GH Distribution Fit
dist-gldFit.Rd
Estimates the distrinbutional parameters for a generalized lambda distribution.
Usage
gldFit(x, lambda1 = 0, lambda2 = -1, lambda3 = -1/8, lambda4 = -1/8,
method = c("mle", "mps", "gof", "hist", "rob"),
scale = NA, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
Arguments
- x
a numeric vector.
- lambda1, lambda2, lambda3, lambda4
are numeric values where
lambda1
is the location parameter,lambda2
is the location parameter,lambda3
is the first shape parameter, andlambda4
is the second shape parameter.- method
a character string, the estimation approach to fit the distributional parameters, see details.
- scale
not used.
- doplot
a logical flag. Should a plot be displayed?
- add
a logical flag. Should a new fit added to an existing plot?
- 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 rigldt 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 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 function nlminb
is used to minimize the objective
function. The following approaches have been implemented:
"mle"
, maximimum log likelihoo estimation.
"mps"
, maximum product spacing estimation.
"gof"
, goodness of fit approaches,
type="ad"
Anderson-Darling,
type="cvm"
Cramer-vonMise,
type="ks"
Kolmogorov-Smirnov.
"hist"
, histogram binning approaches,
"fd"
Freedman-Diaconis binning,
"scott"
, Scott histogram binning,
"sturges"
, Sturges histogram binning.
"rob"
, robust moment matching.
Examples
## gldFit -
# Simulate Random Variates:
set.seed(1953)
s = rgld(n = 1000, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8)
## gldFit -
# Fit Parameters:
gldFit(s, lambda1=0, lambda2=-1, lambda3=-1/8, lambda4=-1/8,
doplot = TRUE, trace = TRUE)
#>
#> Objective Function Value: 81.30868
#> Parameter Estimates: 0 -1 -0.125 -0.125
#>
#> Objective Function Value: 81.30868
#> Parameter Estimates: 1.490116e-08 -1 -0.125 -0.125
#>
#> Objective Function Value: 81.30868
#> Parameter Estimates: 0 -1 -0.125 -0.125
#>
#> Objective Function Value: 81.30868
#> Parameter Estimates: 0 -1 -0.125 -0.125
#>
#> Objective Function Value: 81.30868
#> Parameter Estimates: 0 -1 -0.125 -0.125
#>
#> Objective Function Value: Inf
#> Parameter Estimates: -0.8312542 -1.30886 -0.3002453 -1e-10
#>
#> Objective Function Value: Inf
#> Parameter Estimates: -0.02159336 -1.008023 -0.1295523 -0.03681965
#>
#> Objective Function Value: 80.48536
#> Parameter Estimates: -0.002159336 -1.000802 -0.1254552 -0.116182
#>
#> Objective Function Value: 80.48451
#> Parameter Estimates: -0.002150881 -1.000802 -0.1254552 -0.116182
#>
#> Objective Function Value: 80.48523
#> Parameter Estimates: -0.002159336 -1.000794 -0.1254552 -0.116182
#>
#> Objective Function Value: 80.48536
#> Parameter Estimates: -0.002159336 -1.000802 -0.1254468 -0.116182
#>
#> Objective Function Value: 80.48415
#> Parameter Estimates: -0.002159336 -1.000802 -0.1254552 -0.1161904
#>
#> Objective Function Value: 80.21165
#> Parameter Estimates: 0.006917198 -1.000468 -0.1263326 -0.1162602
#>
#> Objective Function Value: 80.21164
#> Parameter Estimates: 0.006917098 -1.000468 -0.1263326 -0.1162602
#>
#> Objective Function Value: 80.21165
#> Parameter Estimates: 0.006917198 -1.000468 -0.1263326 -0.1162602
#>
#> Objective Function Value: 80.21156
#> Parameter Estimates: 0.006917198 -1.000468 -0.1263336 -0.1162602
#>
#> Objective Function Value: 80.21165
#> Parameter Estimates: 0.006917198 -1.000468 -0.1263326 -0.1162601
#>
#> Objective Function Value: 81.26985
#> Parameter Estimates: 0.006657618 -0.9992349 -0.1353697 -0.1163868
#>
#> Objective Function Value: 80.11669
#> Parameter Estimates: 0.005929076 -1.000284 -0.1279977 -0.1160494
#>
#> Objective Function Value: 80.11669
#> Parameter Estimates: 0.005929139 -1.000284 -0.1279977 -0.1160494
#>
#> Objective Function Value: 80.11669
#> Parameter Estimates: 0.005929076 -1.000285 -0.1279977 -0.1160494
#>
#> Objective Function Value: 80.11669
#> Parameter Estimates: 0.005929076 -1.000284 -0.1279976 -0.1160494
#>
#> Objective Function Value: 80.11669
#> Parameter Estimates: 0.005929076 -1.000284 -0.1279977 -0.1160494
#>
