Rename automatic_differentiation vignette, rebuild docs site

Rename vignette to custom_derivatives.Rmd to match its actual content
("Custom Derivatives for Maximum Likelihood Estimation"). Update all
cross-references in vignettes, README, _pkgdown.yml, and CLAUDE.md.
Rebuild pkgdown site with refreshed navbar and article structure.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: queelius

CLAUDE.md

@@ -254,7 +254,7 @@ Cox-Snell residuals should follow Exp(1) if model is correct.
 - `vignettes/failure_rate.Rmd`: Hazard-based modeling deep dive
 - `vignettes/custom_distributions.Rmd`: How to create custom distributions
 - `vignettes/reliability_engineering.Rmd`: Real-world applications
-- `vignettes/automatic_differentiation.Rmd`: Custom derivatives tutorial
+- `vignettes/custom_derivatives.Rmd`: Custom derivatives tutorial
 
 ## Common Pitfalls
 

README.Rmd

@@ -188,7 +188,7 @@ ll(df, par = c(0.5))
 
 - [Dynamic Failure Rate Distributions](https://queelius.github.io/dfr.dist/articles/failure_rate.html) - Mathematical foundations
 - [Creating Custom Distributions](https://queelius.github.io/dfr.dist/articles/custom_distributions.html) - The three-level optimization paradigm
-- [Custom Derivatives for MLE](https://queelius.github.io/dfr.dist/articles/automatic_differentiation.html) - Analytical score and Hessian functions
+- [Custom Derivatives for MLE](https://queelius.github.io/dfr.dist/articles/custom_derivatives.html) - Analytical score and Hessian functions
 
 **Reference:**
 

README.md

@@ -1,65 +1,64 @@
+---
+output:
+  github_document:
+    toc: true
+---
 
 <!-- README.md is generated from README.Rmd. Please edit that file -->
 
+
+
 # dfr.dist
 
 <!-- badges: start -->
-
 [![R-CMD-check](https://github.com/queelius/dfr.dist/workflows/R-CMD-check/badge.svg)](https://github.com/queelius/dfr.dist/actions)
 <!-- badges: end -->
 
 **Dynamic Failure Rate Distributions for Survival Analysis**
 
-Capacitors that wear out faster than any Weibull can describe. Software
-systems with bathtub-shaped crash rates. Post-surgical patients whose
-risk drops sharply, then slowly climbs again. Standard parametric
-survival families cannot express these hazard patterns — but `dfr.dist`
-can.
+Capacitors that wear out faster than any Weibull can describe. Software systems
+with bathtub-shaped crash rates. Post-surgical patients whose risk drops sharply,
+then slowly climbs again. Standard parametric survival families cannot express
+these hazard patterns — but `dfr.dist` can.
 
-**Write the hazard function you need — any R function of time and
-parameters — and the package derives everything else**: survival curves,
-CDFs, densities, quantiles, sampling, log-likelihoods, MLE fitting, and
-residual diagnostics.
+**Write the hazard function you need — any R function of time and parameters —
+and the package derives everything else**: survival curves, CDFs, densities,
+quantiles, sampling, log-likelihoods, MLE fitting, and residual diagnostics.
 
 ## Why dfr.dist?
 
-| Feature                    | dfr.dist                             | survival     | flexsurv |
-|----------------------------|--------------------------------------|--------------|----------|
-| Custom hazard functions    | **Yes**                              | No           | Limited  |
-| Built-in distributions     | Exp, Weibull, Gompertz, Log-logistic | Weibull, Exp | Many     |
-| User-supplied derivatives  | **score + Hessian**                  | No           | No       |
-| Censoring support          | Right + Left                         | Right        | Right    |
-| Model diagnostics          | Cox-Snell, Martingale, Q-Q           | Limited      | Limited  |
-| Likelihood model interface | **Full**                             | Basic        | Partial  |
+| Feature | dfr.dist | survival | flexsurv |
+|---------|----------|----------|----------|
+| Custom hazard functions | **Yes** | No | Limited |
+| Built-in distributions | Exp, Weibull, Gompertz, Log-logistic | Weibull, Exp | Many |
+| User-supplied derivatives | **score + Hessian** | No | No |
+| Censoring support | Right + Left | Right | Right |
+| Model diagnostics | Cox-Snell, Martingale, Q-Q | Limited | Limited |
+| Likelihood model interface | **Full** | Basic | Partial |
 
