Internal Documentation

Base.rand Method

julia

rand(
    rng::Random.AbstractRNG,
    d::CensoredDistributions.PrimaryCensored
) -> Any

Generate a random sample by summing samples from delay and primary event distributions.

See also: quantile

Base.rand Method

julia

rand(
    rng::Random.AbstractRNG,
    d::CensoredDistributions.Weighted
) -> Any

Generate a random sample (delegates to underlying distribution).

See also: quantile

Base.rand Method

julia

rand(rng::Random.AbstractRNG, d::ExponentiallyTilted) -> Any

Generate a random sample using inverse transform sampling.

See also: quantile

CensoredDistributions._collect_unique_boundaries Method

julia

_collect_unique_boundaries(
    d::CensoredDistributions.IntervalCensored,
    x::AbstractVector{<:Real}
) -> Any

julia

_collect_unique_boundaries(d::IntervalCensored, x::AbstractVector)

Collect all unique interval boundaries needed for vectorised PDF computation.

Returns a sorted vector of unique boundaries with appropriate type promotion. The boundaries are functions of the (constant) lags and the interval spec, not the distribution's AD parameters, so AD rules mark this non-differentiable (the unique/sort internals are never traced); see the AD extensions (#699, #701).

CensoredDistributions._compute_boundary_cdfs Method

julia

_compute_boundary_cdfs(
    d::CensoredDistributions.IntervalCensored,
    boundaries::AbstractVector
) -> Any

julia

_compute_boundary_cdfs(d::IntervalCensored, boundaries)

Evaluate the boundary CDF once per unique boundary, returning a vector parallel to the sorted unique boundaries. cdf_ad_safe keeps the Gamma path differentiable (see #257). CDF values keep their natural type so the AD tangent is not stripped. Boundaries at or below minimum(dist) / at or above maximum(dist) get the literal 0 / 1 (typed via partype) instead of an evaluation, mirroring the scalar pdf guard; evaluating cdf_ad_safe at a degenerate boundary (e.g. LogNormal at 0) would poison the reverse sweep with a -Inf/NaN adjoint (#699).

CensoredDistributions._compute_pdfs_with_cache Method

julia

_compute_pdfs_with_cache(
    d::CensoredDistributions.IntervalCensored,
    x::AbstractVector{<:Real},
    boundaries::AbstractVector,
    cdf_values::AbstractVector
) -> Any

julia

_compute_pdfs_with_cache(d, x, boundaries, cdf_values)

Compute PDFs efficiently using the cached boundary CDFs held in the parallel arrays boundaries (sorted, unique) and cdf_values.

Uses the same boundary case handling as the scalar method.

CensoredDistributions._lookup_boundary_cdf Method

julia

_lookup_boundary_cdf(
    boundaries::AbstractVector,
    cdf_values::AbstractVector,
    b
) -> Any

julia

_lookup_boundary_cdf(boundaries, cdf_values, b)

Look up the cached CDF for boundary b in the sorted, unique boundaries vector via searchsortedfirst, returning the matching cdf_values entry. The concretely-typed parallel arrays plus an index lookup keep the boundary CDF cache type-stable so the AD tangent is tracked through it (#699).

CensoredDistributions._make_weibull_g Method

julia

_make_weibull_g(
    k::Real,
    λ::Real
) -> CensoredDistributions.var"#weibull_g_specialized#_make_weibull_g##0"{<:Real, <:Real}

Function factory for optimized Weibull g function.

Creates a specialized function with pre-computed constants for g(t; k, λ) = γ(1 + 1/k, (t/λ)^k) where γ is the lower incomplete gamma function.

Pre-computes inv_k = 1/k and a = 1 + inv_k to avoid repeated computation in the returned specialized function.

Arguments

k::Real: Weibull shape parameter
λ::Real: Weibull scale parameter

Returns

A specialized function weibull_g_specialized(t::Real) that efficiently computes the Weibull g function using pre-computed constants.

Examples

julia

weibull_g_func = _make_weibull_g(2.0, 1.5)
g_val = weibull_g_func(3.0)

CensoredDistributions._quantile_optimization Method

julia

_quantile_optimization(
    d,
    p::Real;
    initial_guess_fn,
    result_postprocess_fn,
    check_nan
) -> Any

Internal function for quantile optimization using numerical methods.

Solves the equation cdf(d, q) - p = 0 using the Nelder-Mead algorithm. This is shared logic used by both PrimaryCensored and IntervalCensored quantile functions.

Arguments

d: The distribution for which to compute the quantile
p: The probability value in [0, 1]

Keyword Arguments

initial_guess_fn: Function that takes (d, p) and returns initial guess vector. If nothing, uses quantile(get_dist(d), p) as scalar initial guess.
result_postprocess_fn: Function to post-process the optimization result. Defaults to identity (no post-processing).
check_nan: If true, explicitly check for NaN input values.

Returns

The quantile value after optimization and post-processing.

Implementation Details

Validates that p ∈ [0, 1] (with optional NaN checking)
Handles boundary cases p=0 (minimum) and p=1 (maximum) analytically
Creates objective function (cdf(d, q) - p)^2 with support checking
Uses heavy penalty for values outside distribution support
Solves with Nelder-Mead algorithm with tight tolerances
Checks convergence and applies post-processing to result

Type Stability

This function is designed to maintain type stability when the initial guess function and post-processing function are type-stable.

CensoredDistributions.combine_weights Method

julia

combine_weights(_::Missing, _::Missing) -> Missing

Combine constructor weight with observation weight using dispatch-based rules.

