Multi-Distribution Fitting

Fits a list of candidate distributions to a single time series via the L-moments method. Each candidate is dispatched to its corresponding fitlm_* function, which returns the fitted parameters, theoretical L-moments, sample L-moments, and six goodness-of-fit metrics (MLE, CM, KS, MSEquant, DiffOfMax, MeanDiffOf10Max). When diagnostic_plots = TRUE, Q-Q and P-P comparison plots are produced with all candidates overlaid on a single panel, using colour-coded points and a 1:1 reference line. An empty series or one with all values below the zero threshold after filtering returns an NA placeholder for every candidate.

Usage

fitlm_multi(
  ts,
  candidates,
  ignore_zeros = FALSE,
  zero_threshold = 0.01,
  diagnostic_plots = TRUE,
  order = NULL
)

Arguments

ts

An xts object containing the time series data.

candidates

A character vector of distribution names to fit.

ignore_zeros

A logical value, if TRUE zeros will be ignored. Default is FALSE.

zero_threshold

The threshold below which values are considered zero. Default is 0.01.

diagnostic_plots

A logical value controlling whether Q-Q and P-P diagnostic plots are produced. Default is TRUE.

order

Optional named list mapping a candidate name to the vector of L-moment orders matched by its optimiser, e.g. list(gengamma = 1:5, expweibull = 1:3). Only the numerically-fitted distributions (gengamma, gengamma_loc, burr, dagum, expweibull) accept it; entries for other candidates are ignored. Candidates not named keep their own default. Default NULL (every distribution uses its default).

Value

A list with components parameter_list (a named list of per-candidate fit results, each containing Distribution, Param, TheorLMom, DataLMom, and GoF), GoF_summary (a data frame of GoF metrics with candidates as columns), and, when diagnostic_plots = TRUE, diagnostics (a combined Q-Q and P-P panel), QQplot, and PPplot.

Examples

# Daily precipitation-like data: gamma-distributed with zeros
x <- xts::xts(rgamma(365, shape = 0.8, scale = 3),
         order.by = seq.Date(as.Date("2020-01-01"), by = "day", length.out = 365))
x[sample(1:365, 100)] <- 0

candidates <- c('exp', 'gamma3', 'weibull')
fits <- fitlm_multi(x, candidates = candidates, ignore_zeros = TRUE)
fits$diagnostics

fits$GoF_summary
#>                         exp       gamma3      weibull
#> MLE             508.0435026 619.46052289 465.53313018
#> CM                0.2072796   0.03202756   0.01546384
#> KS                0.1145038   0.04504153   0.02364419
#> MSEquant          0.1094933   0.02714489   0.03487785
#> DiffOfMax        -8.5180175   3.02488286   7.04031773
#> MeanDiffOf10Max   1.2045456   0.55540758   0.60125379