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#####################################################
# Phases Transition #
#####################################################
#' Transition range between two successive phases (for phases in temporal order constraint)
#'
#' Finds, if it exists, the shortest interval that satisfies
#' \eqn{P(TransitionRangeInf < Phase1Max_chain < Phase2Min_chain < TransitionRangeSup | M) = level}
#'
#' @param Phase1Max_chain Numeric vector containing the output of the
#' MCMC algorithm for the maximum of the events included in the oldest phase.
#' @param Phase2Min_chain Numeric vector containing the output of the
#' MCMC algorithm for the minimum of the events included in the following phase.
#' @param level Probability corresponding to the level of confidence.
#'
#' @return a vector of values containing the level of confidence and the
#' endpoints of the transition interval between the successive phases.
#' The result is given in calendar years (BC/AD).
#'
#' @author Anne Philippe, \email{Anne.Philippe@@univ-nantes.fr} and
#'
#' @author Marie-Anne Vibet, \email{Marie-Anne.Vibet@@univ-nantes.fr}
#'
#' @examples
#' data(Phases); attach(Phases)
#' PhasesTransition(Phase.1.beta, Phase.2.alpha, 0.95)
#' PhasesTransition(Phase.1.beta, Phase.2.alpha, 0.50)
#'
#' @export
PhasesTransition <- function(Phase1Max_chain, Phase2Min_chain, level=0.95){
result = as.matrix( PhaseTimeRange(Phase1Max_chain, Phase2Min_chain, level=level))
rownames(result)<- c(level=level, "TransitionRangeInf", "TransitionRangeSup")
result <- t(result)
return(result[1,])
}
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