# Compute risk ratio and uncertainty based on generalized extreme value model fit to block maxima or minima

### Description

Compute risk ratio and uncertainty by fitting generalized extreme value model, designed specifically for climate data, to exceedance-only data, using the point process approach. The risk ratio is the ratio of the probability of exceedance of a pre-specified value under the model fit to the first dataset to the probability under the model fit to the second dataset. Default standard errors are based on the usual MLE asymptotics using a delta-method-based approximation, but standard errors based on the nonparametric bootstrap and on a likelihood ratio procedure can also be computed.

### Usage

1 2 3 4 5 6 7 8 9 | ```
calc_riskRatio_gev(returnValue, y1, y2, x1 = NULL, x2 = x1,
locationFun1 = NULL, locationFun2 = locationFun1, scaleFun1 = NULL,
scaleFun2 = scaleFun1, shapeFun1 = NULL, shapeFun2 = shapeFun1,
nReplicates1 = 1, nReplicates2 = 1, replicateIndex1 = NULL,
replicateIndex2 = NULL, weights1 = NULL, weights2 = NULL,
xNew1 = NULL, xNew2 = NULL, maxes = TRUE, scaling1 = 1,
scaling2 = 1, ciLevel = 0.9, bootSE = FALSE, bootControl = list(seed =
0, n = 250, by = "block"), lrtCI = FALSE, lrtControl = list(bounds =
c(0.01, 100)), optimArgs = list(method = "Nelder-Mead"))
``` |

### Arguments

`returnValue` |
numeric value giving the value for which the risk ratio should be calculated, where the resulting period will be the average number of blocks until the value is exceeded and the probability the probability of exceeding the value in any single block. |

`y1` |
a numeric vector of observed maxima or minima values for the first dataset. See |

`y2` |
a numeric vector of observed maxima or minima values for the second dataset. Analogous to |

`x1` |
a data frame, or object that can be converted to a data frame with columns corresponding to covariate/predictor/feature variables and each row containing the values of the variable for the corresponding observed maximum/minimum. The number of rows should either equal the length of |

`x2` |
analogous to |

`locationFun1` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the location parameter using columns from |

`locationFun2` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the location parameter using columns from |

`scaleFun1` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the log of the scale parameter using columns from |

`scaleFun2` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the log of the scale parameter using columns from |

`shapeFun1` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the shape parameter using columns from |

`shapeFun2` |
formula, vector of character strings, or indices describing a linear model (i.e., regression function) for the shape parameter using columns from |

`nReplicates1` |
numeric value indicating the number of replicates for the first dataset. |

`nReplicates2` |
numeric value indicating the number of replicates for the second dataset. |

`replicateIndex1` |
numeric vector providing the index of the replicate corresponding to each element of |

`replicateIndex2` |
numeric vector providing the index of the replicate corresponding to each element of |

`weights1` |
a vector providing the weights for each observation in the first dataset. When there is only one replicate or the weights do not vary by replicate, a vector of length equal to the number of observations. When weights vary by replicate, this should be of equal length to |

`weights2` |
a vector providing the weights for each observation in the second dataset. Analogous to |

`xNew1` |
object of the same form as |

`xNew2` |
object of the same form as |

`maxes` |
logical indicating whether analysis is for block maxima (TRUE) or block minima (FALSE); in the latter case, the function works with the negative of the values, changing the sign of the resulting location parameters |

`scaling1` |
positive-valued scalar used to scale the data values of the first dataset for more robust optimization performance. When multiplied by the values, it should produce values with magnitude around 1. |

`scaling2` |
positive-valued scalar used to scale the data values of the second dataset for more robust optimization performance. When multiplied by the values, it should produce values with magnitude around 1. |

`ciLevel` |
statistical confidence level for confidence intervals; in repeated experimentation, this proportion of confidence intervals should contain the true risk ratio. Note that if only one endpoint of the resulting interval is used, for example the lower bound, then the effective confidence level increases by half of one minus |

`bootSE` |
logical indicating whether to use the bootstrap to estimate standard errors. |

`bootControl` |
a list of control parameters for the bootstrapping. See |

`lrtCI` |
logical indicating whether to calculate a likelihood ratio-based confidence interval |

`lrtControl` |
list containing a single component, |

`optimArgs` |
a list with named components matching exactly any arguments that the user wishes to pass to |

### Details

See `fit_gev`

for more details on fitting the block maxima model for each dataset, including details on blocking and replication. Also see `fit_gev`

for information on the `bootControl`

argument.

### Author(s)

Christopher J. Paciorek

### References

Jeon S., C.J. Paciorek, and M.F. Wehner. 2016. Quantile-based bias correction and uncertainty quantification of extreme event attribution statements. Weather and Climate Extremes. In press. arXiv preprint: http://arxiv.org/abs/1602.04139.

### Examples

1 | ```
# need examples
``` |