Kernels Overview

Setup chunk keeps CausalMixGPD loaded while describing kernels.

Ingredients (mixture kernels)

CausalMixGPD supports multiple mixture kernel families for flexible density estimation. Each kernel has different properties suited to various data types and modeling scenarios.

What’s in the pantry

Location-scale families

These kernels have location and scale parameters, making them suitable for real-valued data:

• Normal - Gaussian kernel with mean and sd parameters. Best for symmetric, bell-shaped distributions.

• Cauchy - Heavy-tailed kernel with location and scale parameters. Robust to outliers but does not support GPD tail.

• Laplace - Double exponential kernel with location and scale parameters. Has heavier tails than Normal.

Positive-support families

These kernels are defined for positive values only, ideal for positive data like durations, sizes, or amounts:

• Lognormal - Log-transformed Normal with meanlog and sdlog parameters. Good for right-skewed positive data.

• Gamma - Flexible positive kernel with shape and scale parameters. Can model various skewness levels.

• Inverse Gaussian - Alternative positive kernel with mean and shape parameters. Often used for waiting times.

Generalized families

• Amoroso - Four-parameter generalization with loc, scale, shape1, and shape2. Includes Gamma, Weibull, and other distributions as special cases.

Ingredient picker

Data Type	Recommended Kernels
Real-valued, symmetric	Normal, Cauchy
Real-valued, heavy-tailed	Cauchy, Laplace
Positive, right-skewed	Lognormal, Gamma
Positive, waiting times	Inverse Gaussian
Positive, flexible shape	Amoroso, Gamma

GPD Tail Support

Most kernels support GPD tail modeling (GPD = TRUE):

Kernel	GPD Support
Normal	Yes
Lognormal	Yes
Gamma	Yes
Inverse Gaussian	Yes
Laplace	Yes
Amoroso	Yes
Cauchy	No

Using ingredients in your recipe

Specify the kernel when building your model:

bundle <- bundle(
  y = your_data,
  backend = "sb",
  kernel = "lognormal",  # Choose your kernel

  GPD = TRUE
)

See the individual kernel pages for detailed examples and parameter descriptions.

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.