gamma_series: Series of independent Gamma components (closed form)

In dist.structure: Structured Random Variables for Reliability System Distributions

Series of independent Gamma components (closed form)

Description

Constructs a dist_structure for a series system whose components are independent Gammas. Closed-form surv is evaluated by the product of per-component upper-tail probabilities; cdf is 1 - surv; sampler generates m independent Gammas and takes the min.

Usage

gamma_series(shapes, rates)

## S3 method for class 'gamma_series'
surv(x, ...)

## S3 method for class 'gamma_series'
sampler(x, ...)

Arguments

shapes	Positive numeric vector of length m: per-component Gamma shape parameters.
rates	Positive numeric vector of length m: per-component Gamma rate parameters.
x	A gamma_series object.
...	Ignored.

Value

gamma_series() returns an object of class c("gamma_series", "series_dist", "coherent_dist", "dist_structure", "univariate_dist", "continuous_dist", "dist").

The associated S3 methods return:

• surv(): a closure ⁠function(t, ...)⁠.

• cdf() is derived via the dist_structure default and returns a closure ⁠function(t, ...)⁠ equal to 1 - surv(x)(t).

• sampler(): a closure ⁠function(n, ...)⁠ returning n random variates from the system lifetime distribution.

Examples

sys <- gamma_series(shapes = c(2, 3), rates = c(1, 2))
algebraic.dist::surv(sys)(1)

dist.structure documentation built on May 13, 2026, 1:07 a.m.