#> Objective Function Value: 80.13324
#> Parameter Estimates: 0.004933141 -1.000014 -0.1270394 -0.1174074
#>
#> Objective Function Value: 80.11374
#> Parameter Estimates: 0.005657212 -1.000207 -0.1277241 -0.1164501
#>
#> Objective Function Value: 80.11374
#> Parameter Estimates: 0.005657296 -1.000207 -0.1277241 -0.1164501
#>
#> Objective Function Value: 80.11374
#> Parameter Estimates: 0.005657212 -1.000208 -0.1277241 -0.1164501
#>
#> Objective Function Value: 80.11374
#> Parameter Estimates: 0.005657212 -1.000207 -0.1277241 -0.1164501
#>
#> Objective Function Value: 80.11374
#> Parameter Estimates: 0.005657212 -1.000207 -0.1277241 -0.1164499
#>
#> Objective Function Value: 80.11163
#> Parameter Estimates: 0.005154562 -1.000169 -0.1276739 -0.1162079
#>
#> Objective Function Value: 80.11163
#> Parameter Estimates: 0.005154679 -1.000169 -0.1276739 -0.1162079
#>
#> Objective Function Value: 80.11163
#> Parameter Estimates: 0.005154562 -1.00017 -0.1276739 -0.1162079
#>
#> Objective Function Value: 80.11163
#> Parameter Estimates: 0.005154562 -1.000169 -0.1276738 -0.1162079
#>
#> Objective Function Value: 80.11163
#> Parameter Estimates: 0.005154562 -1.000169 -0.1276739 -0.116208
#>
#> Objective Function Value: 80.10954
#> Parameter Estimates: 0.004921368 -1.000035 -0.1273897 -0.1166105
#>
#> Objective Function Value: 80.10954
#> Parameter Estimates: 0.004921296 -1.000035 -0.1273897 -0.1166105
#>
#> Objective Function Value: 80.10954
#> Parameter Estimates: 0.004921368 -1.000036 -0.1273897 -0.1166105
#>
#> Objective Function Value: 80.10954
#> Parameter Estimates: 0.004921368 -1.000035 -0.1273899 -0.1166105
#>
#> Objective Function Value: 80.10954
#> Parameter Estimates: 0.004921368 -1.000035 -0.1273897 -0.1166104
#>
#> Objective Function Value: 80.10842
#> Parameter Estimates: 0.00462123 -0.9995811 -0.1273967 -0.116472
#>
#> Objective Function Value: 80.10842
#> Parameter Estimates: 0.004621351 -0.9995811 -0.1273967 -0.116472
#>
#> Objective Function Value: 80.10842
#> Parameter Estimates: 0.00462123 -0.9995819 -0.1273967 -0.116472
#>
#> Objective Function Value: 80.10842
#> Parameter Estimates: 0.00462123 -0.9995811 -0.1273966 -0.116472
#>
#> Objective Function Value: 80.10842
#> Parameter Estimates: 0.00462123 -0.9995811 -0.1273967 -0.1164721
#>
#> Objective Function Value: 80.10755
#> Parameter Estimates: 0.004726668 -0.9990328 -0.1273641 -0.1165213
#>
#> Objective Function Value: 80.10755
#> Parameter Estimates: 0.004726602 -0.9990328 -0.1273641 -0.1165213
#>
#> Objective Function Value: 80.10755
#> Parameter Estimates: 0.004726668 -0.9990348 -0.1273641 -0.1165213
#>
#> Objective Function Value: 80.10755
#> Parameter Estimates: 0.004726668 -0.9990328 -0.1273642 -0.1165213
#>
#> Objective Function Value: 80.10755
#> Parameter Estimates: 0.004726668 -0.9990328 -0.1273641 -0.1165212
#>
#> Objective Function Value: 80.10712
#> Parameter Estimates: 0.004617537 -0.9985454 -0.1271218 -0.1164371
#>
#> Objective Function Value: 80.10712
#> Parameter Estimates: 0.004617618 -0.9985454 -0.1271218 -0.1164371
#>
#> Objective Function Value: 80.10712
#> Parameter Estimates: 0.004617537 -0.9985458 -0.1271218 -0.1164371
#>
#> Objective Function Value: 80.10711
#> Parameter Estimates: 0.004617537 -0.9985454 -0.1271233 -0.1164371
#>
#> Objective Function Value: 80.10712
#> Parameter Estimates: 0.004617537 -0.9985454 -0.1271218 -0.1164372
#>
#> Objective Function Value: 80.10613
#> Parameter Estimates: 0.004624456 -0.9979954 -0.1272207 -0.1163837
#>
#> Objective Function Value: 80.10613
#> Parameter Estimates: 0.004625572 -0.9979954 -0.1272207 -0.1163837
#>
#> Objective Function Value: 80.10613
#> Parameter Estimates: 0.004624456 -0.9979956 -0.1272207 -0.1163837
#>
#> Objective Function Value: 80.10613
#> Parameter Estimates: 0.004624456 -0.9979954 -0.1272207 -0.1163837
#>
#> Objective Function Value: 80.10613
#> Parameter Estimates: 0.004624456 -0.9979954 -0.1272207 -0.1163836
#>
#> Objective Function Value: 80.10545
#> Parameter Estimates: 0.004701004 -0.9974529 -0.1271003 -0.1163594
#>
#> Objective Function Value: 80.10545
