Analytic CRPS formulas tracking issue

[frazane]

Issue to track implementation of analytical CRPS formulas, as implemented in scoringRules.

• beta (betainc missing in torch)
• binomial (betainc missing in torch)
• exponential
• exponential point mass variant
• gamma
• gen. extreme value (expi missing in torch)
• gen. Pareto
• hypergeometric
• Laplace
• log-Laplace
• log-logistic
• log-normal
• logistic
• logistic truncated
• logistic censored
• logistic point mass variant
• mixture of normals (Ready for PR)
• negative binomial (hypergeometric missing in jax, tensorflow and torch)
• normal
• normal truncated
• normal censored
• normal point mass variant
• Poisson
• Student’s t (hypergeometric missing in jax, tensorflow and torch)
• Student’s t truncated (hypergeometric missing in jax, tensorflow and torch)
• Student's t censored (hypergeometric missing in jax, tensorflow and torch)
• Student's t point mass variant (hypergeometric missing in jax, tensorflow and torch)
• two-piece exponential
• two-piece normal
• uniform

Notes:

• gamma, beta and bessel functions not supported in numba (affects beta, gamma, gev, poisson, t, generalised t, negative binomial, binomial, hypergeometric, and log-logistic distribution).
• regularised incomplete beta function not supported in torch (affects beta, log-logistic, binomial, hypergeometric, negative binomial, and generalised t distribution)
• hypergeometric function not supported in torch or tensorflow (affects t and negative binomial distribution)
• exponential integral not supported in torch (affects gev distribution)
• hypergeometric cdf needed

[frazane]

Closing as complete! 🚀