# vinePIT-methods: Vine Probability Integral Transform Methods In vines: Multivariate Dependence Modeling with Vines

## Description

Probability integral transform (PIT) of (Rosenblatt, 1952) for vine models. The PIT converts a set of dependent variables into a new set of variables which are independent and uniformly distributed in (0,1) under the hypothesis that the data follows a given multivariate distribution.

## Usage

 `1` ```vinePIT(vine, u) ```

## Arguments

 `vine` A `Vine` object. `u` Vector with one component for each variable of the vine or a matrix with one column for each variable of the vine.

## Value

A matrix with one column for each variable of the vine and one row for each observation.

## Methods

`signature(vine = "CVine")`

PIT algorithm for `CVine` objects based on the Algorithm 5 of (Aas et al., 2009).

`signature(vine = "DVine")`

PIT algorithm for `DVine` objects based on the Algorithm 6 of (Aas et al., 2009).

## References

Aas, K. and Czado, C. and Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44, 182–198.

Rosenblatt, M. (1952) Remarks on multivariate transformation. Annals of Mathematical Statistics 23, 1052–1057.

`vinePIT`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```dimension <- 3 copulas <- matrix(list(normalCopula(0.5), claytonCopula(2.75), NULL, NULL), ncol = dimension - 1, nrow = dimension - 1, byrow = TRUE) vine <- CVine(dimension = dimension, trees = 1, copulas = copulas) data <- matrix(runif(dimension * 100), ncol = dimension, nrow = 100) vinePIT(vine, data) ```

