Summary: Distribution & Backend Reference
Summary: Distribution & Backend Reference
This section provides a compact reference for the distributions supported by CausalMixGPD and the corresponding user-facing function families.
The CRP backend uses base (single-kernel) functions, while the SB backend uses mixture (multi-component) functions. The “Type” column indicates whether each backend expects scalar parameters (single value per parameter) or vectors indexed by mixture component.
| Distribution | Parameters | Arguments | CRP Type | CRP Function | SB Type | SB Function |
|---|---|---|---|---|---|---|
| Normal | \(\mu, \sigma\) | mean, sd |
scalars | dnorm(), pnorm(), qnorm(), rnorm() |
vectors | dNormMix(), pNormMix(), qNormMix(), rNormMix() |
| Gamma | \(\alpha, \beta\) | shape, scale |
scalars | dgamma(), pgamma(), qgamma(), rgamma() |
vectors | dGammaMix(), pGammaMix(), qGammaMix(), rGammaMix() |
| Lognormal | \(\mu, \sigma\) | meanlog, sdlog |
scalars | dlnorm(), plnorm(), qlnorm(), rlnorm() |
vectors | dLognormalMix(), pLognormalMix(), qLognormalMix(), rLognormalMix() |
| Laplace | \(\ell, b\) | location, scale |
scalars | ddexp(), pdexp(), qdexp(), rdexp() |
vectors | dLaplaceMix(), pLaplaceMix(), qLaplaceMix(), rLaplaceMix() |
| Inverse Gaussian | \(\mu, \lambda\) | mean, shape |
scalars | dinvgauss(), pinvgauss(), qinvgauss(), rinvgauss() |
vectors | dInvGaussMix(), pInvGaussMix(), qInvGaussMix(), rInvGaussMix() |
| Amoroso | \(a, \theta, \alpha, \beta\) | loc, scale, shape1, shape2 |
scalars | damoroso(), pamoroso(), qamoroso(), ramoroso() |
vectors | dAmorosoMix(), pAmorosoMix(), qAmorosoMix(), rAmorosoMix() |
| Cauchy | \(x_0, \gamma\) | location, scale |
scalars | dcauchy(), pcauchy(), qcauchy(), rcauchy() |
vectors | dCauchyMix(), pCauchyMix(), qCauchyMix(), rCauchyMix() |
| GPD | \(u, \sigma, \xi\) | threshold, scale, shape |
scalars | dGpd(), pGpd(), qGpd(), rGpd() |
NA | NA |
| Normal + GPD | \(\mu, \sigma, u, \sigma, \xi\) | mean, sd, threshold, tail_scale, tail_shape |
scalars | dNormGpd(), pNormGpd(), qNormGpd(), rNormGpd() |
vectors + scalars | dNormMixGpd(), pNormMixGpd(), qNormMixGpd(), rNormMixGpd() |
| Gamma + GPD | \(\alpha, \beta, u, \sigma, \xi\) | shape, scale, threshold, tail_scale, tail_shape |
scalars | dGammaGpd(), pGammaGpd(), qGammaGpd(), rGammaGpd() |
vectors + scalars | dGammaMixGpd(), pGammaMixGpd(), qGammaMixGpd(), rGammaMixGpd() |
| Lognormal + GPD | \(\mu, \sigma, u, \sigma, \xi\) | meanlog, sdlog, threshold, tail_scale, tail_shape |
scalars | dLognormalGpd(), pLognormalGpd(), qLognormalGpd(), rLognormalGpd() |
vectors + scalars | dLognormalMixGpd(), pLognormalMixGpd(), qLognormalMixGpd(), rLognormalMixGpd() |
| Laplace + GPD | \(\ell, b, u, \sigma, \xi\) | location, scale, threshold, tail_scale, tail_shape |
scalars | dLaplaceGpd(), pLaplaceGpd(), qLaplaceGpd(), rLaplaceGpd() |
vectors + scalars | dLaplaceMixGpd(), pLaplaceMixGpd(), qLaplaceMixGpd(), rLaplaceMixGpd() |
| InvGauss + GPD | \(\mu, \lambda, u, \sigma, \xi\) | mean, shape, threshold, tail_scale, tail_shape |
scalars | dInvGaussGpd(), pInvGaussGpd(), qInvGaussGpd(), rInvGaussGpd() |
vectors + scalars | dInvGaussMixGpd(), pInvGaussMixGpd(), qInvGaussMixGpd(), rInvGaussMixGpd() |
| Amoroso + GPD | \(a, \theta, \alpha, \beta, u, \sigma, \xi\) | loc, scale, shape1, shape2, threshold, tail_scale, tail_shape |
scalars | dAmorosoGpd(), pAmorosoGpd(), qAmorosoGpd(), rAmorosoGpd() |
vectors + scalars | dAmorosoMixGpd(), pAmorosoMixGpd(), qAmorosoMixGpd(), rAmorosoMixGpd() |
Notes
CRP Backend uses base (single-kernel) functions; parameters are scalar.
SB Backend uses mixture/spliced mixture functions; component-specific parameters are typically vectors indexed by component (j); mixture weights
ware required as vector.For GPD-only, SB entries are NA because there is no mixture-only GPD wrapper in the SB family.
Prereqs
- Required packages and data for this page are listed in the setup chunks above.
Outputs
- This page renders model fits, diagnostics, and summary artifacts generated by package APIs.
Interpretation
- Canonical concept page: Introduction With Gpd Kernel
- Treat this page as an application/example view and use the canonical page for core definitions.
Next
- Continue to the linked canonical concept page, then return for implementation-specific details.