Weight combination rules:

missing, missing → missing (both missing means no weight)
w1, missing → w1 (use constructor weight)
missing, w2 → w2 (use observation weight)
w1, w2 → w1 * w2 (multiply weights)

Vector Extensions

For Product distributions, additional methods handle vectorised weight combinations:

Vector, Vector → combine_weights.(vector1, vector2) (element-wise combination)
Vector, missing → Vector (keep constructor weights)
Vector, scalar → [combine_weights(w, scalar) for w in Vector] (broadcast scalar)

Distributions.ccdf Method

julia

ccdf(d::CensoredDistributions.Weighted, x::Real) -> Any

Compute the complementary cumulative distribution function (delegates to underlying distribution).

See also: cdf

julia

cdf(
    d::CensoredDistributions.Convolved,
    x::AbstractVector{<:Real}
) -> Any

Compute the CDF for a vector of evaluation points using a single quadrature solve (the integrand returns a vector).

See also: cdf

julia

cdf(d::CensoredDistributions.Convolved, x::Real) -> Any

Compute the cumulative distribution function.

Uses an analytical convolution when Distributions.convolve applies to all component pairs, otherwise AD-safe numeric quadrature.

See also: logcdf

julia

cdf(
    d::CensoredDistributions.IntervalCensored,
    x::Real
) -> Any

Compute the cumulative distribution function.

See also: logcdf

julia

cdf(
    d::CensoredDistributions.PrimaryCensored,
    x::Real
) -> Any

Compute the cumulative distribution function.

See also: logcdf

julia

cdf(d::CensoredDistributions.Weighted, x::Real) -> Any

Compute the cumulative distribution function (delegates to underlying distribution).

See also: logcdf

julia

cdf(d::ExponentiallyTilted, x::Real) -> Any

Compute the cumulative distribution function.

See also: logcdf

julia

logcdf(d::CensoredDistributions.Convolved, x::Real) -> Any

Compute the log cumulative distribution function.

See also: cdf

julia

logcdf(
    d::CensoredDistributions.IntervalCensored,
    x::Real
) -> Any

Compute the log cumulative distribution function.

See also: cdf

julia

logcdf(
    d::CensoredDistributions.PrimaryCensored,
    x::Real
) -> Any

Compute the log cumulative distribution function.

See also: cdf

julia

logcdf(d::CensoredDistributions.Weighted, x::Real) -> Any

Compute the log cumulative distribution function (delegates to underlying distribution).

See also: cdf

julia

logcdf(d::ExponentiallyTilted, x::Real) -> Any

Compute the log cumulative distribution function.

See also: cdf

Distributions.logpdf Method

julia

logpdf(
    d::CensoredDistributions.Convolved,
    x::AbstractVector{<:Real}
) -> Any

Compute log densities for a vector of points, reusing the batched PDF solve for the numeric path.

See also: logpdf

Distributions.logpdf Method

julia

logpdf(
    d::Distributions.Product{<:Distributions.ValueSupport, <:CensoredDistributions.Weighted, <:AbstractVector{<:CensoredDistributions.Weighted}},
    obs::NamedTuple{(:values, :weights)}
) -> Any

Efficient vectorised log-probability computation for Product{<:ValueSupport, <:Weighted} with joint observations.

Handles joint observations and weight stacking. Expected format: (values = [...], weights = [...]).

See also: logpdf

Distributions.logpdf Method

julia

logpdf(d::ExponentiallyTilted, x::Real) -> Any

Compute the log probability density function.

See also: logpdf

Distributions.pdf Method

julia

pdf(
    d::CensoredDistributions.IntervalCensored,
    x::AbstractVector{<:Real}
) -> Any

Compute probability masses for an array of values using optimised vectorisation.

This method collects unique interval boundaries, computes CDFs once, then uses cached values for efficient PDF computation across the array.

See also: logpdf

Distributions.pdf Method

julia

pdf(d::CensoredDistributions.Weighted, x::Real) -> Any

Return the probability density from the underlying distribution (unweighted).

See also: logpdf

Distributions.pdf Method

julia

pdf(d::ExponentiallyTilted, x::Real) -> Any

Compute the probability density function.

See also: logpdf

Distributions.sampler Method

julia

sampler(d::CensoredDistributions.Weighted) -> Any

Create a sampler for efficient sampling (delegates to underlying distribution).

See also: cdf

Statistics.quantile Method

julia

quantile(
    d::CensoredDistributions.PrimaryCensored,
    p::Real
) -> Any

Compute the quantile (inverse CDF) using numerical optimization.

See also: cdf

Statistics.quantile Method

julia

quantile(d::CensoredDistributions.Weighted, p::Real) -> Any

Compute the quantile function (delegates to underlying distribution).

See also: cdf

Statistics.quantile Method

julia

quantile(d::ExponentiallyTilted, p::Real) -> Any

Compute the quantile function (inverse CDF) using analytical formula.

See also: cdf

Statistics.std Method

julia

std(d::ExponentiallyTilted) -> Any

Compute the standard deviation of the distribution.

See also: logpdf

StatsAPI.loglikelihood Method

julia

loglikelihood(
    d::CensoredDistributions.Weighted,
    obs::NamedTuple{(:values, :weights)}
) -> Any

Compute log-likelihood for single Weighted distribution with vectorized joint observations.

Handles joint observations as NamedTuple: (values = [...], weights = [...]). This is useful when a single weighted distribution is used with multiple observations.

See also: logpdf

StatsAPI.loglikelihood Method

julia

loglikelihood(
    d::Distributions.Product{<:Distributions.ValueSupport, <:CensoredDistributions.Weighted, <:AbstractVector{<:CensoredDistributions.Weighted}},
    obs::NamedTuple{(:values, :weights)}
) -> Any

Compute log-likelihood for Product{<:ValueSupport, <:Weighted} with joint observations.

Handles joint observations as NamedTuple: (values = [...], weights = [...]).

See also: logpdf