######################
### Epigraph Index ###
######################

## The epigraph index of a curve x (EI) is one minus the proportion of curves in the sample that lie above x.
# This function computes the EI of a bunch of B curves.

EI <- function(curves){
  index <- numeric()
  B <- dim(curves)[1]
  lengthcurves <- dim(curves)[2]
  for (i in 1:B){
    index[i] <- 0
    env.min <- curves[i,]
    for (j in 1:B){
      inpoints <- sum((curves[j,] >= env.min))
      if (inpoints == lengthcurves)
      {index[i] <- index[i]+1}
    }
  }
  index <- index/B
  return (1-index)
}

#######################
### Hypograph Index ###
#######################

## The hypograph index of a curve x (HI) is the proportion of curves in the sample that lie below x.
# This function computes the HI of a bunch of B curves.

HI <- function(curves){
  index <- numeric()
  B <- dim(curves)[1]
  lengthcurves <- dim(curves)[2]
  for (i in 1:B){
    index[i] <- 0
    env.max <- curves[i,]
    for (j in 1:B){
      inpoints <- sum(curves[j,]<=env.max)
      if (inpoints == lengthcurves)
      {index[i] <- index[i]+1}
    }
  }
  index <- index/B
  return (index)
}

##################################
### Generalized Epigraph Index ###
##################################

## The generalized epigraph index of a curve x (MEI) is 
## one minus the "proportion of time" that the curves of the sample are above x.
# This function computes the MEI of a bunch of B curves.

MEI <- function(curves){
  index <- numeric()
  B <- dim(curves)[1]
  lengthcurves <- dim(curves)[2]
  for (i in 1:B){
    index[i] <- 0
    env.min <- curves[i,]
    for (j in 1:B){
      inpoints <- sum(curves[j,] >= env.min)
      index[i] <- index[i]+inpoints
    }
  }
  index <- index/(B*lengthcurves)
  return (1-index)
}

###################################
### Generalized Hypograph Index ###
###################################

## The generalized hypograph index of a curve x (MHI) is 
## the "proportion of time" that the curves of the sample are below x.
# This function computes the MHI of a bunch of B curves.

MHI <- function(curves){
  index <- numeric()
  B <- dim(curves)[1]
  lengthcurves <- dim(curves)[2]
  for (i in 1:B){
    index[i] <- 0
    env.max <- curves[i,]
    for (j in 1:B){
      inpoints <- sum(curves[j,]<=env.max)
      index[i] <- index[i]+inpoints
    }
  }
  index <- index/(B*lengthcurves)
  return (index)
}