| Title: | Computation of v Values for U and Copula C(U, v) |
|---|---|
| Description: | Computation the value of one of two uniformly distributed marginals if the copula probability value is known and the value of the second marginal is also known. Computation and plotting corresponding cumulative distribution function or survival function. The numerical definition of a common area limited by lines of the cumulative distribution function and survival function. Approximate quantification of the probability of this area. In addition to 'amh', the copula dimension may be larger than 2. |
| Authors: | Josef Brejcha |
| Maintainer: | Josef Brejcha <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.4.0 |
| Built: | 2024-12-12 07:07:01 UTC |
| Source: | CRAN |
Computation v when u and C(u, v) copula are
known. Calculation and plotting of cumulative distribution
and survival function when u, C(u, v) copula
and marginal distributions are known. These calculations can
be tabulated as option. The numerical definition of a common
area limited by lines of the cumulative distribution function
and survival function. Approximate quantification of the
probability of this area. In addition to 'amh', the copula
dimension may be larger than 2.
| Package: | vfcp |
| Type: | Package |
| Version: | 1.4.0 |
| Date: | 2017-10-24 |
| License: | GPL (>= 3) |
Josef Brejcha
Maintainer: Josef Brejcha <[email protected]>
A.K. SUZUKI, F. LOUZADA and V.G. CANCHO, On estimation and
influence diagnostics for a Bivariate Promotion Lifetime Model
Based on the FGM Copula: A Fully Bayesian Computation, Tendencias em Matematica Aplicada e Computacional, 14, N. 3 (2013), 441-461, http://www.scielo.br/pdf/tema/v14n3/a14v14n3.pdf
M. Mahfoud, "Bivariate Archimedean copulas: an application to two stock market
indices", Vrije Universiteit Amsterdam, BMI Paper, Amsterdam-2012,
http://docplayer.net/24882927-Bivariate-archimedean-copulas-an-application-to-two-stock-market-indices.html
Copula (probability theory), https://en.wikipedia.org/wiki/Copula_(probability_theory)
Statistical - Distributions - Inverted Beta distribution - Example, http://www.xycoon.com/ibeta.htm
For given inputs, the coordinates of the object defined by the CDF and the survival function for the copula object are created.
gentruk(tht, fm, C, pro)gentruk(tht, fm, C, pro)
tht |
Copula parameter. If |
fm |
Family name copula. These can be: "clayton", "gumbel", "frank", "joe", "amh", "fgm". |
C |
Probability value of the copula. Single value. |
pro |
Numeric vector. Its |
A list with components as trimeze value.
Josef Brejcha
tht = 0.6 cx = c(0.025, 0.05, 0.1, 0.15, 0.25) pro = c(0.99999, 0.9999, 0.999, 0.99, 24, 16, 8, 4) dm = 2 fam = "fgm" marg = c("weibull", "betapr") xo = c(200, 2.75, 16.5, 6.60) e12 = vfenuo(marg, xo) p = numeric(length(cx)) x12 = qweibull(0.975, scale = xo[1], shape = xo[2]) y12 = qbetapr(0.975, shape1 = xo[3], shape2 = xo[4]) mtit = paste(fam, " ... ", marg[1], "(", xo[1], ", ", xo[2], ")", " ", marg[2], "(", xo[3], ", ", xo[4], ")", sep = "") plot(NULL, NULL, xlim = c(0, x12), ylim = c(0, y12), xlab = paste("x, E[x] = ", round(e12[1], 2)), ylab = paste("y, E[y] = ", round(e12[2], 2)), main = mtit) points(e12[1], e12[2], pch = 20) abline(h = e12[2], v = e12[1]) grid(col = "grey50") #=========================== kop2 = kopula(fam, tht, dm) fmc = c("", "", "clayton", "gumbel", "frank", "joe") pro = c(0.999999, 0.99999, 0.9999, 16, 8, 4, 2) tm3 = list() tmk = list() for (k in 1:length(cx)){ tm3 = gentruk(tht, fm=fam, C=cx[k], pro) tmk[[k]] = tm3 } p = prosim(C = cx, fam, tht, dm, no = 100000) # ============= xa = c("u") ya = c("v") for (k in 1:length(cx)){ mspx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$sp$s1, yo=xo, cdf=TRUE) mspy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$sp$s2, yo=xo, cdf=TRUE) mcpx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$cp$c1, yo=xo, cdf=TRUE) mcpy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$cp$c2, yo=xo, cdf=TRUE) lines(mspx,mspy, col=k) lines(mcpx, mcpy, col = k) } legend("topleft", legend = c("C", cx), text.col = c(1, 1:length(cx)), bty = "n") legend("topright", legend = c("p", round(p, 4)), text.col = c(1, 1:length(cx)), bty = "n")tht = 0.6 cx = c(0.025, 0.05, 0.1, 0.15, 0.25) pro = c(0.99999, 0.9999, 0.999, 0.99, 24, 16, 8, 4) dm = 2 fam = "fgm" marg = c("weibull", "betapr") xo = c(200, 2.75, 16.5, 6.60) e12 = vfenuo(marg, xo) p = numeric(length(cx)) x12 = qweibull(0.975, scale = xo[1], shape = xo[2]) y12 = qbetapr(0.975, shape1 = xo[3], shape2 = xo[4]) mtit = paste(fam, " ... ", marg[1], "(", xo[1], ", ", xo[2], ")", " ", marg[2], "(", xo[3], ", ", xo[4], ")", sep = "") plot(NULL, NULL, xlim = c(0, x12), ylim = c(0, y12), xlab = paste("x, E[x] = ", round(e12[1], 2)), ylab = paste("y, E[y] = ", round(e12[2], 2)), main = mtit) points(e12[1], e12[2], pch = 20) abline(h = e12[2], v = e12[1]) grid(col = "grey50") #=========================== kop2 = kopula(fam, tht, dm) fmc = c("", "", "clayton", "gumbel", "frank", "joe") pro = c(0.999999, 0.99999, 0.9999, 16, 8, 4, 2) tm3 = list() tmk = list() for (k in 1:length(cx)){ tm3 = gentruk(tht, fm=fam, C=cx[k], pro) tmk[[k]] = tm3 } p = prosim(C = cx, fam, tht, dm, no = 100000) # ============= xa = c("u") ya = c("v") for (k in 1:length(cx)){ mspx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$sp$s1, yo=xo, cdf=TRUE) mspy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$sp$s2, yo=xo, cdf=TRUE) mcpx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$cp$c1, yo=xo, cdf=TRUE) mcpy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$cp$c2, yo=xo, cdf=TRUE) lines(mspx,mspy, col=k) lines(mcpx, mcpy, col = k) } legend("topleft", legend = c("C", cx), text.col = c(1, 1:length(cx)), bty = "n") legend("topright", legend = c("p", round(p, 4)), text.col = c(1, 1:length(cx)), bty = "n")
Generate the copula object.
kopula(fam, tht, dm)kopula(fam, tht, dm)
fam |
Family name copula. These can be: "clayton", "gumbel", "frank", "joe", "amh", "fgm". |
tht |
Copula parameter. |
dm |
Copula dimension. |
Copula object
Josef Brejcha
Probability of the inside of an object as defined by CDF and survival. For this, the Monte Carlo method is used.