#> Parameter Estimates: 0.004700872 -0.9974529 -0.1271003 -0.1163594
#>
#> Objective Function Value: 80.10546
#> Parameter Estimates: 0.004701004 -0.9974532 -0.1271003 -0.1163594
#>
#> Objective Function Value: 80.10545
#> Parameter Estimates: 0.004701004 -0.9974529 -0.1271003 -0.1163594
#>
#> Objective Function Value: 80.10545
#> Parameter Estimates: 0.004701004 -0.9974529 -0.1271003 -0.116359
#>
#> Objective Function Value: 80.10474
#> Parameter Estimates: 0.004719374 -0.9969078 -0.1270951 -0.1162259
#>
#> Objective Function Value: 80.10395
#> Parameter Estimates: 0.004803703 -0.9960943 -0.1270184 -0.1160673
#>
#> Objective Function Value: 80.10301
#> Parameter Estimates: 0.004968606 -0.9945035 -0.1268685 -0.115757
#>
#> Objective Function Value: 80.10301
#> Parameter Estimates: 0.00496868 -0.9945035 -0.1268685 -0.115757
#>
#> Objective Function Value: 80.10301
#> Parameter Estimates: 0.004968606 -0.9945048 -0.1268685 -0.115757
#>
#> Objective Function Value: 80.10301
#> Parameter Estimates: 0.004968606 -0.9945035 -0.1268685 -0.115757
#>
#> Objective Function Value: 80.10301
#> Parameter Estimates: 0.004968606 -0.9945035 -0.1268685 -0.1157571
#>
#> Objective Function Value: 80.09814
#> Parameter Estimates: 0.004876245 -0.9914836 -0.1266369 -0.1156882
#>
#> Objective Function Value: 80.09814
#> Parameter Estimates: 0.004876513 -0.9914836 -0.1266369 -0.1156882
#>
#> Objective Function Value: 80.09814
#> Parameter Estimates: 0.004876245 -0.9914839 -0.1266369 -0.1156882
#>
#> Objective Function Value: 80.09814
#> Parameter Estimates: 0.004876245 -0.9914836 -0.1266366 -0.1156882
#>
#> Objective Function Value: 80.09814
#> Parameter Estimates: 0.004876245 -0.9914836 -0.1266369 -0.1156881
#>
#> Objective Function Value: 80.09462
#> Parameter Estimates: 0.00466128 -0.9885297 -0.1261029 -0.1153269
#>
#> Objective Function Value: 80.09145
#> Parameter Estimates: 0.004476204 -0.9853703 -0.1257366 -0.1149965
#>
#> Objective Function Value: 80.087
#> Parameter Estimates: 0.004078282 -0.9785773 -0.1249491 -0.114286
#>
#> Objective Function Value: 80.087
#> Parameter Estimates: 0.004078692 -0.9785773 -0.1249491 -0.114286
#>
#> Objective Function Value: 80.087
#> Parameter Estimates: 0.004078282 -0.9785776 -0.1249491 -0.114286
#>
#> Objective Function Value: 80.087
#> Parameter Estimates: 0.004078282 -0.9785773 -0.1249492 -0.114286
#>
#> Objective Function Value: 80.087
#> Parameter Estimates: 0.004078282 -0.9785773 -0.1249491 -0.114286
#>
#> Objective Function Value: 80.06895
#> Parameter Estimates: 0.0047637 -0.9656057 -0.1237352 -0.1129383
#>
#> Objective Function Value: 80.06101
#> Parameter Estimates: 0.005286883 -0.9511446 -0.1224159 -0.1110312
#>
#> Objective Function Value: 80.06101
#> Parameter Estimates: 0.005286811 -0.9511446 -0.1224159 -0.1110312
#>
#> Objective Function Value: 80.06101
#> Parameter Estimates: 0.005286883 -0.951145 -0.1224159 -0.1110312
#>
#> Objective Function Value: 80.06101
#> Parameter Estimates: 0.005286883 -0.9511446 -0.1224162 -0.1110312
#>
#> Objective Function Value: 80.06101
#> Parameter Estimates: 0.005286883 -0.9511446 -0.1224159 -0.1110311
#>
#> Objective Function Value: 81.15985
#> Parameter Estimates: 0.005911393 -0.896392 -0.1131535 -0.1112879
#>
#> Objective Function Value: 80.81863
#> Parameter Estimates: 0.006389145 -0.95053 -0.1213521 -0.1163337
#>
#> Objective Function Value: 80.05601
#> Parameter Estimates: 0.00539711 -0.9510831 -0.1223096 -0.1115614
#>
#> Objective Function Value: 80.05601
#> Parameter Estimates: 0.005396959 -0.9510831 -0.1223096 -0.1115614
#>
#> Objective Function Value: 80.05601
#> Parameter Estimates: 0.00539711 -0.9510842 -0.1223096 -0.1115614
#>
#> Objective Function Value: 80.05601
#> Parameter Estimates: 0.00539711 -0.9510831 -0.1223098 -0.1115614
#>
#> Objective Function Value: 80.05601
#> Parameter Estimates: 0.00539711 -0.9510831 -0.1223096 -0.1115613
#>
#> Objective Function Value: 80.05456
#> Parameter Estimates: 0.005253695 -0.9505863 -0.1222276 -0.1113763
#>
#> Objective Function Value: 80.05456
#> Parameter Estimates: 0.005253775 -0.9505863 -0.1222276 -0.1113763
#>
