% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/stochastic_orders.R
\name{biv_whr_order}
\alias{biv_whr_order}
\title{Weak Bivariate Hazard Rate Order}
\usage{
biv_whr_order(
  surv_X,
  surv_Y,
  t1_grid = seq(0.1, 3, by = 0.5),
  t2_grid = seq(0.1, 3, by = 0.5),
  tol = 1e-06
)
}
\arguments{
\item{surv_X, surv_Y}{Joint survival functions.}

\item{t1_grid, t2_grid}{Evaluation grids.}

\item{tol}{Tolerance.}
}
\value{
A list: \code{order_holds} (logical), \code{violations} (data frame).
}
\description{
Checks whether \eqn{X \le_{\rm whr} Y}: the ratio
\eqn{\bar{F}_Y(x_1,x_2) / \bar{F}_X(x_1,x_2)} is increasing in
\eqn{(x_1,x_2)}, i.e.\ \eqn{h_{i,X}(t_1,t_2) \ge h_{i,Y}(t_1,t_2),\; i=1,2}.
}
\examples{
sX <- function(x1, x2) sgumbel_biv(x1, x2, k1 = 1, k2 = 1, theta = 0)
sY <- function(x1, x2) sgumbel_biv(x1, x2, k1 = 2, k2 = 2, theta = 0)
biv_whr_order(sX, sY)

}
\references{
Shaked M., Shanthikumar J.G. (2007). *Stochastic Orders*. Springer.
Jayalekshmi S., Rajesh G., Nair N.U. (2022).
\doi{10.1080/03610926.2022.2085874}
}
