Determines Optimum Strata Boundaries (OSB) and Optimum Sample
Sizes (OSS) for univariate stratified sampling designs under Neyman
allocation. The stratification variable is described by a best-fitting
parametric distribution, selected automatically by AIC from a set of
continuous families (normal, log-normal, gamma, Weibull, exponential,
Cauchy, uniform, Pareto, triangular and right-triangular), and the
optimum boundaries are obtained by minimising the Neyman objective.
Version 2.0 keeps the Dynamic Programming (DP) solver of Reddy and Khan
(2020), which is globally optimal for the fitted distribution, as the
default. It adds two fast derivative-free solvers, a multi-start
'COBYLA' solver and a two-phase global solver that couples 'DIRECT-L'
with 'BOBYQA' refinement, and an exact solver that runs dynamic
programming on the sorted data and returns the partition with the
smallest empirical Neyman cost. It also provides cost-constrained
allocation with unequal per-stratum costs, a design-efficiency comparison
(compare_designs), two- and three-dimensional and interactive
visualisations, solution-quality diagnostics (a Cauchy-Schwarz optimality
gap and KKT first-order residuals for the derivative-free solvers) and a
self-contained 'shiny' application, while remaining backward compatible
with the strata.data() and strata.distr() interface of version 1.x. The
methodology follows Khan et al. (2008)
< https://www150.statcan.gc.ca/n1/pub/12-001-x/2008002/article/10761-eng.pdf>,
Reddy and Khan (2018)