#> Objective Function Value: 80.05456
#> Parameter Estimates: 0.005253695 -0.9505867 -0.1222276 -0.1113763
#>
#> Objective Function Value: 80.05456
#> Parameter Estimates: 0.005253695 -0.9505863 -0.1222278 -0.1113763
#>
#> Objective Function Value: 80.05456
#> Parameter Estimates: 0.005253695 -0.9505863 -0.1222276 -0.1113763
#>
#> Objective Function Value: 80.05374
#> Parameter Estimates: 0.005063493 -0.9501045 -0.1221171 -0.1115433
#>
#> Objective Function Value: 80.05374
#> Parameter Estimates: 0.005063572 -0.9501045 -0.1221171 -0.1115433
#>
#> Objective Function Value: 80.05374
#> Parameter Estimates: 0.005063493 -0.9501049 -0.1221171 -0.1115433
#>
#> Objective Function Value: 80.05374
#> Parameter Estimates: 0.005063493 -0.9501045 -0.1221173 -0.1115433
#>
#> Objective Function Value: 80.05374
#> Parameter Estimates: 0.005063493 -0.9501045 -0.1221171 -0.1115432
#>
#> Objective Function Value: 80.05282
#> Parameter Estimates: 0.004984107 -0.9495914 -0.1220121 -0.1113767
#>
#> Objective Function Value: 80.05282
#> Parameter Estimates: 0.004984201 -0.9495914 -0.1220121 -0.1113767
#>
#> Objective Function Value: 80.05282
#> Parameter Estimates: 0.004984107 -0.9495917 -0.1220121 -0.1113767
#>
#> Objective Function Value: 80.05282
#> Parameter Estimates: 0.004984107 -0.9495914 -0.1220123 -0.1113767
#>
#> Objective Function Value: 80.05282
#> Parameter Estimates: 0.004984107 -0.9495914 -0.1220121 -0.1113767
#>
#> Objective Function Value: 80.05224
#> Parameter Estimates: 0.004945148 -0.9490417 -0.1219463 -0.1113984
#>
#> Objective Function Value: 80.05134
#> Parameter Estimates: 0.004940851 -0.9480131 -0.1217983 -0.1113058
#>
#> Objective Function Value: 80.04808
#> Parameter Estimates: 0.004921138 -0.9432946 -0.1211195 -0.110881
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883668 -0.9343255 -0.1198291 -0.1100734
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883754 -0.9343255 -0.1198291 -0.1100734
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883668 -0.9343258 -0.1198291 -0.1100734
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883668 -0.9343255 -0.1198291 -0.1100734
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883668 -0.9343255 -0.1198292 -0.1100734
#>
#> Objective Function Value: 80.04593
#> Parameter Estimates: 0.004883668 -0.9343255 -0.1198291 -0.1100733
#>
#> Objective Function Value: 80.02964
#> Parameter Estimates: 0.004519392 -0.9189811 -0.1185823 -0.1085293
#>
#> Objective Function Value: 80.02964
#> Parameter Estimates: 0.00451946 -0.9189811 -0.1185823 -0.1085293
#>
#> Objective Function Value: 80.02964
#> Parameter Estimates: 0.004519392 -0.9189815 -0.1185823 -0.1085293
#>
#> Objective Function Value: 80.02964
#> Parameter Estimates: 0.004519392 -0.9189811 -0.1185823 -0.1085293
#>
#> Objective Function Value: 80.02964
#> Parameter Estimates: 0.004519392 -0.9189811 -0.1185823 -0.1085294
#>
#> Objective Function Value: 80.02133
#> Parameter Estimates: 0.004476024 -0.9036811 -0.1167822 -0.1070503
#>
#> Objective Function Value: 80.01816
#> Parameter Estimates: 0.004326312 -0.8731304 -0.113351 -0.1042778
#>
#> Objective Function Value: 80.01816
#> Parameter Estimates: 0.004326243 -0.8731304 -0.113351 -0.1042778
#>
#> Objective Function Value: 80.01816
#> Parameter Estimates: 0.004326312 -0.8731302 -0.113351 -0.1042778
#>
#> Objective Function Value: 80.01816
#> Parameter Estimates: 0.004326312 -0.8731304 -0.1133511 -0.1042778
#>
#> Objective Function Value: 80.01816
#> Parameter Estimates: 0.004326312 -0.8731304 -0.113351 -0.1042779
#>
#> Objective Function Value: 80.00676
#> Parameter Estimates: 0.005166929 -0.8522508 -0.1113376 -0.1012214
#>
#> Objective Function Value: 80.00676
#> Parameter Estimates: 0.005166996 -0.8522508 -0.1113376 -0.1012214
#>
#> Objective Function Value: 80.00676
#> Parameter Estimates: 0.005166929 -0.8522506 -0.1113376 -0.1012214
#>
#> Objective Function Value: 80.00676
#> Parameter Estimates: 0.005166929 -0.8522508 -0.1113376 -0.1012214
#>
#> Objective Function Value: 80.00676
#> Parameter Estimates: 0.005166929 -0.8522508 -0.1113376 -0.1012214
#>
