mev (version 1.17)

.Joint_MLE_NHPP: 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)

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 \(\xi\)

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)

Author

Jennifer L. Wadsworth