -0.2714886 1.104297 -1.274969
#>
#> Objective Function Value: -1393.207
#> Parameter Estimates: 0.9484807 -0.2715238 1.104261 -1.274969
#>
#> Objective Function Value: -1393.212
#> Parameter Estimates: 0.9484807 -0.2715238 1.104297 -1.274934
#>
#> Objective Function Value: -1368.376
#> Parameter Estimates: 1.154588 -0.0887069 0.9729932 -1.61842
#>
#> Objective Function Value: -1368.376
#> Parameter Estimates: 1.154584 -0.0887069 0.9729932 -1.61842
#>
#> Objective Function Value: -1368.376
#> Parameter Estimates: 1.154588 -0.08870801 0.9729932 -1.61842
#>
#> Objective Function Value: -1368.376
#> Parameter Estimates: 1.154588 -0.0887069 0.9729958 -1.61842
#>
#> Objective Function Value: -1368.376
#> Parameter Estimates: 1.154588 -0.0887069 0.9729932 -1.618419
#>
#> Objective Function Value: -1404.634
#> Parameter Estimates: 1.062064 0.3250035 1.147836 -1.589885
#>
#> Objective Function Value: -1362.03
#> Parameter Estimates: 1.130711 0.0277694 0.9984241 -1.526042
#>
#> Objective Function Value: -1362.03
#> Parameter Estimates: 1.130714 0.0277694 0.9984241 -1.526042
#>
#> Objective Function Value: -1362.03
#> Parameter Estimates: 1.130711 0.02776652 0.9984241 -1.526042
#>
#> Objective Function Value: -1362.03
#> Parameter Estimates: 1.130711 0.0277694 0.9984199 -1.526042
#>
#> Objective Function Value: -1362.03
#> Parameter Estimates: 1.130711 0.0277694 0.9984241 -1.526044
#>
#> Objective Function Value: -1353.398
#> Parameter Estimates: 1.087529 0.07355573 1.048191 -1.655963
#>
#> Objective Function Value: -1353.398
#> Parameter Estimates: 1.087535 0.07355573 1.048191 -1.655963
#>
#> Objective Function Value: -1353.398
#> Parameter Estimates: 1.087529 0.07355694 1.048191 -1.655963
#>
#> Objective Function Value: -1353.398
#> Parameter Estimates: 1.087529 0.07355573 1.048185 -1.655963
#>
#> Objective Function Value: -1353.398
#> Parameter Estimates: 1.087529 0.07355573 1.048191 -1.655962
#>
#> Objective Function Value: -1353.605
#> Parameter Estimates: 1.018147 0.2015899 1.015051 -1.687778
#>
#> Objective Function Value: -1352.735
#> Parameter Estimates: 1.074745 0.1420491 1.025164 -1.656674
#>
#> Objective Function Value: -1352.735
#> Parameter Estimates: 1.074749 0.1420491 1.025164 -1.656674
#>
#> Objective Function Value: -1352.735
#> Parameter Estimates: 1.074745 0.1420474 1.025164 -1.656674
#>
#> Objective Function Value: -1352.735
#> Parameter Estimates: 1.074745 0.1420491 1.025167 -1.656674
#>
#> Objective Function Value: -1352.735
#> Parameter Estimates: 1.074745 0.1420491 1.025164 -1.656676
#>
#> Objective Function Value: -1350.972
#> Parameter Estimates: 1.033818 0.1360954 0.9857381 -1.702725
#>
#> Objective Function Value: -1350.972
#> Parameter Estimates: 1.033812 0.1360954 0.9857381 -1.702725
#>
#> Objective Function Value: -1350.972
#> Parameter Estimates: 1.033818 0.1360965 0.9857381 -1.702725
#>
#> Objective Function Value: -1350.972
#> Parameter Estimates: 1.033818 0.1360954 0.9857461 -1.702725
#>
#> Objective Function Value: -1350.972
#> Parameter Estimates: 1.033818 0.1360954 0.9857381 -1.702724
#>
#> Objective Function Value: -1350.416
#> Parameter Estimates: 0.9827402 0.1703297 0.9458791 -1.706703
#>
#> Objective Function Value: -1350.415
#> Parameter Estimates: 0.9827471 0.1703297 0.9458791 -1.706703
#>
#> Objective Function Value: -1350.416
#> Parameter Estimates: 0.9827402 0.1703284 0.9458791 -1.706703
#>
#> Objective Function Value: -1350.416
#> Parameter Estimates: 0.9827402 0.1703297 0.9458849 -1.706703
#>
#> Objective Function Value: -1350.415
#> Parameter Estimates: 0.9827402 0.1703297 0.9458791 -1.706704
#>
#> Objective Function Value: -1350.454
#> Parameter Estimates: 0.9391718 0.1628042 0.8910938 -1.727421
#>
#> Objective Function Value: -1350.314
#> Parameter Estimates: 0.9691065 0.1635911 0.9212719 -1.726361
#>
#> Objective Function Value: -1350.314
#> Parameter Estimates: 0.9691017 0.1635911 0.9212719 -1.726361
#>
#> Objective Function Value: -1350.314
#> Parameter Estimates: 0.9691065 0.1635923 0.9212719 -1.726361
#>
#> Objective Function Value: -1350.314
#> Parameter Estimates: 0.9691065 0.1635911 0.9212788 -1.726361
#>
#> Objective Function Value: -1350.314
#> Parameter Estimates: 0.9691065 0.1635911 0.9212719 -1.72636
