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likelihood.model - Likelihood-Based Statistical Inference in the Fisherian Tradition

Facilitates building likelihood models in the Fisherian tradition following Richard Royall (1997, ISBN:978-0412044113) "Statistical Evidence: A Likelihood Paradigm". Defines generic methods for working with likelihoods (loglik(), score(), hess_loglik(), fim()) and provides functions for pure likelihood-based inference (support(), relative_likelihood(), likelihood_interval(), profile_loglik()).

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fisher-information-matrixlikelihoodmaximum-likelihood-estimationsampling-distribution

7.54 score 2 stars 6 dependents 13 scripts 516 downloads

algebraic.mle - Algebraic Maximum Likelihood Estimators

The maximum likelihood estimator (MLE) is a technology: under regularity conditions, any MLE is asymptotically normal with variance given by the inverse Fisher information. This package exploits that structure by defining an algebra over MLEs. Compose independent estimators into joint MLEs via block-diagonal covariance ('joint'), optimally combine repeated estimates via inverse-variance weighting ('combine'), propagate transformations via the delta method ('rmap'), and bridge to distribution algebra via conversion to normal or multivariate normal objects ('as_dist'). Supports asymptotic ('mle', 'mle_numerical') and bootstrap ('mle_boot') estimators with a unified interface for inference: confidence intervals, standard errors, AIC, Fisher information, and predictive intervals. For background on maximum likelihood estimation, see Casella and Berger (2002, ISBN:978-0534243128). For the delta method and variance estimation, see Lehmann and Casella (1998, ISBN:978-0387985022).

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7.50 score 1 stars 8 dependents 73 scripts 600 downloads

algebraic.dist - Algebra over Probability Distributions

Provides an algebra over probability distributions enabling composition, sampling, and automatic simplification to closed forms. Supports normal, exponential, gamma, Weibull, chi-squared, uniform, beta, log-normal, Poisson, multivariate normal, empirical, and mixture distributions with algebraic operators (addition, subtraction, multiplication, division, power, exp, log, min, max) that automatically simplify when mathematical identities apply. Includes closed-form MVN conditioning (Schur complement), affine transformations, mixture marginals/conditionals (Bayes rule), and limiting distribution builders (CLT, LLN, delta method). Uses S3 classes for distributions and R6 for support objects.

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data-sciencedistributionsmonte-carloprobabilitystatistics

7.04 score 1 stars 11 dependents 55 scripts 632 downloads

flexhaz - Dynamic Failure Rate Distributions for Survival Analysis

Flexible framework for specifying survival distributions through their hazard (failure rate) functions. Define arbitrary time-varying hazard functions to model complex failure patterns including bathtub curves, proportional hazards with covariates, and other non-standard hazard behaviors. Provides automatic computation of survival, CDF, PDF, quantiles, and sampling. Implements the likelihood model interface for maximum likelihood estimation with right-censored and left-censored survival data.

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automatic-differentiationcensored-datafailure-ratehazard-functionlikelihood-functionsmlereliabilitystatistical-inferencesurvival-analysis

6.90 score 3 dependents 39 scripts 517 downloads

maskedcauses - Likelihood Models for Systems with Masked Component Cause of Failure

Maximum likelihood estimation for series systems where the component cause of failure is masked. Implements analytical log-likelihood, score, and Hessian functions for exponential, homogeneous Weibull, and heterogeneous Weibull component lifetimes under masked cause conditions (C1, C2, C3). Supports exact, right-censored, left-censored, and interval-censored observations via composable observation functors. Provides random data generation, model fitting, and Fisher information for asymptotic inference. See Lin, Loh, and Bai (1993) <doi:10.1109/24.257799> and Craiu and Reiser (2006) <doi:10.1111/j.1541-0420.2005.00498.x>.

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censoringmasked-datamaximum-likelihoodreliabilityseries-systemsstatisticssurvival-analysis

6.13 score 1 stars 1 dependents 16 scripts 523 downloads

compositional.mle - Compositional Maximum Likelihood Estimation

Provides composable optimization strategies for maximum likelihood estimation (MLE). Solvers are first-class functions that combine via sequential chaining, parallel racing, and random restarts. Implements gradient ascent, Newton-Raphson, quasi-Newton (BFGS), and derivative-free methods with support for constrained optimization and tracing. Returns 'mle' objects compatible with 'algebraic.mle' for downstream analysis. Methods based on Nocedal J, Wright SJ (2006) "Numerical Optimization" <doi:10.1007/978-0-387-40065-5>.

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composabledslestimationmaximum-likelihoodmlemle-estimationnumerical-methodsoptimizationstatistics

5.88 score 1 dependents 9 scripts 485 downloads

serieshaz - Series System Distributions from Dynamic Failure Rate Components

Compose multiple dynamic failure rate distributions into series system distributions where the system hazard equals the sum of component hazards. Supports hazard, survival, cumulative distribution function, density, sampling, and maximum likelihood estimation fitting via the dfr_dist() class from 'flexhaz'. Series distributions implement the 'dist.structure' protocol so structural queries (phi, min_paths, min_cuts, system_signature, structural importance, reliability, dual) and the importance measures from 'dist.structure' work directly on serieshaz objects. Methods for series system reliability follow Barlow and Proschan (1975, ISBN:0898713692).

