Internal Documentation

Documentation for ModifiedDistributions's internal interface.

Contents

• Internal Documentation
  • Contents
  • Index
  • Internal API

Index

• Base.rand
• Distributions.ccdf
• Distributions.cdf
• Distributions.logccdf
• Distributions.logcdf
• Distributions.logpdf
• Distributions.pdf
• Distributions.sampler
• ModifiedDistributions.combine_weights
• Statistics.mean
• Statistics.quantile
• Statistics.var
• StatsAPI.loglikelihood

Internal API

Distributions.ccdf Function

ccdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the complementary cumulative distribution function via change of variables (avoids the 1 - cdf fallback, keeping precision in the upper tail).

See also: cdf, logccdf

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

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

See also: cdf

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ccdf(d::ModifiedDistributions.Modified, x::Real) -> Any

Compute the complementary cumulative distribution function.

See also: logccdf

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Distributions.cdf Function

cdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the cumulative distribution function.

See also: logcdf, quantile

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

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

See also: logcdf

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cdf(d::ModifiedDistributions.Modified, x::Real) -> Any

Compute the cumulative distribution function.

See also: ccdf, logcdf

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ModifiedDistributions.combine_weights Function

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)

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Distributions.logccdf Function

logccdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the log complementary cumulative distribution function.

See also: ccdf

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logccdf(d::ModifiedDistributions.Weighted, x::Real) -> Any

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

See also: logcdf

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logccdf(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(log), typeof(exp)}},
    x::Real
) -> Any

Compute the log survival function on the proportional-hazards path.

See also: ccdf, logpdf

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logccdf(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(identity), typeof(identity)}},
    x::Real
) -> Any

Compute the log survival function on the additive-hazards path.

See also: ccdf, logpdf

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Distributions.logcdf Function

logcdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the log cumulative distribution function.

See also: cdf

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

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

See also: cdf

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logcdf(d::ModifiedDistributions.Modified, x::Real) -> Any

Compute the log cumulative distribution function.

See also: cdf

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StatsAPI.loglikelihood Function

loglikelihood(
    d::ModifiedDistributions.Weighted,
    obs::NamedTuple{(:value, :weight)}
) -> Any

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

Handles joint observations as NamedTuple: (value = x, weight = w).

See also: logpdf

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

Compute log-likelihood for single Weighted distribution with vectorised 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

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loglikelihood(
    d::Distributions.Product{<:Distributions.ValueSupport, <:ModifiedDistributions.Weighted, <:AbstractVector{<:ModifiedDistributions.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

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Distributions.logpdf Function

logpdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the log probability density function via change of variables. For a continuous inner distribution this includes the log-Jacobian -log(scale); for a discrete inner distribution the mass transforms without it.

See also: pdf, cdf

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logpdf(d::ModifiedDistributions.Weighted, x::Real) -> Any

Return the weighted log-probability for scalar observations.

See also: pdf

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logpdf(
    d::ModifiedDistributions.Weighted,
    obs::NamedTuple{(:value, :weight)}
) -> Any

Return the weighted log-probability for joint observations as NamedTuple.

Combines constructor weight with observation weight via multiplication. Expected format: (value = x, weight = w).

See also: pdf

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logpdf(
    d::Distributions.Product{<:Distributions.ValueSupport, <:ModifiedDistributions.Weighted, <:AbstractVector{<:ModifiedDistributions.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

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logpdf(
    d::Distributions.Product{<:Distributions.ValueSupport, <:ModifiedDistributions.Weighted, <:AbstractVector{<:ModifiedDistributions.Weighted}},
    x::AbstractVector{<:Real}
) -> Any

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

See also: logpdf

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logpdf(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(log), typeof(exp)}},
    x::Real
) -> Any

Compute the log probability density on the proportional-hazards path.

See also: pdf, ccdf

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logpdf(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(identity), typeof(identity)}},
    x::Real
) -> Any

Compute the log probability density on the additive-hazards path.

See also: pdf, ccdf

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Statistics.mean Function

mean(d::ModifiedDistributions.Affine) -> Any

Compute the mean via the affine transform of the inner mean.

See also: var

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Distributions.pdf Function

pdf(d::ModifiedDistributions.Affine, y::Real) -> Any

Compute the probability density function.

See also: logpdf

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

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

See also: logpdf

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pdf(d::ModifiedDistributions.Modified, x::Real) -> Any

Compute the probability density function.

See also: logpdf

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Statistics.quantile Function

quantile(d::ModifiedDistributions.Affine, p::Real) -> Any

Compute the quantile function (inverse CDF).

See also: cdf

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

Compute the quantile function (delegates to underlying distribution).

See also: cdf

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quantile(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(log), typeof(exp)}},
    p::Real
) -> Any

Compute the quantile by closed-form inversion of the modified survival.

See also: cdf

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quantile(
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(identity), typeof(identity)}},
    p::Real
) -> Any

Compute the quantile by monotone bisection of the modified CDF.

See also: cdf

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Base.rand Function

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

Generate a random sample by transforming an inner draw.

See also: quantile

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

Generate a random sample (delegates to underlying distribution).

See also: quantile

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rand(
    rng::Random.AbstractRNG,
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(log), typeof(exp)}}
) -> Any

Generate a random sample by closed-form inversion of the modified survival.

See also: quantile

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rand(
    rng::Random.AbstractRNG,
    d::ModifiedDistributions.Modified{<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, <:Real, ModifiedDistributions.HazardLink{typeof(identity), typeof(identity)}}
) -> Any

Generate a random sample by quantile inversion of a uniform draw.

See also: quantile

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Distributions.sampler Function

sampler(
    d::ModifiedDistributions.Weighted
) -> Union{ModifiedDistributions.Weighted{D, Missing} where D<:(Distributions.UnivariateDistribution), ModifiedDistributions.Weighted{D, T} where {D<:(Distributions.UnivariateDistribution), T<:Real}}

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

See also: rand

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Statistics.var Function

var(d::ModifiedDistributions.Affine) -> Any

Compute the variance via the affine transform of the inner variance.

See also: mean

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