| Title: | 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. |
| Authors: | Okechukwu J. Obulezi [aut, cre] (ORCID: <https://orcid.org/0000-0002-7753-1868>) |
| Maintainer: | Okechukwu J. Obulezi <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.1.0 |
| Built: | 2026-10-09 11:28:29 UTC |
| Source: | https://github.com/cran/fuzzyurn |
Computes tail upper bound P(|X_n - E[X_n]| >= epsilon).
fuzzyurn_bound(epsilon, n, M_mu = 1)fuzzyurn_bound(epsilon, n, M_mu = 1)
epsilon |
Numeric. Deviation threshold. |
n |
Integer. Sample draw size. |
M_mu |
Numeric. Upper bound on fuzzy membership measure. Default is 1.0. |
Upper bound probability value.
Computes discrete drift b_N(y, tau) and diffusion a_N(y, tau) operators.
fuzzyurn_generator(y, weights, mu_unobserved)fuzzyurn_generator(y, weights, mu_unobserved)
y |
Numeric. Scaled fuzzy state y in [0, 1]. |
weights |
Vector. Unobserved element weights. |
mu_unobserved |
Vector. Fuzzy membership values for unobserved elements. |
List containing drift 'b' and diffusion 'a'.
Simulates continuous Itô Diffusion Limit process dY(tau).
fuzzyurn_sde(N, y0, T_max = 1, steps = 1000, drift_fn, diff_fn)fuzzyurn_sde(N, y0, T_max = 1, steps = 1000, drift_fn, diff_fn)
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). |
Data frame with time 'tau' and continuous trajectory 'Y'.
Computes exact invariant potential landscape density p_infinity(y).
fuzzyurn_stationary(y_grid, N, drift_fn, diff_fn)fuzzyurn_stationary(y_grid, N, drift_fn, diff_fn)
y_grid |
Vector. Discretized grid on [0, 1]. |
N |
Integer. Population size. |
drift_fn |
Function b(y). |
diff_fn |
Function a(y). |
Vector of normalized density values over 'y_grid'.
Simulates discrete trajectory of fuzzy success accumulation under dynamic state-dependent weights.
rfuzzyurn(n, Z, mu, w0, gamma_kernel = NULL, delta = NULL)rfuzzyurn(n, Z, mu, w0, gamma_kernel = NULL, delta = NULL)
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). |
List containing selected indices, trajectory of fuzzy mass X_t, and final mass.