DistributionExt<T>

Closed-form analytics for every distribution that has them.

pub trait DistributionExt<T: FloatExt> {
    fn pdf(&self, x: T) -> T;
    fn cdf(&self, x: T) -> T;
    fn characteristic_fn(&self, t: T) -> Complex<T>;
    fn mean(&self) -> T;
    fn variance(&self) -> T;
    fn skewness(&self) -> T { unimplemented_moment::<T>() }
    fn kurtosis(&self) -> T { unimplemented_moment::<T>() }
}

Coverage

18 / 19 distributions implement closed-form pdf, cdf, characteristic function, mean, and variance. The exception is ComplexDistribution, which is a wrapper used by Fourier-domain pricers and intentionally opaque.

For higher-order moments, 5 named distributions carry unimplemented! for skewness and / or kurtosis — those are documented on each distribution's reference page. The remaining 14 ship full closed-form skewness and excess kurtosis.

Default behaviour: panic, never zero

Project rule: an unimplemented moment panics with a helpful message including the type name, never silently returns 0. This was a deliberate choice after a v1.x bug where a silent-zero kurtosis caused a downstream calibration to converge on garbage.

fn unimplemented_moment<T>() -> ! {
    let name = std::any::type_name::<T>();
    unimplemented!("moment not implemented for {name}")
}

If you hit such a panic, you have two options:

1. Use a different distribution if the moment is non-essential.
2. Open an issue / PR — the feedback_implementation.md rule says we follow papers exactly, so closed forms get added with a citation.

Why no statrs::distribution::*

The library deliberately writes closed forms from scratch in stochastic-rs-distributions, never delegating to statrs. Reasons:

1. Generic precision. statrs is f64-only. We need f32 support for GPU + memory-bound bulk sampling.
2. No-allocation guarantees. statrs allocates in some cdfs; the bulk samplers in this library cannot afford that.
3. Audit trail. Every formula in this crate is anchored to a paper citation, with a comparison test against the paper's numerical tables. statrs's implementations are competent but lack that audit trail.

See the per-distribution pages under Distributions for the formulas, tests, and references.