# Joint exceedance curves

### Description

Calculate bivariate joint exceedance curves

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
JointExceedanceCurve(Sample, ExceedanceProb,...)
## Default S3 method:
JointExceedanceCurve(Sample, ExceedanceProb, n = 50,
x = NULL, ...)
## S3 method for class 'mexMC'
JointExceedanceCurve(Sample, ExceedanceProb, n = 50,
x = NULL, which = 1:2, ...)
## S3 method for class 'predict.mex'
JointExceedanceCurve(Sample, ExceedanceProb, n = 50,
x = NULL, which = 1:2, ...)
calcJointExceedanceCurve(Sample, ExceedanceProb, n = 50, x = NULL)
## S3 method for class 'jointExcCurve'
print(x, ...)
geom_jointExcCurve(x, ...)
``` |

### Arguments

`Sample` |
Monte Carlo (or other) sample from which to calculate joint exceedance curve |

`ExceedanceProb` |
Takes values between 0 and 1, constant value of joint exceedance probability for which the curve will be calculated |

`...` |
Further aguments to be passed to methods |

`n` |
If |

`x` |
If specified by the user, the values of in the first dimension of |

`which` |
Vector length two identifying which margins to use for joint exceedance curve estimation. Can be integer vector, giving column numbers of original data matrix, or character vector identifying variables by name (these must match column names in original data). |

### Details

Calculates pairs of points (x,y) for which the point exceedance
probability P(X>x and Y>y) is constant. This is available only in
two dimensions: for higher dimensional data, the bivariate margin
will be used and other variables ignored. Takes as input either a
two column matrix of observations, output from `mexMonteCarlo`

(in which case samples from all fitted models are used to calculate curves)
or output from a call to the `predict`

method for an object of
class `mex`

(in which case just the single fitted model is used
for estimation, with the importance sample generated in the call
to `predict`

being used to calculate the joint exceedance curve).

### Value

Returns an object of class `jointExcCurve`

. This is a
list of length two, one for each variable for which the curve is
calculated. Each item of the list is a vector of coordinate values
for the variable in question. Attributes include `names`

and
the exceedance probability used to calculate the curve `ExceedanceProb`

.

The curve is calculated by finding pairs of points (x,y) for which the empirical
probability P(X>x, Y>y) of both variables exceeding their corresponding value is equal
to the specified `ExceedanceProb`

. Note that when this is calculated
for an object of class `predict.mex`

(returned by a call to the `predict`

method for an object of class `mex`

) then the exceedance probability is
interpreted as the UNCONDITIONAL exceedance probability of the importance sample,
ie the probability of sampled values occurring from the original modelled joint
distribution, and NOT the conditional distribution used to generate the
importance sample.

Estimated curve can be added to a ggplot of the data (and/or importance sample) by using the function `geom_jointExcCurve`

, see examples below.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
# for data frame of raw data
# m1 <- rmvnorm(5000,sigma=Sigma)
# m1 <- as.data.frame(m1)
# j1 <- JointExceedanceCurve(m1,0.01)
# j2 <- JointExceedanceCurve(m1,0.005)
# j3 <- JointExceedanceCurve(m1,0.001)
# ggplot(m1,aes(V1,V2)) + geom_point(colour="dark blue",alpha=0.5) +
# geom_jointExcCurve(j1,colour="orange") +
# geom_jointExcCurve(j2,colour="orange") +
# geom_jointExcCurve(j3,colour="orange")
# using importance sample generated by call to predict for object of class mex
# m <- mex(winter,mqu=0.7,dqu=0.7,which="NO")
# m2 <- predict(m,nsim=5000,pqu=0.999)
# g <- ggplot(m2,plot.=FALSE)
# j4 <- JointExceedanceCurve(m2,0.0005,which=c("NO","NO2"))
# j5 <- JointExceedanceCurve(m2,0.0002,which=c("NO","NO2"))
# j6 <- JointExceedanceCurve(m2,0.0001,which=c("NO","NO2"))
# g[[2]] +
# geom_jointExcCurve(j4,aes(NO,NO2),col="orange") +
# geom_jointExcCurve(j5,aes(NO,NO2),col="orange") +
# geom_jointExcCurve(j6,aes(NO,NO2),col="orange")
#
# for augmented dataset, generated by MC sampling from collection of fitted H+T models
# m <- mexAll(winter,mqu=0.7,dqu=rep(0.7,5))
# m3 <- mexMonteCarlo(nSample=5000,mexList=m)
# j7 <- JointExceedanceCurve(m3,0.05,which=c("NO","NO2"))
# j8 <- JointExceedanceCurve(m3,0.02,which=c("NO","NO2"))
# j9 <- JointExceedanceCurve(m3,0.01,which=c("NO","NO2"))
# ggplot(as.data.frame(m3$MCsample[,c("NO","NO2")]),aes(NO,NO2)) +
# geom_point(col="light blue",alpha=0.5) +
# geom_jointExcCurve(j7,col="orange") +
# geom_jointExcCurve(j8,col="orange") +
# geom_jointExcCurve(j9,col="orange")
``` |