dot-Joint_MLE_NHPP: Joint maximum likelihood for the non-homogeneous Poisson...

In mev: Modelling of Extreme Values

Joint maximum likelihood for the non-homogeneous Poisson Process

Description

Calculates the MLEs of the parameters (\mu, \sigma, \xi), and joint asymptotic covariance matrix of these MLEs over a range of thresholds as supplied by the user.

Usage

.Joint_MLE_NHPP(x, u = NULL, k, q1, q2 = 1, par, M)

Arguments

x	vector of data
u	optional vector of thresholds. If not supplied, then k thresholds between quantiles (q1, q2) will be used
k	number of thresholds to consider if u not supplied
q1	lower quantile to consider for threshold
q2	upper quantile to consider for threshold. Default to 1
par	starting values for the optimization
M	number of superpositions or 'blocks' / 'years' the process corresponds to. It affects the estimation of mu and sigma, but these can be changed post-hoc to correspond to any number)

Value

a list with components

• mle matrix of MLEs above the supplied thresholds; columns are (\mu, \sigma, \xi)

• Cov.all joint asymptotic covariance matrix of all MLEs

• Cov.mu joint asymptotic covariance matrix of MLEs for \mu

• Cov.sig joint asymptotic covariance matrix of MLEs for \sigma

• Cov.xi joint asymptotic covariance matrix of MLEs for \xi

Author(s)

Jennifer L. Wadsworth

mev documentation built on Sept. 11, 2024, 8:14 p.m.