prosim(C, fam, tht, dm, no)prosim(C, fam, tht, dm, no)
C |
single numeric; CDF value. Survival value is |
fam |
Family name copula. These can be: "clayton", "gumbel", "frank", "joe", "amh", "fgm". |
tht |
Copula parameter. If |
dm |
Copula dimension |
no |
Monte Carlo sample size |
Probability
Josef Brejcha
tht = 10.6 cx = c(0.05, 0.1, 0.15, 0.25) pro = c(0.99999, 0.9999, 0.999, 0.99, 24, 16, 8, 4) dm = 4 fam = "gumbel" marg = rep(c("weibull", "betapr"), 2) xo = rep(c(200, 2.75, 16.5, 6.60), 2) #=========================== kop2 = kopula(fam, tht, dm) fmc = c("", "", "clayton", "gumbel", "frank", "joe") pro = c(0.999999, 0.99999, 0.9999, 16, 8, 4, 2) tm3 = list() tmk = list() # di = dm*(dm - 1)/2 for (k in 1:length(cx)){ tm3 = gentruk(tht, fm=fam, C=cx[k], pro) tmk[[k]] = tm3 } np = 5 no = 100000 ncx = length(cx) p = array(0, c(np*ncx, 2)) colnames(p) = c("C", "p") k = 0 for (i in 1:length(cx)){ for (j in 1:np){ k = k + 1 p[k, 1] = cx[i] p[k, 2] = prosim(C = cx[i], fam, tht, dm, no) } } plst = list() print(paste(fam, "dim =", dm, "tht =", tht, "n =", no, "nrep.", np)) for (k in 1:ncx){ plst[[k]] = summary(p[p[, 1] == cx[k], 2]) print(paste("cx =", cx[k])) print(plst[[k]]) }tht = 10.6 cx = c(0.05, 0.1, 0.15, 0.25) pro = c(0.99999, 0.9999, 0.999, 0.99, 24, 16, 8, 4) dm = 4 fam = "gumbel" marg = rep(c("weibull", "betapr"), 2) xo = rep(c(200, 2.75, 16.5, 6.60), 2) #=========================== kop2 = kopula(fam, tht, dm) fmc = c("", "", "clayton", "gumbel", "frank", "joe") pro = c(0.999999, 0.99999, 0.9999, 16, 8, 4, 2) tm3 = list() tmk = list() # di = dm*(dm - 1)/2 for (k in 1:length(cx)){ tm3 = gentruk(tht, fm=fam, C=cx[k], pro) tmk[[k]] = tm3 } np = 5 no = 100000 ncx = length(cx) p = array(0, c(np*ncx, 2)) colnames(p) = c("C", "p") k = 0 for (i in 1:length(cx)){ for (j in 1:np){ k = k + 1 p[k, 1] = cx[i] p[k, 2] = prosim(C = cx[i], fam, tht, dm, no) } } plst = list() print(paste(fam, "dim =", dm, "tht =", tht, "n =", no, "nrep.", np)) for (k in 1:ncx){ plst[[k]] = summary(p[p[, 1] == cx[k], 2]) print(paste("cx =", cx[k])) print(plst[[k]]) }
The coordinates of the intersection lines of the cumulative distribution function and survival function.
prunikus(x, y)prunikus(x, y)
x |
Numeric vector of size 4. The horizontal coordinates of opposite points. |
y |
Numeric vector of size 4. The vertical coordinates of opposite points. |
Numeric vector size 2.
Josef Brejcha
Line-line intersection, https://en.wikipedia.org/wiki/Line-line_intersection
Calculates the coordinates of the object defined matrices C1
and C23. Both matrices are two-row.
trimeze(C1, C23)trimeze(C1, C23)
C1 |
numerical probability two-row matrix defining survival line |
C23 |
numerical probability two-row matrix defining CDF line |
A list with components as follows:
tlc |
upper left corner coordinates |
brc |
bottom right corner coordinates |
sp |
survival line coordinates |
cp |
CDF line coordinates |
Josef Brejcha
v for Ali-Mikhail-Haq copula C(u, v) given probability
C(u, v) and u.
