| Type: | Package |
| Title: | Generalized Non-Central Fuzzy Dynamic Hypergeometric Processes |
| Version: | 0.1.0 |
| Description: | Implements Generalized Non-Central Fuzzy Dynamic Hypergeometric Processes. Includes discrete Markov chain sampling under dynamic weight decay and continuous fuzzy membership maps, infinitesimal generator evaluation, weak convergence to Itô diffusion SDEs, numerical solutions for Fokker-Planck PDEs, stationary Gibbs-Boltzmann densities, and Azuma-Hoeffding concentration bounds. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| Imports: | stats |
| Suggests: | deSolve, graphics, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| Config/roxygen2/version: | 8.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2026-08-19 22:20:47 UTC; Dr. O. J. Obulezi |
| Author: | Okechukwu J. Obulezi
 [aut, cre] |
| Maintainer: | Okechukwu J. Obulezi <oj.obulezi@unizik.edu.ng> |
| Repository: | CRAN |
| Date/Publication: | 2026-08-21 13:30:20 UTC |
fuzzyurn: Generalized Non-Central Fuzzy Dynamic Hypergeometric Processes
Description
Implements Generalized Non-Central Fuzzy Dynamic Hypergeometric Processes. Includes discrete Markov chain sampling under dynamic weight decay and continuous fuzzy membership maps, infinitesimal generator evaluation, weak convergence to Itô diffusion SDEs, numerical solutions for Fokker-Planck PDEs, stationary Gibbs-Boltzmann densities, and Azuma-Hoeffding concentration bounds.
Author(s)
Maintainer: Okechukwu J. Obulezi oj.obulezi@unizik.edu.ng (ORCID)
Authors:
Okechukwu J. Obulezi oj.obulezi@unizik.edu.ng (ORCID)
Non-Asymptotic Azuma-Hoeffding Concentration Bound
Description
Computes tail upper bound P(|X_n - E[X_n]| >= epsilon).
Usage
fuzzyurn_bound(epsilon, n, M_mu = 1)
Arguments
epsilon |
Numeric. Deviation threshold. |
n |
Integer. Sample draw size. |
M_mu |
Numeric. Upper bound on fuzzy membership measure. Default is 1.0. |
Value
Upper bound probability value.
Infinitesimal Generator, Drift, and Diffusion Functions
Description
Computes discrete drift b_N(y, tau) and diffusion a_N(y, tau) operators.
Usage
fuzzyurn_generator(y, weights, mu_unobserved)
Arguments
y |
Numeric. Scaled fuzzy state y in [0, 1]. |
weights |
Vector. Unobserved element weights. |
mu_unobserved |
Vector. Fuzzy membership values for unobserved elements. |
Value
List containing drift 'b' and diffusion 'a'.
Diffusion Limit SDE Simulator
Description
Simulates continuous Itô Diffusion Limit process dY(tau).
Usage
fuzzyurn_sde(N, y0, T_max = 1, steps = 1000, drift_fn, diff_fn)
Arguments
N |
Integer. Total population size. |
y0 |
Numeric. Initial state y(0). |
T_max |
Numeric. Time horizon. |
steps |
Integer. Number of Euler-Maruyama discretization steps. |
drift_fn |
Function b(y, tau). |
diff_fn |
Function a(y, tau). |
Value
Data frame with time 'tau' and continuous trajectory 'Y'.
Stationary Invariant Gibbs-Boltzmann Density
Description
Computes exact invariant potential landscape density p_infinity(y).
Usage
fuzzyurn_stationary(y_grid, N, drift_fn, diff_fn)
Arguments
y_grid |
Vector. Discretized grid on [0, 1]. |
N |
Integer. Population size. |
drift_fn |
Function b(y). |
diff_fn |
Function a(y). |
Value
Vector of normalized density values over 'y_grid'.
Generalized Non-Central Fuzzy Dynamic Sampling
Description
Simulates discrete trajectory of fuzzy success accumulation under dynamic state-dependent weights.
Usage
rfuzzyurn(n, Z, mu, w0, gamma_kernel = NULL, delta = NULL)
Arguments
n |
Integer. Number of draws (sample size). |
Z |
Matrix. Latent feature matrix (N x d) for finite population universe. |
mu |
Function or Vector. Fuzzy membership mapping mu(z) in [0, 1]. |
w0 |
Function or Vector. Baseline intrinsic attraction weights w0(z) > 0. |
gamma_kernel |
Function. Symmetric interaction kernel gamma(z_i, z_j). |
delta |
Vector or Matrix. Depletion/decay rates delta_i(t). |
Value
List containing selected indices, trajectory of fuzzy mass X_t, and final mass.