Package 'HiddenTrunc'

Hidden Truncation Probability Distributions and Inference

Description

Probability functions, simulation, likelihood inference and Bayesian computation for hidden-truncation models.

Details

The initial implementation contains upper hidden-truncated Pareto IV and two-sided hidden-truncated Arnold-Strauss exponential models, plus generic hidden-truncation utilities.

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Hidden-truncated Arnold-Strauss exponential distribution

Description

Functions for the two-sided hidden-truncated Arnold-Strauss bivariate exponential construction.

Usage

dhtbexp(x, a, b, c, d1, d2, log = FALSE)
phtbexp(q, a, b, c, d1, d2,
        lower.tail = TRUE, log.p = FALSE)
qhtbexp(p, a, b, c, d1, d2)
rhtbexp(n, a, b, c, d1, d2)

Arguments

x	Numeric evaluation points for density.
q	Numeric quantiles for the CDF.
p	Numeric probabilities for the quantile function.
n	Number of generated observations.
a	Positive exponential rate parameter.
b	Positive exponential rate parameter.
c	Positive interaction parameter.
d1	Lower hidden truncation bound, non-negative.
d2	Upper hidden truncation bound, strictly larger than d1.
log	Logical; if TRUE, return log-density.
lower.tail	Logical; use the lower tail when TRUE.
log.p	Logical; return log-probabilities when TRUE.

Value

Numeric vector of density, CDF, quantile, or random values.

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Hidden-truncated Pareto IV distribution

Description

Density, cumulative distribution, quantile, random generation, and hazard functions for the hidden-truncated Pareto IV model.

Usage

dhtp4(x, alpha, sigma, theta, delta1, delta2, log = FALSE)
phtp4(q, alpha, sigma, theta, delta1, delta2,
      lower.tail = TRUE, log.p = FALSE)
qhtp4(p, alpha, sigma, theta, delta1, delta2,
      lower.tail = TRUE, log.p = FALSE)
rhtp4(n, alpha, sigma, theta, delta1, delta2)
hhtp4(x, alpha, sigma, theta, delta1, delta2)

Arguments

x	Numeric evaluation points (for the density or hazard).
q	Numeric quantiles for the CDF.
p	Numeric probabilities for the quantile function.
n	Non-negative number of observations to generate.
alpha	Positive Pareto IV tail-shape parameter.
sigma	Positive scale parameter.
theta	Positive selection parameter.
delta1	Positive power parameter.
delta2	Positive parameter controlling the hidden-selection transform.
log	Logical; return logarithm of the density.
lower.tail	Logical; return lower-tail probabilities when TRUE.
log.p	Logical; probabilities are on the logarithmic scale when TRUE.

Value

Numeric vector of evaluated values, quantiles, simulated observations, or hazards.

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Inference for hidden-truncated exponential distribution

Description

Maximum likelihood estimation, likelihood evaluation, and Bayesian sampling for the two-sided hidden-truncated exponential model.

Usage

fit_htbexp(x, start = NULL, control = list(maxit = 5000))
loglik_htbexp(par, x, transformed = FALSE)
bayes_htbexp(x, niter = 10000, burn = 2000, thin = 5,
             init = c(a = 1, b = 1, c = 0.2, d1 = 0.1, d2 = 1),
             gamma_shape = c(1, 1, 1),
             gamma_rate = c(1, 1, 1),
             delta = max(10, init[5] * 2),
             proposal_sd = rep(0.12, 5), seed = NULL)

Arguments

x	Positive numeric observations.
start	Optional five-parameter starting vector for MLE.
control	Optimization control list.
par	Parameter vector for the log-likelihood.
transformed	Logical; use transformed optimization coordinates when TRUE.
niter	Total number of MCMC iterations.
burn	Number of initial draws to discard.
thin	Thinning interval.
init	Initial positive five-parameter MCMC state with ordered truncation bounds.
gamma_shape	Shape hyperparameters for three Gamma priors.
gamma_rate	Rate hyperparameters for three Gamma priors.
delta	Upper MCMC truncation bound, exceeding the initial d2.
proposal_sd	Standard deviations for five Gaussian random-walk proposals.
seed	Optional random seed.