vfalihaq(C, u, tht)vfalihaq(C, u, tht)
C |
Probability value of the Ali-Mikhail-Haq copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
require(copula) C = 0.3 tht = 0.5 u = c(0.35, 0.40, 0.45) v <- vfalihaq(C, u, tht) kali <- archmCopula(family = "amh", param = tht, dim = 2) pCopula(cbind(u, v), kali) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfalihaq(C = Cf, u = mx , tht=0.5) # [,1] [,2] [,3] # 0.3 0.8019802 0.6774194 0.5918367 # 0.4 0.7500000 0.6739130 0.6153846require(copula) C = 0.3 tht = 0.5 u = c(0.35, 0.40, 0.45) v <- vfalihaq(C, u, tht) kali <- archmCopula(family = "amh", param = tht, dim = 2) pCopula(cbind(u, v), kali) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfalihaq(C = Cf, u = mx , tht=0.5) # [,1] [,2] [,3] # 0.3 0.8019802 0.6774194 0.5918367 # 0.4 0.7500000 0.6739130 0.6153846
v for Clayton copula C(u, v) given probability
C(u, v) and u.
vfclayton(C, u, tht)vfclayton(C, u, tht)
C |
Probability value of the Clayton copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfclayton(C, u, tht) kop = claytonCopula(tht) pCopula(cbind(u, v), kop) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfclayton(C = Cf, u = mx , tht=7) # [,1] [,2] [,3] # 0.3 0.3183261 0.3061926 0.3025859 # 0.4 0.4135555 0.4064530 0.4033610C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfclayton(C, u, tht) kop = claytonCopula(tht) pCopula(cbind(u, v), kop) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfclayton(C = Cf, u = mx , tht=7) # [,1] [,2] [,3] # 0.3 0.3183261 0.3061926 0.3025859 # 0.4 0.4135555 0.4064530 0.4033610
Auxiliary function that calculates the expected values of marginal distributions.
vfenuo(marg, xo)vfenuo(marg, xo)
marg |
Character vector size greater than or equal to 2. Its components can now be c("weibull", "gamma", "lnorm", "norm", "betapr", "beta"). |
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xo |
Vector size
|
Numeric vector size equal to length(marg).
Josef Brejcha
vfenuo(marg = c("betapr", "beta", "norm", "weibull"), xo = c(5, 5, 3, 20, 30, 5, 100, 1.5))vfenuo(marg = c("betapr", "beta", "norm", "weibull"), xo = c(5, 5, 3, 20, 30, 5, 100, 1.5))
A vector v is computed for C and numeric probability
vector u.
vfex(C, u, th, fm)vfex(C, u, th, fm)
C |
Copula probability. It is a single value. |
u |
Probability vector. All its components are greater than |
th |
Copula parameter. |
fm |
character; A name of copula. One of c("clayton", "frank", "gumbel", "amh", "joe", "fgm"). "amh", "joe", "fgm" names are for Ali-Mikhail-Haq, Joe, Farlie-Gumbel-Morgenstern copulas. |
Numeric vector.
Josef Brejcha
v for Farlie-Gumbel-Morgenstern copula C(u, v)
given probability C(u, v) and u.
vffgm(C, u, tht)vffgm(C, u, tht)
C |
Probability value of the Farlie-Gumbel-Morgenstern copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
A.K. SUZUKI, F. LOUZADA and V.G. CANCHO, On estimation and influence diagnostics for a Bivariate Promotion Lifetime Model Based on the FGM Copula: A Fully Bayesian Computation, Tendˆencias em Matem´ atica Aplicada e Computacional, 14, N. 3 (2013), 441-461, http://www.scielo.br/pdf/tema/v14n3/a14v14n3.pdf
require(copula) C = 0.3 tht = 0.5 u = c(0.35, 0.40, 0.45) v <- vffgm(C, u, tht) kfgm <- fgmCopula(tht) pCopula(c(u, v), kfgm) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vffgm(C = Cf, u = mx , tht=0.5) # [,1] [,2] [,3] # 0.3 0.8064052 0.6853009 0.6007056 # 0.4 0.7535751 0.6781648 0.6195239require(copula) C = 0.3 tht = 0.5 u = c(0.35, 0.40, 0.45) v <- vffgm(C, u, tht) kfgm <- fgmCopula(tht) pCopula(c(u, v), kfgm) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vffgm(C = Cf, u = mx , tht=0.5) # [,1] [,2] [,3] # 0.3 0.8064052 0.6853009 0.6007056 # 0.4 0.7535751 0.6781648 0.6195239
v for Frank copula C(u, v) given probability
C(u, v) and u.