#> Objective Function Value: 80.00555
#> Parameter Estimates: 0.005063101 -0.8463574 -0.110531 -0.10076
#>
#> Objective Function Value: 80.00555
#> Parameter Estimates: 0.005063036 -0.8463574 -0.110531 -0.10076
#>
#> Objective Function Value: 80.00555
#> Parameter Estimates: 0.005063101 -0.8463576 -0.110531 -0.10076
#>
#> Objective Function Value: 80.00555
#> Parameter Estimates: 0.005063101 -0.8463574 -0.1105311 -0.10076
#>
#> Objective Function Value: 80.00555
#> Parameter Estimates: 0.005063101 -0.8463574 -0.110531 -0.10076
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484594 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.004956252 -0.8484594 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.004955768 -0.8484594 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484592 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484595 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484594 -0.1107138 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484594 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.00495601 -0.8484594 -0.1107139 -0.1010462
#>
#> Objective Function Value: 80.00552
#> Parameter Estimates: 0.004983147 -0.8462698 -0.1104878 -0.1008017
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969639 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969336 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473716 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473722 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.00551
#> Parameter Estimates: 0.004969487 -0.8473719 -0.1106016 -0.1009248
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.84803 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005029562 -0.84803 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005027579 -0.84803 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.8480296 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.8480305 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.84803 -0.1107077 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.84803 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.84803 -0.1107078 -0.1009632
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005028571 -0.84803 -0.1107078 -0.1009633
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486041 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005022464 -0.8486041 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005020461 -0.8486041 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486039 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486044 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486041 -0.1107661 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486041 -0.1107662 -0.1010236
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486041 -0.1107662 -0.1010235
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005021463 -0.8486041 -0.1107662 -0.1010237
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485423 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002954 -0.8485423 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005001177 -0.8485423 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485413 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485432 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485423 -0.1107499 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485423 -0.1107501 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485423 -0.11075 -0.1010286
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002066 -0.8485423 -0.11075 -0.1010287
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484966 -0.1107454 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.00500527 -0.8484966 -0.1107454 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002841 -0.8484966 -0.1107454 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484934 -0.1107454 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484998 -0.1107454 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484966 -0.1107448 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484966 -0.1107461 -0.1010223
