chibar | R Documentation |

`\bar{\chi}`

The function fits a generalized Pareto distribution to minima of Pareto variates, using the representation

`\Pr(\min(X) > x) = \frac{L(x)}{x^{1/\eta}},`

where `\bar{\chi}=2\eta-1`

. The data are transformed to the unit Pareto scale and
a generalized Pareto variable is fitted to the minimum. The parameter `\eta`

corresponds to the shape of the latter.
The confidence intervals can be based either on the delta-method, a profile likelihood or a tangent exponential model approximation.

```
chibar(dat, confint = c("delta", "profile", "tem"), qu = 0, level = 0.95)
```

`dat` |
an |

`confint` |
string indicating the type of confidence interval. |

`qu` |
percentile level at which to threshold. Default to all observations. |

`level` |
the confidence level required |

a named vector of length 3 containing the point estimate, the lower and the upper confidence intervals

`chiplot`

for empirical estimates of `\chi`

and `\bar{\chi}`

.

```
## Not run:
set.seed(765)
# Max-stable model, chibar = 1
dat <- rmev(n = 1000, model = "log", d = 2, param = 0.5)
chibar(dat, 'profile', qu = 0.5)
s <- seq(0.05,1, length = 30)
chibar_est <- t(sapply(s, function(keep){chibar(dat, 'delta', qu = keep)}))
matplot(s, chibar_est, type = 'l', col = c(1, 2, 2), lty = c(1, 2, 2),
ylab = expression(bar(chi)), xlab = 'p')
abline(h = 1, lty = 3, col = 'grey')
# Multivariate normal sample, chibar = 0 - strong asymptotic independence at penultimate level
dat <- mvrnorm(n = 1000, mu = c(0, 0), Sigma = cbind(c(1, 0.75), c(0.75, 1)))
chibar(dat, 'tem', q = 0.1)
chibar_est <- t(sapply(s, function(keep){chibar(dat, 'profile', qu = keep)}))
matplot(s, chibar_est, type = 'l', col = c(1, 2, 2), lty = c(1, 2, 2),
ylab = expression(bar(chi)), xlab = 'p')
abline(h = 1, lty = 3, col = 'grey')
## End(Not run)
```

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