Value

A fitted-model object, numeric log-likelihood, or a list containing posterior draws and diagnostics.

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Inference and simulation for hidden-truncated Pareto IV

Description

Maximum likelihood fitting, log-likelihood, likelihood-ratio comparison, and Monte Carlo simulation under the Pareto IV hidden-truncation model.

Usage

fit_htp4(x, start = NULL, method = "L-BFGS-B",
          control = list(maxit = 3000), hessian = TRUE,
          delta2_fixed = 3, n_starts = 5)
loglik_htp4(par, x, transformed = FALSE)
lrt_htp4(x, fit = NULL, B = 0, seed = NULL)
sim_htp4(n = c(50, 100, 200), R = 100,
         par = c(alpha = 3, sigma = 2, theta = 1,
                 delta1 = 2, delta2 = 3), seed = NULL)

Arguments

x	Positive numeric sample.
start	Optional positive five-parameter starting vector for optimization.
method	Optimization algorithm passed to the fitter.
control	List of optimization control parameters.
hessian	Logical; whether to compute a numerical Hessian.
delta2_fixed	Positive value fixed for the non-identifiable delta2 coordinate.
n_starts	Number of optimization starting points.
par	Five-parameter model vector; for loglik_htp4, optionally on log scale.
transformed	Logical; whether par contains log-transformed parameters.
fit	Previously fitted htfit model; if NULL a model is fitted.
B	Number of bootstrap replications for the likelihood ratio test.
seed	Optional random seed.
n	Vector of simulated sample sizes.
R	Number of simulation replications.

Value

fit_htp4 returns an htfit object; loglik_htp4 returns a log-likelihood; lrt_htp4 returns a test object; sim_htp4 returns a simulation summary.

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Floyd River data and Pareto IV model assessments

Description

Access Floyd River annual discharge data; compute a Kolmogorov-Smirnov discrepancy with optional parametric bootstrap; or obtain percentile bootstrap confidence intervals.

Usage

floyd_river()
gof_htp4(x, fit = NULL, B = 0, seed = NULL)
boot_ci_htp4(x, fit = NULL, B = 499,
             level = 0.95, seed = NULL)

Arguments

x	Positive numeric sample used to fit or assess the model.
fit	Optional htfit object. If NULL, fit_htp4 is called.
B	Number of parametric bootstrap replicates. Zero disables the bootstrap in gof_htp4.
seed	Optional seed for reproducibility.
level	Confidence level strictly between zero and one.

Value

floyd_river returns a numeric vector; gof_htp4 returns an htgof object; boot_ci_htp4 returns a data frame of confidence bounds.

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Generic hidden-truncation utilities

Description

Generic construction of hidden-truncated densities and inference using an explicit baseline density and selection probability.

Usage

ht_density(x, fx, selection_prob, normalizer, log = FALSE, ...)
dhidden(x, fx, selection_prob, normalizer, ...)
phidden(q, fx, selection_prob, normalizer, lower = 0, ...)
rhidden(n, fx, selection_prob, normalizer,
        lower = 0, upper_start = 1, ...)
ht_loglik(par, x, density, ...)
ht_mle(par, x, loglik, transform = exp, ...)

Arguments

x	Numeric evaluation points or observed data, depending on the function.
q	Quantiles at which to evaluate the CDF.
n	Number of random observations.
fx	Callable function for the baseline density.
selection_prob	Callable function for conditional selection probabilities.
normalizer	Positive normalization probability for the selection model.
log	Logical; return the log-density when TRUE.
lower	Lower integration/inversion bound.
upper_start	Positive starting upper bound for inverse CDF search.
par	Parameter vector for optimization or likelihood evaluation.
density	Density function accepting observations and a parameter vector.
loglik	Log-likelihood function for maximum likelihood estimation.
transform	Transformation mapping optimization coordinates to parameters.
...	Additional arguments passed to the density, selection, or likelihood functions.

Value

Density/CDF values, random observations, log-likelihood, or an optimization result, as appropriate.

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