 ## Features
 
-- **Flexible hazard specification**: Define any hazard function h(t,
-  par, …)
-- **Built-in distributions**: Exponential, Weibull, Gompertz,
-  Log-logistic with optimized implementations
-- **Complete distribution interface**: hazard, survival, CDF, PDF,
-  quantiles, sampling
+- **Flexible hazard specification**: Define any hazard function h(t, par, ...)
+- **Built-in distributions**: Exponential, Weibull, Gompertz, Log-logistic with optimized implementations
+- **Complete distribution interface**: hazard, survival, CDF, PDF, quantiles, sampling
 - **Likelihood model support**: Log-likelihood, score, Hessian for MLE
-- **Custom derivatives**: Supply analytical score and Hessian functions,
-  or let the package fall back to numerical differentiation via numDeriv
+- **Custom derivatives**: Supply analytical score and Hessian functions, or let the package fall back to numerical differentiation via numDeriv
 - **Model diagnostics**: Residuals (Cox-Snell, Martingale) and Q-Q plots
-- **Censoring support**: Handle exact, right-censored, and left-censored
-  survival data
-- **Ecosystem integration**: Works with `algebraic.dist`,
-  `likelihood.model`, `algebraic.mle`
+- **Censoring support**: Handle exact, right-censored, and left-censored survival data
+- **Ecosystem integration**: Works with `algebraic.dist`, `likelihood.model`, `algebraic.mle`
 
 ## Installation
 
 Install from GitHub:
 
-``` r
+```r
 # install.packages("devtools")
 devtools::install_github("queelius/dfr.dist")
 ```
 
 ## Quick Start
 
+
 ``` r
 library(dfr.dist)
 ```
@@ -68,6 +67,7 @@ library(dfr.dist)
 
 Use the convenient constructors for classic survival distributions:
 
+
 ``` r
 # Exponential: constant hazard (memoryless)
 exp_dist <- dfr_exponential(lambda = 0.5)
@@ -84,6 +84,7 @@ ll_dist <- dfr_loglogistic(alpha = 10, beta = 2)
 
 All distribution functions are automatically available:
 
+
 ``` r
 S <- surv(exp_dist)
 S(2)  # Survival probability at t=2
@@ -96,6 +97,7 @@ h(1)  # Hazard at t=1
 
 ### Maximum Likelihood Estimation
 
+
 ``` r
 # Simulate failure times
 set.seed(42)
@@ -113,6 +115,7 @@ coef(result)  # Estimated rate
 
 Model complex failure patterns like bathtub curves:
 
+
 ``` r
 # h(t) = a*exp(-b*t) + c + d*t^k
 # Infant mortality + useful life + wear-out
@@ -128,12 +131,16 @@ curve(sapply(x, h), 0, 15, xlab = "Time", ylab = "Hazard rate",
       main = "Bathtub hazard curve")
 ```
 
-<img src="man/figures/README-bathtub-1.png" width="100%" />
+<div class="figure">
+<img src="man/figures/README-bathtub-1.png" alt="plot of chunk bathtub" width="100%" />
+<p class="caption">plot of chunk bathtub</p>
+</div>
 
 ### Model Diagnostics
 
 Check model fit with residual analysis:
 
+
 ``` r
 # Fit exponential to data
 fitted_exp <- dfr_exponential(lambda = coef(result))
@@ -142,27 +149,32 @@ fitted_exp <- dfr_exponential(lambda = coef(result))
 qqplot_residuals(fitted_exp, df)
 ```
 
-<img src="man/figures/README-diagnostics-1.png" width="100%" />
+<div class="figure">
+<img src="man/figures/README-diagnostics-1.png" alt="plot of chunk diagnostics" width="100%" />
+<p class="caption">plot of chunk diagnostics</p>
+</div>
 
 ## Mathematical Background
 
-For a lifetime $T$, the hazard function is: $$h(t) = \frac{f(t)}{S(t)}$$
+For a lifetime $T$, the hazard function is:
+$$h(t) = \frac{f(t)}{S(t)}$$
 
