Description Usage Arguments Details Value References See Also Examples

Calculates initial estimates and estimated standard errors (SEs) for the generalized Pareto parameters sigma and xi based on an assumed random sample from this distribution. Also, calculates initial estimates and estimated standard errors for phi1 = sigma and phi2 = xi + sigma / xm.

1 2 |

`gpd_data` |
A numeric vector containing positive sample values. |

`m` |
A numeric scalar. The sample size, i.e. the length of gpd_data. |

`xm` |
A numeric scalar. The sample maximum. |

`sum_gp` |
A numeric scalar. The sum of the sample values. |

`xi_eq_zero` |
A logical scalar. If TRUE assume that the shape parameter xi = 0. |

`init_ests` |
A numeric vector. Initial estimate of
theta = (sigma, xi). If supplied |

The main aim is to calculate an admissible estimate of theta,
i.e. one at which the log-likelihood is finite (necessary for the
posterior log-density to be finite) at the estimate, and associated
estimated SEs. These are converted into estimates and SEs for phi. The
latter can be used to set values of `min_phi`

and `max_phi`

for input to `find_lambda`

.

In the default setting (`xi_eq_zero = FALSE`

and
`init_ests = NULL`

) the methods tried are Maximum Likelihood
Estimation (MLE) (Grimshaw, 1993), Probability-Weighted Moments (PWM)
(Hosking and Wallis, 1987) and Linear Combinations of Ratios of Spacings
(LRS) (Reiss and Thomas, 2007, page 134) in that order.

For xi < -1 the likelihood is unbounded, MLE may fail when xi is not
greater than -0.5 and the observed Fisher information for (sigma, xi) has
finite variance only if xi > -0.25. We use the ML estimate provided that
the estimate of xi returned from `gpd_mle`

is greater than -1. We only
use the SE if the MLE of xi is greater than -0.25.

If either the MLE or the SE are not OK then we try PWM. We use the PWM
estimate only if is admissible, and the MLE was not OK. We use the PWM SE,
but this will be `c(NA, NA)`

is the PWM estimate of xi is > 1/2. If
the estimate is still not OK then we try LRS. As a last resort, which
will tend to occur only when xi is strongly negative, we set xi = -1 and
estimate sigma conditional on this.

If `init_ests`

is not supplied by the user, a list is returned
with components

`init` |
A numeric vector. Initial estimates of sigma and xi. |

`se` |
A numeric vector. Estimated standard errors of sigma and xi. |

`init_phi` |
A numeric vector. Initial estimates of
phi1 = sigma and phi2 = xi + sigma / xm,
where xm is the maximum of |

`se_phi` |
A numeric vector. Estimated standard errors of phi1 and phi2. |

If `init_ests`

is supplied then only the numeric vector
`init_phi`

is returned.

Grimshaw, S. D. (1993) Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution. Technometrics, 35(2), 185-191. and Computing (1991) 1, 129-133. http://dx.doi.org/10.1007/BF01889987.

Hosking, J. R. M. and Wallis, J. R. (1987) Parameter and Quantile Estimation for the Generalized Pareto Distribution. Technometrics, 29(3), 339-349. http://dx.doi.org/10.2307/1269343.

Reiss, R.-D., Thomas, M. (2007) Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields.Birkhauser. http://dx.doi.org/10.1007/978-3-7643-7399-3.

`gpd_sum_stats`

to calculate summary statistics for
use in `gpd_loglik`

.

`rgpd`

for simulation from a generalized Pareto

`find_lambda`

to produce (somewhat) automatically
a list for the argument `lambda`

of `ru`

.

1 2 3 4 5 6 7 8 9 | ```
## Not run:
# Sample data from a GP(sigma, xi) distribution
gpd_data <- rgpd(m = 100, xi = 0, sigma = 1)
# Calculate summary statistics for use in the log-likelihood
ss <- gpd_sum_stats(gpd_data)
# Calculate initial estimates
do.call(gpd_init, ss)
## End(Not run)
``` |

paulnorthrop/rust documentation built on Jan. 6, 2019, 3:09 a.m.

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