### Example output

```Loading required package: copula
[,1]         [,2]         [,3]
[1,] 0.018438263 0.8923089099 0.9997874722
[2,] 0.509698909 0.3224246949 0.9180647457
[3,] 0.267071351 0.4355738864 0.2866992744
[4,] 0.951228976 0.0064479451 0.0182912232
[5,] 0.895143813 0.2922753407 0.5915777115
[6,] 0.884646370 0.0251004403 0.7031727196
[7,] 0.831243980 0.1624073919 0.8709698257
[8,] 0.768559664 0.2380959697 0.0222356881
[9,] 0.383599752 0.9921817386 0.5466416380
[10,] 0.986779061 0.0512131524 0.2034994737
[11,] 0.819554011 0.1999538157 0.0002223636
[12,] 0.012137194 0.9973134896 0.9998302723
[13,] 0.294553801 0.4732115486 0.2393901320
[14,] 0.225737043 0.8607909836 0.9834074934
[15,] 0.387859431 0.1064453976 0.0114826569
[16,] 0.180215531 0.1637512977 0.0204613851
[17,] 0.985164629 0.1479907920 0.0822963418
[18,] 0.814403180 0.2903481947 0.2813934464
[19,] 0.584821066 0.0069542913 0.0001220703
[20,] 0.039416073 0.4747071717 0.9961612377
[21,] 0.489620967 0.7992452963 0.8781832761
[22,] 0.896729457 0.1675479329 0.6241387175
[23,] 0.214221895 0.9943605966 0.1026302025
[24,] 0.075472115 0.7723486915 0.9990120017
[25,] 0.267140783 0.9936911950 0.0001594083
[26,] 0.502784186 0.0195324508 0.6908972619
[27,] 0.297182409 0.6866016285 0.2657175115
[28,] 0.989806449 0.1303030752 0.0025650374
[29,] 0.039144031 0.7998810568 0.9982846602
[30,] 0.331822052 0.5399824430 0.4439204024
[31,] 0.506234891 0.0015059752 0.7478181192
[32,] 0.840779737 0.0235445380 0.7245765392
[33,] 0.422392069 0.7981084771 0.7744843676
[34,] 0.441856649 0.1576088411 0.8112018770
[35,] 0.001930989 0.9858286947 0.9998779297
[36,] 0.793925218 0.1174465995 0.2445594509
[37,] 0.291641995 0.8800995950 0.9413243015
[38,] 0.768427394 0.3995238231 0.7063946283
[39,] 0.757152784 0.0986404729 0.4104939447
[40,] 0.004578309 0.9846465674 0.9998779297
[41,] 0.824236114 0.0023585361 0.1102542225
[42,] 0.826212192 0.3474392833 0.0036558504
[43,] 0.229341633 0.9314491673 0.9361566558
[44,] 0.764693386 0.0194134007 0.0027020466
[45,] 0.381351850 0.9319133392 0.9519702728
[46,] 0.675560747 0.5411549125 0.0001220703
[47,] 0.267582448 0.5030757820 0.0209539194
[48,] 0.259420736 0.8745731725 0.9814300785
[49,] 0.839268828 0.1366531375 0.0265636912
[50,] 0.237911925 0.4742409269 0.9666936701
[51,] 0.841962999 0.1621486303 0.1458292950
[52,] 0.256203709 0.0424164785 0.9983261142
[53,] 0.557302311 0.9750121027 0.0939459313
[54,] 0.600490610 0.3498566554 0.0031093438
[55,] 0.551192145 0.3737899121 0.5432656754
[56,] 0.382128914 0.9105049552 0.9866731589
[57,] 0.849270063 0.7163541469 0.9506582817
[58,] 0.687638408 0.4806574965 0.2585073190
[59,] 0.925012809 0.4536230993 0.2799068416
[60,] 0.269880863 0.1638057424 0.0878140398
[61,] 0.243204555 0.7399573342 0.3368382194
[62,] 0.261784943 0.0092730679 0.2578480364
[63,] 0.585626337 0.9140409245 0.0069646084
[64,] 0.479502896 0.3144920214 0.0523591476
[65,] 0.777388746 0.2946196687 0.1857022461
[66,] 0.006626250 0.9380954733 0.9998779297
[67,] 0.614542108 0.0174726973 0.0271128497
[68,] 0.497556386 0.0878016256 0.0555661109
[69,] 0.107087944 0.7957394309 0.9835720924
[70,] 0.626779363 0.2003275005 0.2378317011
[71,] 0.281214621 0.6235897530 0.9574813493
[72,] 0.744459749 0.2549693935 0.6821363544
[73,] 0.498825934 0.5329326971 0.4870791762
[74,] 0.030092790 0.7275156971 0.9996414773
[75,] 0.263207110 0.8384147367 0.9814564439
[76,] 0.994881813 0.4937624332 0.1340515568
[77,] 0.978200833 0.0601543015 0.1347726566
[78,] 0.487353475 0.0392464064 0.4743429126
[79,] 0.365110751 0.8385832773 0.3158361903
[80,] 0.580110905 0.6395953780 0.7190241957
[81,] 0.359516421 0.2458616118 0.0339863139
[82,] 0.648724267 0.4677909171 0.8220641694
[83,] 0.959069925 0.1860327581 0.2479572923
[84,] 0.282039572 0.5438312072 0.8233227435
[85,] 0.712894524 0.4940614822 0.8276055757
[86,] 0.393932179 0.9157278845 0.8575298389
[87,] 0.742153140 0.1887696345 0.0001530378
[88,] 0.313860164 0.9871827299 0.2823846619
[89,] 0.789848690 0.9303154535 0.8775530935
[90,] 0.476575038 0.4817862228 0.0102548216
[91,] 0.524349187 0.5240180277 0.0001220703
[92,] 0.544823730 0.8649962921 0.8147517703
[93,] 0.139407016 0.7369928806 0.9703052560
[94,] 0.012989619 0.4797941253 0.9977882500
[95,] 0.295231677 0.8336265925 0.4886656398
[96,] 0.930505456 0.0025881014 0.2219570521
[97,] 0.750825125 0.1398009595 0.8557403459
[98,] 0.751099201 0.0080280920 0.0001220703
[99,] 0.705080681 0.0004932066 0.0147541526
[100,] 0.664656165 0.0324351212 0.0129767546
```

vines documentation built on May 2, 2019, 5:55 a.m.