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484966 -0.1107454 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005004056 -0.8484966 -0.1107454 -0.1010226
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484909 -0.1107449 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005005174 -0.8484909 -0.1107449 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002371 -0.8484909 -0.1107449 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484878 -0.1107449 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.848494 -0.1107449 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484909 -0.1107443 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484909 -0.1107455 -0.1010221
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484909 -0.1107449 -0.1010216
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003772 -0.8484909 -0.1107449 -0.1010225
#>
#> Objective Function Value: 80.00561
#> Parameter Estimates: 0.004953363 -0.8473986 -0.110639 -0.1009652
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.004998735 -0.8483816 -0.1107343 -0.1010164
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484792 -0.1107438 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.00500391 -0.8484792 -0.1107438 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002563 -0.8484792 -0.1107438 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484774 -0.1107438 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.848481 -0.1107438 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484792 -0.1107433 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484792 -0.1107442 -0.1010214
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484792 -0.1107438 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003236 -0.8484792 -0.1107438 -0.1010215
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002967 -0.8484733 -0.1107432 -0.1010211
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484765 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003379 -0.8484765 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002844 -0.8484765 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484759 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.848477 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484765 -0.1107433 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484765 -0.1107436 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484765 -0.1107435 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003111 -0.8484765 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005002861 -0.848471 -0.110743 -0.101021
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003043 -0.848475 -0.1107433 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003082 -0.8484758 -0.1107434 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003195 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003001 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484759 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484764 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107434 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003071 -0.8484756 -0.1107434 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003089 -0.848476 -0.1107434 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003096 -0.8484761 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003131 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003065 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484761 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107434 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010212
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Objective Function Value: 80.0055
#> Parameter Estimates: 0.005003098 -0.8484762 -0.1107435 -0.1010213
#>
#> Title:
#> GLD Region 4 Parameter Estimation
#>
#> Call:
#> .gldFit.mle(x = x, lambda1 = lambda1, lambda2 = lambda2, lambda3 = lambda3,
#> lambda4 = lambda4, scale = scale, doplot = doplot, add = add,
#> span = span, trace = trace, title = title, description = description)
#>
#> Model:
#> GLD Region 4 Distribution
#>
#> Estimated Parameter(s):
#> lambda1 lambda2 lambda3 lambda4
#> 0.005003098 -0.848476173 -0.110743460 -0.101021255
#>