BiCopPDF: Density of a bivariate copula

In CDVine: Statistical Inference of C- And D-Vine Copulas

Description

This function evaluates the probability density function (PDF) of a given parametric bivariate copula.

Usage

BiCopPDF(u1, u2, family, par, par2=0)

Arguments

u1,u2	Numeric vectors of equal length with values in [0,1].
family	An integer defining the bivariate copula family: 0 = independence copula 1 = Gaussian copula 2 = Student t copula (t-copula) 3 = Clayton copula 4 = Gumbel copula 5 = Frank copula 6 = Joe copula 7 = BB1 copula 8 = BB6 copula 9 = BB7 copula 10 = BB8 copula 13 = rotated Clayton copula (180 degrees; “survival Clayton”) 14 = rotated Gumbel copula (180 degrees; “survival Gumbel”) 16 = rotated Joe copula (180 degrees; “survival Joe”) 17 = rotated BB1 copula (180 degrees; “survival BB1”) 18 = rotated BB6 copula (180 degrees; “survival BB6”) 19 = rotated BB7 copula (180 degrees; “survival BB7”) 20 = rotated BB8 copula (180 degrees; “survival BB8”) 23 = rotated Clayton copula (90 degrees) 24 = rotated Gumbel copula (90 degrees) 26 = rotated Joe copula (90 degrees) 27 = rotated BB1 copula (90 degrees) 28 = rotated BB6 copula (90 degrees) 29 = rotated BB7 copula (90 degrees) 30 = rotated BB8 copula (90 degrees) 33 = rotated Clayton copula (270 degrees) 34 = rotated Gumbel copula (270 degrees) 36 = rotated Joe copula (270 degrees) 37 = rotated BB1 copula (270 degrees) 38 = rotated BB6 copula (270 degrees) 39 = rotated BB7 copula (270 degrees) 40 = rotated BB8 copula (270 degrees)
par	Copula parameter.
par2	Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8; default: par2 = 0).

Value

A numeric vector of the bivariate copula density evaluated at u1 and u2.

Author(s)

Eike Brechmann

See Also

BiCopCDF, BiCopHfunc, BiCopSim

Examples

# simulate from a bivariate t-copula
simdata = BiCopSim(300,2,-0.7,par2=4)

# evaluate the density of the bivariate t-copula
u1 = simdata[,1]
u2 = simdata[,2]
BiCopPDF(u1,u2,2,-0.7,par2=4)

Example output

The CDVine package is no longer developed actively.
Please consider using the more general VineCopula package
(see https://CRAN.R-project.org/package=VineCopula),
which extends and improves the functionality of CDVine.