vffrank(C, u, tht)vffrank(C, u, tht)
C |
Probability value of the Frank copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vffrank(C, u, tht) kop = frankCopula(tht) pCopula(cbind(u, v), kop)C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vffrank(C, u, tht) kop = frankCopula(tht) pCopula(cbind(u, v), kop)
v for Gumbel copula C(u, v) given probability
C(u, v) and u.
vfgumbel(C, u, tht)vfgumbel(C, u, tht)
C |
Probability value of the Gumbel copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfgumbel(C, u, tht) kop = gumbelCopula(tht) pCopula(cbind(u, v), kop) # vfgumbel(c(0.3, 0.4), u = rbind(seq(0.35, 0.45, 0.05), seq(0.45, 0.55, 0.05)), 8) # [,1] [,2] [,3] # [1,] 0.3184504 0.3053987 0.3017235 # [2,] 0.4184819 0.4051936 0.4015295C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfgumbel(C, u, tht) kop = gumbelCopula(tht) pCopula(cbind(u, v), kop) # vfgumbel(c(0.3, 0.4), u = rbind(seq(0.35, 0.45, 0.05), seq(0.45, 0.55, 0.05)), 8) # [,1] [,2] [,3] # [1,] 0.3184504 0.3053987 0.3017235 # [2,] 0.4184819 0.4051936 0.4015295
v for Joe copula C(u, v) given probability
C(u, v) and u.
vfjoe(C, u, tht)vfjoe(C, u, tht)
C |
Probability value of the Joe copula. It can be a vector. |
u |
The first variable value of the |
tht |
Copula parameter |
The value of the u must be grater than C.
The value of the second variable depending on the first variable and copula probability value.
Josef Brejcha
C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfjoe(C, u, tht) kop = joeCopula(tht) pCopula(cbind(u, v), kop) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfjoe(C = Cf, u = mx , tht=6) # [,1] [,2] [,3] # [1,] 0.4021216 0.3513741 0.3274672 # [2,] 0.4379531 0.4184746 0.4087143C <- 0.3 tht <- 6 u <- c(0.35, 0.4, 0.45) v <- vfjoe(C, u, tht) kop = joeCopula(tht) pCopula(cbind(u, v), kop) # Cf <- c(0.3, 0.4) mx <- matrix(c(seq(0.35, 0.45, 0.05), seq(0.5, 0.6, 0.05)), nrow = 2, ncol = 3, byrow = TRUE) rownames(mx) <- Cf vfjoe(C = Cf, u = mx , tht=6) # [,1] [,2] [,3] # [1,] 0.4021216 0.3513741 0.3274672 # [2,] 0.4379531 0.4184746 0.4087143
Auxiliary function used in vfploto. It computes random
variable value of the CDF or survival which can be
one of the c("weibull", "gamma", "lnorm", "norm", "betapr", "beta").
vfmrg(rdj, i, cosi, yo, cdf)vfmrg(rdj, i, cosi, yo, cdf)
rdj |
A character vector. Its components are from c("weibull", "gamma", "lnorm", "norm", "betapr", "beta"). |
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i |
An index of the |
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cosi |
A vector of probabilities |
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yo |
Vector size
|
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cdf |
Cumulative distribution function when |
"betapr" is the name of 'BetaPrime' distribution from
extrDistr package. The other name 'BetaPrime' is 'Inverted Beta'.
