dBivariateWeibullCountFrankCopula: Density and log-likelihood of the Bivariate Frank Copula...

In Countr: Flexible Univariate Count Models Based on Renewal Processes

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

Description

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.

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.

Value

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

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

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)
## rdname dRenewalFrankCopula_user

Countr documentation built on Dec. 6, 2025, 5:08 p.m.