R/amhExpr.R

In copula: Multivariate Dependence with Copulas

## This file is not to be edited. It is generated by ../inst/docs/mathnb/exprPrep.R
`amhCopula.cdf.expr` <-
expression(u1, -((u1 * u2)/(-1 + alpha * (-1 + u1) * (-1 + u2))))
`amhCopula.cdf.algr` <-
expression({
    .value <- u1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr2 <- -1
    .value <- -(u1 * u2/(.expr2 + alpha * (.expr2 + u1) * (.expr2 + 
        u2)))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.cdfDerWrtArg.expr` <-
expression(1, -(u2/(-1 + alpha * (-1 + u1) * (-1 + u2)) - (u1 * 
    u2) * (alpha * (-1 + u2))/(-1 + alpha * (-1 + u1) * (-1 + 
    u2))^2))
`amhCopula.cdfDerWrtArg.algr` <-
expression({
    .value <- 1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .expr4 <- .expr1 + u2
    .expr6 <- .expr1 + alpha * (.expr1 + u1) * .expr4
    .value <- -(u2/.expr6 - u1 * u2 * (alpha * .expr4)/.expr6^2)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.cdfDerWrtPar.expr` <-
expression(0, (u1 * u2) * ((-1 + u1) * (-1 + u2))/(-1 + alpha * 
    (-1 + u1) * (-1 + u2))^2)
`amhCopula.cdfDerWrtPar.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr2 <- -1
    .expr3 <- .expr2 + u1
    .expr4 <- .expr2 + u2
    .value <- u1 * u2 * (.expr3 * .expr4)/(.expr2 + alpha * .expr3 * 
        .expr4)^2
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.pdf.expr` <-
expression(1, -((1 + alpha^2 * (-1 + u1) * (-1 + u2) + alpha * 
    (-2 + u1 + u2 + u1 * u2))/(-1 + alpha * (-1 + u1) * (-1 + 
    u2))^3))
`amhCopula.pdf.algr` <-
expression({
    .value <- 1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr2 <- -1
    .expr3 <- .expr2 + u1
    .expr5 <- .expr2 + u2
    .value <- -((1 + alpha^2 * .expr3 * .expr5 + alpha * (-2 + 
        u1 + u2 + u1 * u2))/(.expr2 + alpha * .expr3 * .expr5)^3)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.pdfDerWrtArg.expr` <-
expression(0, -((alpha^2 * (-1 + u2) + alpha * (1 + u2))/(-1 + 
    alpha * (-1 + u1) * (-1 + u2))^3 - (1 + alpha^2 * (-1 + u1) * 
    (-1 + u2) + alpha * (-2 + u1 + u2 + u1 * u2)) * (3 * (alpha * 
    (-1 + u2) * (-1 + alpha * (-1 + u1) * (-1 + u2))^2))/((-1 + 
    alpha * (-1 + u1) * (-1 + u2))^3)^2))
`amhCopula.pdfDerWrtArg.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- alpha^2
    .expr2 <- -1
    .expr3 <- .expr2 + u2
    .expr8 <- .expr2 + u1
    .expr11 <- .expr2 + alpha * .expr8 * .expr3
    .expr12 <- .expr11^3
    .value <- -((.expr1 * .expr3 + alpha * (1 + u2))/.expr12 - 
        (1 + .expr1 * .expr8 * .expr3 + alpha * (-2 + u1 + u2 + 
            u1 * u2)) * (3 * (alpha * .expr3 * .expr11^2))/.expr12^2)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.pdfDerWrtPar.expr` <-
expression(0, -((2 * alpha * (-1 + u1) * (-1 + u2) + (-2 + u1 + 
    u2 + u1 * u2))/(-1 + alpha * (-1 + u1) * (-1 + u2))^3 - (1 + 
    alpha^2 * (-1 + u1) * (-1 + u2) + alpha * (-2 + u1 + u2 + 
    u1 * u2)) * (3 * ((-1 + u1) * (-1 + u2) * (-1 + alpha * (-1 + 
    u1) * (-1 + u2))^2))/((-1 + alpha * (-1 + u1) * (-1 + u2))^3)^2))
`amhCopula.pdfDerWrtPar.algr` <-
expression({
    .value <- 0
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr2 <- -1
    .expr3 <- .expr2 + u1
    .expr5 <- .expr2 + u2
    .expr11 <- -2 + u1 + u2 + u1 * u2
    .expr15 <- .expr2 + alpha * .expr3 * .expr5
    .expr16 <- .expr15^3
    .value <- -((2 * alpha * .expr3 * .expr5 + .expr11)/.expr16 - 
        (1 + alpha^2 * .expr3 * .expr5 + alpha * .expr11) * (3 * 
            (.expr3 * .expr5 * .expr15^2))/.expr16^2)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})
`amhCopula.genfunDer.expr` <-
expression((-1 + alpha)/((1 + alpha * (-1 + u)) * u), -(((-1 + 
    alpha) * (1 + alpha * (-1 + 2 * u)))/((1 + alpha * (-1 + 
    u))^2 * u^2)))
`amhCopula.genfunDer.algr` <-
expression({
    .expr1 <- -1
    .value <- (.expr1 + alpha)/((1 + alpha * (.expr1 + u)) * 
        u)
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
}, {
    .expr1 <- -1
    .value <- -((.expr1 + alpha) * (1 + alpha * (.expr1 + 2 * 
        u))/((1 + alpha * (.expr1 + u))^2 * u^2))
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
    .grad[, "s"] <- 0
    attr(.value, "gradient") <- .grad
    .value
})