It would be great to have a basic set of probability distributions implemented.

Umbrella issue for implementing sktime probability distributions.

Recipe: use the extension_templates/distribution.py extension template.
Examples:

• Normal, for de-novo implementations or manual interfaces
• Fisk, for interfacing scipy distributions - this is much easier than using the full template

High priority:

• laplace - [ENH] Laplace distribution #19
• empirical incl delta - [ENH] empirical distribution #25

mid priority:

• t-distribution - [ENH] Student's t-distribution #49
• Cauchy (special case of t) - [ENH] Student's t-distribution #49
• mixture composition - [ENH] mixture of distributions #26
• truncation, compositor

low priority:

• uniform continuous [ENH] Uniform Continuous distribution #223
• beta [ENH] Beta Distribution #298
• chi-squared [ENH] Chi-Squared Distribution #217
• exponential [ENH] Exponential distribution #325
• logistic [ENH] Logistic distribution #241
• log-normal [ENH] Log-normal probability distribution #218
• Weibull [ENH] Weibull distribution #242

lower priority:

• alpha [ENH] Alpha distribution #356
• binomial
• burr III
• burr XII
• erlang
• f
• fatigue-life
• generalized Pareto
• gamma [ENH] Gamma Distribution #355
• geometric
• half-cauchy
• half-normal
• half-logistic
• levy
• log-gamma
• log-laplace
• negative binomial
• pareto
• skellam
• truncated normal
• truncated pareto

list of many more (lowest priority)
https://docs.scipy.org/doc/scipy/reference/stats.html#probability-distributions - can be interfaced via _ScipyDist adapter easily!
https://en.wikipedia.org/wiki/File:ProbOnto2.5.jpg

Moved here from sktime/sktime#4518