fitlm_burr — fitlm_burr • anyFit

Fits the three-parameter Burr Type XII distribution to an xts series by numerical minimisation of L-moments. Closed-form L-moment expressions via Beta-function PWMs are evaluated at each optimisation step. The L-BFGS-B optimiser minimises the normalised root-sum-square error between the sample and theoretical L-moments of orders specified by order. A two-step seeding procedure initialises the shape parameters by min-max nearest-neighbour search over the scale-free L-ratios in the Burr_InitValues lookup table, and the scale is then derived analytically from the sample first L-moment and the matched shapes' unit-scale L-moment. The mean exists only when \(\theta < 1\), imposing an effective upper bound on the tail index during optimisation. Zero values below zero_threshold may be excluded via ignore_zeros.

Usage

fitlm_burr(x, ignore_zeros = FALSE, zero_threshold = 0.01, order = c(1:5))

Arguments

x: An xts object containing the time series data.
ignore_zeros: Logical. If TRUE, values below zero_threshold are excluded. Default FALSE.
zero_threshold: Numeric. Threshold below which values are treated as zero. Default 0.01.
order: Integer vector of L-moment orders matched by the optimiser. Default 1:5.

Value

A list with elements Distribution, Param (named list of fitted scale, shape1, shape2), TheorLMom (theoretical L-moments), DataLMom (sample L-moments), and GoF (goodness-of-fit metrics).

Examples

x <- xts::xts(rburr(365, scale = 1.5, shape1 = 2, shape2 = 0.3),
              order.by = as.Date("2020-01-01") + 0:364)
if (FALSE) { # \dontrun{
fit <- fitlm_burr(x)
fit$Param
} # }