#>
#> Objective Function Value: -1350.242
#> Parameter Estimates: 0.9680782 0.1858798 0.9460066 -1.737019
#>
#> Objective Function Value: -1350.242
#> Parameter Estimates: 0.9680831 0.1858798 0.9460066 -1.737019
#>
#> Objective Function Value: -1350.242
#> Parameter Estimates: 0.9680782 0.1858786 0.9460066 -1.737019
#>
#> Objective Function Value: -1350.242
#> Parameter Estimates: 0.9680782 0.1858798 0.9460036 -1.737019
#>
#> Objective Function Value: -1350.242
#> Parameter Estimates: 0.9680782 0.1858798 0.9460066 -1.73702
#>
#> Objective Function Value: -1350.078
#> Parameter Estimates: 0.987342 0.1951129 0.9191215 -1.730379
#>
#> Objective Function Value: -1350.078
#> Parameter Estimates: 0.9873395 0.1951129 0.9191215 -1.730379
#>
#> Objective Function Value: -1350.078
#> Parameter Estimates: 0.987342 0.1951112 0.9191215 -1.730379
#>
#> Objective Function Value: -1350.078
#> Parameter Estimates: 0.987342 0.1951129 0.9191232 -1.730379
#>
#> Objective Function Value: -1350.078
#> Parameter Estimates: 0.987342 0.1951129 0.9191215 -1.730381
#>
#> Objective Function Value: -1350.274
#> Parameter Estimates: 1.007734 0.1940269 0.9335209 -1.754851
#>
#> Objective Function Value: -1350.042
#> Parameter Estimates: 0.9857484 0.1927684 0.9226369 -1.739619
#>
#> Objective Function Value: -1350.042
#> Parameter Estimates: 0.9857512 0.1927684 0.9226369 -1.739619
#>
#> Objective Function Value: -1350.042
#> Parameter Estimates: 0.9857484 0.1927707 0.9226369 -1.739619
#>
#> Objective Function Value: -1350.042
#> Parameter Estimates: 0.9857484 0.1927684 0.922635 -1.739619
#>
#> Objective Function Value: -1350.042
#> Parameter Estimates: 0.9857484 0.1927684 0.9226369 -1.739617
#>
#> Objective Function Value: -1350.012
#> Parameter Estimates: 0.9901976 0.1984988 0.9296047 -1.737477
#>
#> Objective Function Value: -1350.012
#> Parameter Estimates: 0.9902049 0.1984988 0.9296047 -1.737477
#>
#> Objective Function Value: -1350.012
#> Parameter Estimates: 0.9901976 0.1984976 0.9296047 -1.737477
#>
#> Objective Function Value: -1350.012
#> Parameter Estimates: 0.9901976 0.1984988 0.9295999 -1.737477
#>
#> Objective Function Value: -1350.012
#> Parameter Estimates: 0.9901976 0.1984988 0.9296047 -1.737478
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999543 0.9334693 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988198 0.1999543 0.9334693 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999549 0.9334693 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999537 0.9334693 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999543 0.9334705 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999543 0.933468 -1.74126
#>
#> Objective Function Value: -1349.999
#> Parameter Estimates: 0.9988236 0.1999543 0.9334693 -1.741259
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002549 0.2080177 0.9315512 -1.746076
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002553 0.2080177 0.9315512 -1.746076
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002549 0.2080165 0.9315512 -1.746076
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002549 0.2080177 0.9315484 -1.746076
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002549 0.2080177 0.9315512 -1.746075
#>
#> Objective Function Value: -1349.985
#> Parameter Estimates: 1.002549 0.2080177 0.9315512 -1.746076
#>
#> Objective Function Value: -1349.993
#> Parameter Estimates: 0.9989379 0.2113539 0.939144 -1.750969
#>
#> Objective Function Value: -1349.981
#> Parameter Estimates: 1.001175 0.2092873 0.9344407 -1.747938
#>
#> Objective Function Value: -1349.981
#> Parameter Estimates: 1.001178 0.2092873 0.9344407 -1.747938
#>
#> Objective Function Value: -1349.981
#> Parameter Estimates: 1.001175 0.2092861 0.9344407 -1.747938
#>
#> Objective Function Value: -1349.981
#> Parameter Estimates: 1.001175 0.2092873 0.9344383 -1.747938
#>
#> Objective Function Value: -1349.981
#> Parameter Estimates: 1.001175 0.2092873 0.9344407 -1.747937
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116973 0.9336798 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.003798 0.2116973 0.9336798 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.211698 0.9336798 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116967 0.9336798 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116973 0.933682 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116973 0.9336777 -1.749367
