fit_dist: Unified Parameter Estimation for Probability Distributions

In dendrometry: Forest Estimations and Dendrometric Computations

Unified Parameter Estimation for Probability Distributions

Description

Estimates parameters of probability distributions using various methods: Maximum Likelihood (MLE), Maximum Product Spacing (MPS), or Method of Moments (MOM).

Usage

fit_dist(
  data,
  dist = "normal",
  method = "mle",
  start = NULL,
  lower = NULL,
  upper = NULL,
  optim_method = "Nelder-Mead",
  custom_functions = NULL,
  tol_spacing = 1e-16,
  tol_param = 1e-06,
  ties_method = "cheng_amin",
  ...
)

Arguments

data	numeric vector of observed data.
dist	character string specifying the distribution. Options include: "normal", "exponential", "gamma", "weibull", "weibull3", "lognormal", "lognormal3", "beta", or "custom".
method	character string specifying estimation method. Options: "mle" (Maximum Likelihood - default), "mps" (Maximum Product Spacing), "mom" (Method of Moments).
start	named list or numeric vector of initial parameter values. Required for "custom" distributions with "mps" or "mle" methods.
lower	named list or numeric vector of lower bounds for parameters.
upper	named list or numeric vector of upper bounds for parameters.
optim_method	optimization method passed to optim. Default is "Nelder-Mead".
custom_functions	list containing custom distribution functions (for dist="custom"): pdf: probability density function f(x, params) (for MLE and ties correction) cdf: cumulative distribution function F(x, params) (for MPS) param_names: character vector of parameter names start_fn: function to compute starting values (optional)
tol_spacing	numeric tolerance for spacings/densities to avoid log(0). Default is 1e-16.
tol_param	numeric tolerance for parameter lower bounds. Default is 1e-6.
ties_method	character string for handling ties in MPS. Options: "cheng_amin" (default - Cheng & Amin 1983), "none", "cheng_stephens" (Cheng & Stephens 1989). Only applicable when method = "mps".
...	Additional arguments passed to optim.

Value

A list with class "fit_dist" containing:

estimate	Named vector of parameter estimates
vcov	Variance-covariance matrix (for mps/mle)
se	Standard errors (for mps/mle)
loglik	Log-likelihood value
aic	Akaike Information Criterion
bic	Bayesian Information Criterion
objective	Maximum value of objective function (logspacing for mps, loglik for mle)
ks_statistic	Kolmogorov-Smirnov test statistic
ks_pvalue	Kolmogorov-Smirnov test p-value
convergence	Convergence code from optim (0 indicates success)
message	Convergence message from optim
data	Original data (sorted)
dist	Distribution name
method	Estimation method used
n	Sample size
k	Number of parameters
tol_spacing	Tolerance used for spacings/densities
tol_param	Tolerance used for parameter bounds
ties_method	Ties correction method (for MPS only)

References

Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B, 45(3), 394-403.

Cheng, R. C. H., & Stephens, M. A. (1989). A goodness-of-fit test using Moran's statistic with estimated parameters. Biometrika, 76(2), 385-392.

Examples

# MLE estimation (default)
set.seed(123)
x <- rweibull(100, shape = 2.5, scale = 1.5)
fit1 <- fit_dist(x, dist = "weibull")
print(fit1)

# MPS estimation with Cheng-Amin ties correction
fit2 <- fit_dist(x, dist = "weibull", method = "mps")

# L-Moments estimation (under development)
# fit3 <- fit_dist(x, dist = "weibull", method = "lm")

# Method of Moments
fit4 <- fit_dist(x, dist = "weibull", method = "mom")

# Compare fits
cat("AIC - MLE:", fit1$aic, "MPS:", fit2$aic, "\n")

dendrometry documentation built on Nov. 5, 2025, 5:23 p.m.