Numeric vector
Josef Brejcha
Plotting the cumulative distribution function or survival function.
vfploto(cx, pro, fam, marg, xo, tht, cdf=TRUE, plt=TRUE, rtn=FALSE, ped = TRUE)vfploto(cx, pro, fam, marg, xo, tht, cdf=TRUE, plt=TRUE, rtn=FALSE, ped = TRUE)
cx |
A vector of copula probabilities. |
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pro |
Numeric vector. Its |
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fam |
character; A name of copula. One of c("clayton", "frank", "gumbel", "amh", "joe", "fgm"). "amh", "joe", "fgm" names are for Ali-Mikhail-Haq, Joe, Farlie-Gumbel-Morgenstern copulas. |
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marg |
A vector size 2. Combination of these marginals: |
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xo |
A vector of marginal distribution parameters. It is size 4
with these components:
|
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tht |
copula parameter |
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cdf |
logical; Computation for CDF when TRUE. If FALSE is the same for Survival. |
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plt |
Plot only when TRUE. |
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rtn |
Print output value only when TRUE. |
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ped |
Compute and add to plot an expected values o f marginal
distributions when |
Must not be plt and rtn at the same time equal to FALSE.
If rtn is TRUE, then a list of these components:
Type |
character; "CDF" or "Survival" |
P |
numeric; CDF or Survival value |
x |
numeric vector of the first marginal values for P |
y |
numeric vector of the second marginal values for P |
u |
numeric vector of the first copula marginal values |
v |
numeric vector of the second copula marginal values |
Josef Brejcha
require(copula) tht = 0.475 cx = c(0.0025, 0.05, seq(0.1, 0.9, 0.1), 0.95, 0.975) # nC = length(cx) proh = c(0.9999999, 8, 4, 4, 4) prod = c(0.999, 8, 4, 4, 4) fam = "clayton" marg = c("weibull", "lnorm") xo = c(100, 1.5, 3, 0.425) suro = vfploto(cx, proh, fam, marg, xo, tht, cdf=FALSE, plt=TRUE, rtn=FALSE) cdfo = vfploto(cx, prod, fam, marg, xo, tht, cdf=TRUE, plt=TRUE, rtn=FALSE) ## cx = 0.4 vfploto(cx, proh, fam, marg, xo, tht, cdf=TRUE, plt=FALSE, rtn=TRUE, ped = TRUE)require(copula) tht = 0.475 cx = c(0.0025, 0.05, seq(0.1, 0.9, 0.1), 0.95, 0.975) # nC = length(cx) proh = c(0.9999999, 8, 4, 4, 4) prod = c(0.999, 8, 4, 4, 4) fam = "clayton" marg = c("weibull", "lnorm") xo = c(100, 1.5, 3, 0.425) suro = vfploto(cx, proh, fam, marg, xo, tht, cdf=FALSE, plt=TRUE, rtn=FALSE) cdfo = vfploto(cx, prod, fam, marg, xo, tht, cdf=TRUE, plt=TRUE, rtn=FALSE) ## cx = 0.4 vfploto(cx, proh, fam, marg, xo, tht, cdf=TRUE, plt=FALSE, rtn=TRUE, ped = TRUE)
u to compute the second vector v
Auxiliary function. Each vector value u must be greater
than the probability of the copula.
vfprifo(ck, pro)vfprifo(ck, pro)
ck |
Copula probability. Single value. Not a vector. |
pro |
Numeric vector. All its components are less than 1. |
Numeric vector.
Josef Brejcha
u to compute the second vector v
Auxiliary function. Each vector value u must be greater
than the probability of the copula.
vfpripo(ck, pro)vfpripo(ck, pro)
ck |
Copula probability. Single value. Not a vector. |
pro |
Numeric vector. Its |
Numeric vector.
Josef Brejcha
prk = c(0.99999, 0.9999, 0.999, 0.99, 8, 4, 2) C = 0.1 u = vfpripo(ck = C, pro = prk)prk = c(0.99999, 0.9999, 0.999, 0.99, 8, 4, 2) C = 0.1 u = vfpripo(ck = C, pro = prk)