Density and log-likelihood of the Bivariate Frank Copula Weibull Count model

Compute density and log-likelihood of the Bivariate Frank Copula Weibull Count model.

Usage

dBivariateWeibullCountFrankCopula(
  x,
  y,
  shapeX,
  scaleX,
  shapeY,
  scaleY,
  theta,
  method = c("series_acc", "conv_dePril"),
  time = 1,
  log = FALSE,
  conv_steps = 100,
  conv_extrap = TRUE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10
)

dBivariateWeibullCountFrankCopula_loglik(
  x,
  y,
  shapeX,
  scaleX,
  shapeY,
  scaleY,
  theta,
  method = c("series_acc", "conv_dePril"),
  time = 1,
  na.rm = TRUE,
  conv_steps = 100,
  conv_extrap = TRUE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10,
  weights = NULL
)

Arguments

x, y

numeric, the desired counts.

shapeX, shapeY

numeric, shape parameters. Either length(x) or length(1).

scaleX, scaleY

numeric, scale parameters (length(x)).

theta

numeric, Frank copula parameter.

method

character method to be used. Choices are "series_acc" (accelerated series expansion) or "conv_dePril" (convolution by dePril algorithm).

time

numeric, length of the observation window (defaults to 1).

log

TODO

conv_steps

integer, number of steps to use in the computation of the integral.

conv_extrap

logical, if TRUE, Richardson extrapolation will be applied to improve accuracy.

series_terms

number of terms used in series expansion.

series_acc_niter

number of iterations in the acceleration algorithm.

series_acc_eps

double, tolerance to declare convergence in the acceleration algorithm.

na.rm

logical, should NAs (obtained from log of small probabilities) be replaced with the smallest allowed probability?

weights

numeric vector of weights to apply. If NULL, a vector of ones.

Value

for dBivariateWeibullCountFrankCopula, a vector of the (log-)probabilities.

for dBivariateWeibullCountFrankCopula_loglik, the log-likelihood of the model, a number.

Details

dBivariateWeibullCountFrankCopula computes the probabilities \(P(X(t) = x(t), Y(t) = y(t))\), where \(X(t),Y(t)\) is a bivariate Weibull count process in which the bivariate distribution is modelled by Frank copulas.

Examples

## first 10 cases from "estimationParams.RDS", rounded for presentation
gam_weiH <-  0.9530455
gam_weiA <-  1.010051
theta    <- -0.3703702
HG <- c(0, 0, 0, 2, 1, 0, 2, 0, 1, 2)
AG <- c(2, 2, 1, 1, 6, 1, 0, 2, 0, 1)
lambdaHome <- c(1.5, 1.0, 1.3, 1.8, 1.3, 1.2, 1.3, 1.0, 2.0, 1.4)
lambdaAway <- c(1.2, 2.4, 1.3, 0.7, 1.3, 1.4, 0.6, 1.6, 0.6, 1.3)

weiFrank0 <- dBivariateWeibullCountFrankCopula(
    HG, AG, gam_weiH, lambdaHome, gam_weiA, lambdaAway, theta,
    "series_acc", 1, TRUE)

weiFrank1 <- dBivariateWeibullCountFrankCopula(
    HG, AG, gam_weiH, lambdaHome, gam_weiA, lambdaAway, theta,
    "conv_dePril", 1, TRUE, conv_extrap = TRUE)


weights <- c(0.01355306, 0.01355306, 0.01355306, 0.01355306, 0.01355306,
             0.01355306, 0.01355306, 0.01355306, 0.01357825, 0.01357825)

weiFrank2 <- dBivariateWeibullCountFrankCopula_loglik(
    HG, AG, gam_weiH, lambdaHome, gam_weiA, lambdaAway, theta,
    "conv_dePril", 1, TRUE, conv_extrap = TRUE, weights = weights)

weiFrank3 <- dBivariateWeibullCountFrankCopula_loglik(
    HG, AG, gam_weiH, lambdaHome, gam_weiA, lambdaAway, theta,
    "series_acc", 1, TRUE, weights = weights)

cbind(weiFrank0, weiFrank1, weiFrank2, weiFrank3)
#>                            weiFrank2  weiFrank3
#>  [1,] -3.110436 -3.110436 -0.3893715 -0.3893715
#>  [2,] -2.319851 -2.319851 -0.3893715 -0.3893715
#>  [3,] -2.319555 -2.319555 -0.3893715 -0.3893715
#>  [4,] -2.384469 -2.384469 -0.3893715 -0.3893715
#>  [5,] -7.466125 -7.466124 -0.3893715 -0.3893715
#>  [6,] -2.237400 -2.237400 -0.3893715 -0.3893715
#>  [7,] -2.112886 -2.112886 -0.3893715 -0.3893715
#>  [8,] -2.387953 -2.387953 -0.3893715 -0.3893715
#>  [9,] -1.915774 -1.915774 -0.3893715 -0.3893715
#> [10,] -2.466820 -2.466820 -0.3893715 -0.3893715
## rdname dRenewalFrankCopula_user