API reference

DistributionHazards.jl — hazard, cumulative hazard, survival, density (and log-scale variants) for any continuous univariate distribution in Distributions.jl, plus expected_cumhazard(d1, d2) via QuadGK.

Distributions.jl already provides pdf, cdf, ccdf, logpdf, logccdf, and quantile. It does not expose hazard, cumulative hazard, or survival as named functions, even though they are trivially defined for any survival distribution. This package fills that gap, plus an iszero(t) guard so ForwardDiff stays stable through 0^shape expressions at t = 0.

hazard(d, t)

Hazard h(t) = f(t) / S(t) of a continuous univariate distribution d at analysis time t.

The generic method evaluates exp(logpdf(d, t) - logccdf(d, t)) rather than pdf(d, t) / ccdf(d, t) directly, so the value stays finite at extreme t where both pdf and ccdf underflow to zero. Closed-form specialisations exist for Exponential, Weibull, Rayleigh, Pareto, and Frechet.

cumhazard(d, t)

Cumulative hazard H(t) = -log S(t). Returns zero at t = 0 to keep ForwardDiff stable through distributions whose logccdf evaluates 0^shape at the boundary (Weibull, Gamma, log-logistic, …).

survival(d, t)

Survival function S(t) = 1 - F(t), equal to Distributions.ccdf(d, t).

density(d, t)

Probability density f(t) = pdf(d, t).

log_hazard(d, t)

log h(t) = log f(t) - log S(t). Evaluated via logpdf and logccdf so it stays AD-stable on the log scale.

log_survival(d, t)

log S(t) = -H(t). Evaluated as -cumhazard(d, t) so it inherits the t = 0 guard.

log_density(d, t)

log f(t) = logpdf(d, t).

expected_cumhazard(d1, d2; atol=1e-10, rtol=1e-8) -> Float64

E[H_{d1}(X)] for X ~ d2, computed by adaptive Gauss–Kronrod quadrature over the support of d2.

In branching-process epidemiology, with d1 a contact-interval distribution and d2 an infectious-period distribution, this is the basic reproduction number R₀ in the no-depletion limit.