  [1]  1.4709124  1.5085608  1.8837902  1.0463854  1.7558926  3.8344803
  [7]  2.4419117  0.3896044  0.5604050  0.9719919  1.4506954  1.5103550
 [13]  0.3406783  1.4374909 13.5717793  1.6300637  1.2140922  1.5451539
 [19]  1.5752399  2.2237762  2.8359801  1.8702994  2.5146284  0.9839572
 [25]  1.3863049  4.1309287  0.2671751  0.6206050  1.6264211  0.5229017
 [31]  2.6712406  1.6452058  4.6924589  1.5581232  4.1164123  0.3671735
 [37]  1.2871762  0.1204903  1.4081825  1.4227593  1.1469583  1.5930492
 [43]  1.7426889  1.4215272  1.8604183  0.4066204  1.5440049  1.4231771
 [49]  1.5894553  1.7426647  1.5208052  1.2293177  2.0773622  1.4731995
 [55]  2.2100131 17.2992092  2.0891311  0.4515155  2.1641338  0.8317684
 [61]  1.4230029  1.5791654  1.2722353  1.5623883  4.7336114  1.4389207
 [67]  2.4905775  1.0351205  1.5034656  1.6886199  1.1362747  1.3684102
 [73]  2.1315207  1.2893673  1.6294272  1.9799385  6.0306449  0.1197091
 [79]  3.5221450  1.4261904  1.4862563  1.1794198  0.3046086  1.5410233
 [85]  1.3227771  1.5220675  1.2764753  1.6842614  1.4170036  0.8913249
 [91]  2.7383111  1.4316401  4.5655875  1.5048212  2.1577987  2.6583867
 [97]  0.4883694  1.5189092  2.3025814 28.4416419  1.6116693  1.4874618
[103]  0.5622060  0.4696036  1.2527005  1.5796025  1.4383528  1.5045836
[109]  1.9630878  1.0631738  1.5117042  1.9435901  3.0441589  1.7605307
[115]  1.9403535  1.1146984  0.9217708  3.0300583  1.5988050  0.6730584
[121]  2.6911661  1.6417174  0.5175607  3.1704480  0.2384279  0.8801140
[127]  6.4152278  0.5172050  1.5253045  1.9817045  3.6017361  1.7048178
[133]  1.5314116  2.4660085  0.7499226  0.4333003  1.5163776  0.5321356
[139]  1.0704583  1.5345893  3.2287042  1.7304641  1.4286259  0.7518983
[145]  3.0366796  3.6017346  1.5880366  1.5944696  0.8269082  1.3632551
[151]  3.4439393  2.8963401 18.7102725  2.2934520  0.9800447  0.9278572
[157]  0.2489857  1.3219537  1.4553836  1.1454339  0.4398461  1.6149878
[163]  0.6009133  3.0969676 13.0720667  1.0609013  8.9021148  1.6357917
[169]  1.8307321  2.3940175  1.3892699  1.4937797  1.7489073  2.2731584
[175]  2.5252983  2.3798698  0.2439749  0.8920789  2.3747117  0.7057036
[181]  1.6770354  1.9365396  0.7207996  1.5942183  1.4475857  1.4037521
[187]  1.3576963  2.1951146  1.5418938  1.7453585  1.4930767  1.0777691
[193]  0.2157433  1.6347706  2.2588110  2.1656881  1.7549451  1.7286048
[199]  0.5854196  1.6318034  0.7084709  2.1449252  5.0040990  0.4995241
[205]  1.8872720  2.7406339  1.6604068  0.7059240  1.4412815  0.9146326
[211]  0.8489601  0.9720754  0.2156537  0.8672817  1.7910670  2.9417292
[217]  1.4496709  1.5997549  1.1687619  1.8233782  4.4374123  7.7199729
[223]  2.2407342  1.6784298  0.4081043  1.3337031  2.3714458  1.6104937
[229]  5.6999540  1.1089039  0.8579211  1.1048844  1.3098071  0.6067449
[235]  1.5625228  3.7097463  1.4451679  0.3914559  1.7915819  1.4640259
[241]  0.7467532  1.3062666  0.5303318  2.1266302  1.5705520  0.3294149
[247]  1.6282378  0.4716353  0.8465821  0.4391964  0.5259970  3.0229501
[253]  0.7320533  1.5704361  1.5992921  1.2744453  0.6340088  0.2949505
[259]  4.4601707  0.9111354  1.9093475  1.5834355  1.7687534  1.9533051
[265]  0.5431821  1.5870425  0.2103842  1.6050408  1.1551664  1.4121827
[271]  2.1351105  1.5301505  3.9726924  1.4364402  2.0451165  3.4332597
[277]  0.4849848  1.6002920  4.5364836  0.3554352  0.6607665  2.2815468
[283]  0.9268108  0.8820309  1.5655685  1.4760351  1.7724053  5.5785785
[289]  1.0761677  0.8359824  1.2091326  0.4978203  1.7275202  2.0372403
[295]  1.6570893  1.4532276  1.5927532  1.5069844  1.3519555  1.9075302

CDVine documentation built on May 2, 2019, 9:28 a.m.