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hazard-functionmlereliabilityseries-systemssurvival-analysis

5.56 score 1 dependents 12 scripts 498 downloads

likelihood.contr - Likelihood Contribution Models for Heterogeneous Observation Types

Constructs likelihood models from heterogeneous observation types by composing named contributions. Each observation type (exact, left-censored, right-censored, interval-censored, or custom) contributes independently to the total log-likelihood, which is summed under an i.i.d. assumption. Provides contr_name() for standard R distributions and contr_fn() for user-defined contributions, composed via likelihood_contr() into objects compatible with the likelihood.model inference framework.

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5.32 score 5 scripts 470 downloads

dist.structure - Structured Random Variables for Reliability System Distributions

Extends the 'algebraic.dist' distribution algebra to random variables with internal structure: coherent reliability systems decomposed into components arranged by a structure function (series, parallel, k-out-of-n, bridge, and arbitrary topologies via minimal path sets). Every 'dist_structure' object is a 'dist', so the full distribution algebra (mean, vcov, sampler, surv, cdf) works automatically via default methods that compose component-level distributions through the topology. Adds structural queries: structure function evaluation, minimal path and cut sets, system signature, critical states, dual, Birnbaum structural importance, and system reliability. Topology shortcut constructors (series_dist, parallel_dist, kofn_dist, bridge_dist) produce ready-to-use dists from component dists and a chosen structure.

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5.10 score 4 dependents 10 scripts

hypothesize - Consistent API for Hypothesis Testing

Provides a consistent API for hypothesis testing built on principles from 'Structure and Interpretation of Computer Programs': data abstraction, closure (combining tests yields tests), and higher-order functions (transforming tests). Implements z-tests, Wald tests, likelihood ratio tests, Fisher's method for combining p-values, and multiple testing corrections. Designed for use by other packages that want to wrap their hypothesis tests in a consistent interface.

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hypothesis-testinglikelihoodlikelihood-ratio-teststatisticswald-test

4.90 score 2 stars 6 scripts 490 downloads

nabla - Exact Derivatives via Automatic Differentiation

Exact automatic differentiation for R functions. Provides a composable derivative operator D that computes gradients, Hessians, Jacobians, and arbitrary-order derivative tensors at machine precision. D(D(f)) gives Hessians, D(D(D(f))) gives third-order tensors for skewness of maximum likelihood estimators, and so on to any order. Works through any R code including loops, branches, and control flow.

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automatic-differentiationderivative-operatorgradienthessianhigher-order-derivativesjacobianmle

4.88 score 8 scripts 127 downloads

dist.structure - Structured Random Variables for Reliability System Distributions

Extends the 'algebraic.dist' distribution algebra to random variables with internal structure: coherent reliability systems decomposed into components arranged by a structure function (series, parallel, k-out-of-n, bridge, and arbitrary topologies via minimal path sets). Every 'dist_structure' object is a 'dist', so the full distribution algebra (mean, vcov, sampler, surv, cdf) works automatically via default methods that compose component-level distributions through the topology. Adds structural queries: structure function evaluation, minimal path and cut sets, system signature, critical states, dual, Birnbaum structural importance, and system reliability. Topology shortcut constructors (series_dist, parallel_dist, kofn_dist, bridge_dist) produce ready-to-use dists from component dists and a chosen structure.

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4.66 score 4 dependents 11 scripts

maskedhaz - Masked-Cause Likelihood Models for Series Systems with Arbitrary Hazard Components

Likelihood-based inference for series systems with masked component cause of failure, using arbitrary dynamic failure rate component distributions. Computes log-likelihood, score, Hessian, and maximum likelihood estimates for masked data satisfying conditions C1, C2, C3 under general component hazard functions. Implements the 'series_md' protocol defined in the 'maskedcauses' package.

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censored-datahazard-functionlikelihood-functionsmasked-datamlereliabilityseries-systemssurvival-analysis

4.60 score 6 scripts 505 downloads

kofn - Maximum Likelihood Estimation for k-out-of-n System Data

Maximum likelihood estimation of component lifetime parameters from system-level observations of k-out-of-n systems. Supports exponential and Weibull component distributions under multiple observation schemes: Scheme 0 (system lifetime only), Scheme 1 (periodic inspection), and Scheme 2 (complete monitoring). Provides an EM algorithm for Weibull parallel systems and Fisher information comparison across schemes. The k-out-of-n framework unifies series (k=1) and parallel (k=m) systems as a censoring problem on component lifetimes. Conforms to the 'likelihood.model' generics and returns fitted objects compatible with 'algebraic.mle'. The data-generating process and topology infrastructure (system survival, density, signature, structure function, importance measures) are delegated to the 'dist.structure' package; kofn focuses exclusively on inference for the k-out-of-n family.

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4.39 score 9 scripts

femtograd - Automatic Differentiation for Statistical Computing

Provides automatic differentiation via reverse-mode AD (backpropagation) for first-order gradients and forward-over-reverse AD for Hessian computation. Includes log-likelihood functions for exponential family distributions (normal, exponential, Poisson, binomial, gamma, beta, negative binomial, Weibull, Pareto), MLE optimization via fit() with base R generics (coef, vcov, confint, logLik, AIC/BIC), hypothesis testing (likelihood ratio, Wald), profile likelihood, bootstrap inference, and model diagnostics. Designed for pedagogy and modern statistics rather than large-scale ML.

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automatic-differentiationbackpropagationmaximum-likelihoodhessianstatisticscomputational-graphinferencepedagogy

4.18 score 1 stars 12 scripts