 From the hazard, all other quantities follow:
 
-| Function          | Formula                   | Method      |
-|-------------------|---------------------------|-------------|
+| Function | Formula | Method |
+|----------|---------|--------|
 | Cumulative hazard | $H(t) = \int_0^t h(u) du$ | `cum_haz()` |
-| Survival          | $S(t) = e^{-H(t)}$        | `surv()`    |
-| CDF               | $F(t) = 1 - S(t)$         | `cdf()`     |
-| PDF               | $f(t) = h(t) \cdot S(t)$  | `density()` |
+| Survival | $S(t) = e^{-H(t)}$ | `surv()` |
+| CDF | $F(t) = 1 - S(t)$ | `cdf()` |
+| PDF | $f(t) = h(t) \cdot S(t)$ | `density()` |
 
 ## Likelihood for Survival Data
 
 For exact observations: $\log L = \log h(t) - H(t)$
 
 For right-censored: $\log L = -H(t)$
 
+
 ``` r
 # Mixed data with censoring
 df <- data.frame(
@@ -179,40 +191,25 @@ ll(df, par = c(0.5))
 
 **Start Here:**
 
-- [Package
-  Overview](https://queelius.github.io/dfr.dist/articles/dfr.dist-package.html) -
-  Motivation, complete example, and audience guide
-- [Quick Start
-  Guide](https://queelius.github.io/dfr.dist/articles/getting_started.html) -
-  5-minute introduction
+- [Package Overview](https://queelius.github.io/dfr.dist/articles/dfr.dist-package.html) - Motivation, complete example, and audience guide
+- [Quick Start Guide](https://queelius.github.io/dfr.dist/articles/getting_started.html) - 5-minute introduction
 
 **Real-World Applications:**
 
-- [Reliability
-  Engineering](https://queelius.github.io/dfr.dist/articles/reliability_engineering.html) -
-  Five case studies
+- [Reliability Engineering](https://queelius.github.io/dfr.dist/articles/reliability_engineering.html) - Five case studies
 
 **Going Deeper:**
 
-- [Dynamic Failure Rate
-  Distributions](https://queelius.github.io/dfr.dist/articles/failure_rate.html) -
-  Mathematical foundations
-- [Creating Custom
-  Distributions](https://queelius.github.io/dfr.dist/articles/custom_distributions.html) -
-  The three-level optimization paradigm
-- [Custom Derivatives for
-  MLE](https://queelius.github.io/dfr.dist/articles/automatic_differentiation.html) -
-  Analytical score and Hessian functions
+- [Dynamic Failure Rate Distributions](https://queelius.github.io/dfr.dist/articles/failure_rate.html) - Mathematical foundations
+- [Creating Custom Distributions](https://queelius.github.io/dfr.dist/articles/custom_distributions.html) - The three-level optimization paradigm
+- [Custom Derivatives for MLE](https://queelius.github.io/dfr.dist/articles/custom_derivatives.html) - Analytical score and Hessian functions
 
 **Reference:**
 
 - [Function Reference](https://queelius.github.io/dfr.dist/reference/)
 
 ## Related Packages
 
-- [`algebraic.dist`](https://github.com/queelius/algebraic.dist):
-  Generic distribution interface
-- [`likelihood.model`](https://github.com/queelius/likelihood.model):
-  Likelihood model framework
-- [`algebraic.mle`](https://github.com/queelius/algebraic.mle): MLE
-  utilities
+- [`algebraic.dist`](https://github.com/queelius/algebraic.dist): Generic distribution interface
+- [`likelihood.model`](https://github.com/queelius/likelihood.model): Likelihood model framework
+- [`algebraic.mle`](https://github.com/queelius/algebraic.mle): MLE utilities

_pkgdown.yml

@@ -29,7 +29,7 @@ navbar:
         - text: Creating Custom Distributions
           href: articles/custom_distributions.html
         - text: Custom Derivatives for MLE
-          href: articles/automatic_differentiation.html
+          href: articles/custom_derivatives.html
 
 articles:
   - title: Motivation & Applications
@@ -44,4 +44,4 @@ articles:
   - title: Advanced
     contents:
       - custom_distributions
-      - automatic_differentiation
+      - custom_derivatives