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116973 0.9336798 -1.749366
#>
#> Objective Function Value: -1349.979
#> Parameter Estimates: 1.0038 0.2116973 0.9336798 -1.749368
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124718 0.9365982 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006241 0.2124718 0.9365982 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006229 0.2124718 0.9365982 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124734 0.9365982 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124702 0.9365982 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124718 0.9365965 -1.749888
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124718 0.9365982 -1.749886
#>
#> Objective Function Value: -1349.978
#> Parameter Estimates: 1.006235 0.2124718 0.9365982 -1.749889
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131193 0.9380693 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009799 0.2131193 0.9380693 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131209 0.9380693 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131177 0.9380693 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131193 0.9380724 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131193 0.9380662 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131193 0.9380693 -1.750002
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.009802 0.2131193 0.9380693 -1.750003
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150106 0.9395315 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.012087 0.2150106 0.9395315 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.012074 0.2150106 0.9395315 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150117 0.9395315 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150096 0.9395315 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150106 0.9395341 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150106 0.9395289 -1.752103
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.01208 0.2150106 0.9395315 -1.752102
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145723 0.9391637 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011498 0.2145723 0.9391637 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011429 0.2145723 0.9391637 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145753 0.9391637 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145694 0.9391637 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145723 0.9391771 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145723 0.9391504 -1.751617
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145723 0.9391637 -1.751616
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011464 0.2145723 0.9391637 -1.751619
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391594 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011505 0.2145678 0.9391594 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011408 0.2145678 0.9391594 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145922 0.9391594 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145434 0.9391594 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391935 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391253 -1.751614
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391594 -1.751594
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391594 -1.751634
#>
#> Objective Function Value: -1349.977
#> Parameter Estimates: 1.011456 0.2145678 0.9391594 -1.751614
#>
#> Objective Function Value: -833.1119
#> Parameter Estimates: 1.695972 0.3597793 0.5601027 -1.04464
#> Warning: NaNs produced
#>
#> Title:
#> Normal Inverse Gaussian Parameter Estimation
#>
#> Call:
#> .nigFit.mle(x = x, alpha = alpha, beta = beta, delta = delta,
#> mu = mu, scale = scale, doplot = doplot, span = span, trace = trace,
#> title = title, description = description)
#>
#> Model:
#> Normal Inverse Gaussian Distribution
#>
#> Estimated Parameter(s):
#> alpha beta delta mu
#> 1.6959724 0.3597793 0.5601027 -1.0446402
#>