stdlib-js / stdlib-js/stdlib

[RFC]: implement a broader range of statistical distributions (tracking issue)

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Feature Needs Discussion RFC Statistics Tracking Issue
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Descripción

### Description

This RFC proposes implement large number of probability distributions. The purpose of this issue is to serve as a tracking issue for implement large number of probability distributions.

### Probability distributions

### Continuous distributions

**supported on a bounded interval**

- [X] arcsine
- [ ] ARGUS
- [ ] balding–Nichols
- [ ] bates
- [X] beta
- [ ] beta rectangular
- [ ] continuous Bernoulli
- [ ] Irwin–Hall
- [X] Kumaraswamy
- [ ] logit-normal
- [ ] noncentral beta
- [ ] PERT
- [X] cosine
- [ ] reciprocal
- [X] triangular
- [ ] U-quadratic
- [X] uniform
- [ ] Wigner semicircle

**supported on a semi-infinite interval**

- [ ] benini
- [ ] benktander 1st kind
- [ ] benktander 2nd kind
- [X] beta prime
- [ ] burr
- [X] chi
- [X] chi-squared
- [ ] inverse chi-squared
- [ ] scaled inverse chi-squared
- [ ] dagum
- [ ] davis
- [X] erlang
- [ ] hyper Erlang
- [X] exponential
- [ ] hyperexponential
- [ ] hypoexponential
- [ ] exponential-logarithmic
- [X] F
- [ ] noncentral F-distribution
- [ ] folded normal
- [X] fréchet
- [X] gamma
- [ ] generalized gamma
- [X] inverse-gamma
- [ ] gamma/Gompertz
- [ ] gompertz
- [ ] shifted Gompertz
- [ ] half-logistic
- [ ] half-normal
- [ ] hotelling's T-squared
- [ ] inverse Gaussian
- [ ] generalized inverse Gaussian
- [ ] kolmogorov
- [X] lévy
- [ ] log-Cauchy
- [ ] log-Laplace
- [ ] log-logistic
- [X] log-normal
- [ ] log-t
- [ ] lomax
- [ ] matrix-exponential
- [ ] maxwell–Boltzmann
- [ ] maxwell–Jüttner
- [ ] Mittag-Leffler
- [ ] nakagami
- [X] pareto-type1
- [ ] phase-type
- [ ] poly-Weibull
- [X] rayleigh
- [ ] relativistic Breit–Wigner
- [ ] rice
- [X] truncated-normal
- [ ] type-2 Gumbel
- [X] weibull
- [ ] discrete Weibull
- [ ] wilks's lambda

**supported on the whole real line**

- [X] cauchy
- [ ] exponential power
- [ ] fisher's z
- [ ] kaniadakis κ-Gaussian
- [ ] gaussian q
- [ ] generalized normal
- [ ] generalized hyperbolic
- [ ] geometric stable
- [X] gumbel
- [ ] holtsmark
- [ ] hyperbolic secant
- [ ] Johnson's SU
- [ ] landau
- [X] laplace
- [ ] asymmetric laplace
- [X] logistic
- [ ] noncentral t
- [X] normal
- [ ] normal-inverse Gaussian
- [ ] skew normal
- [ ] slash
- [ ] stable
- [x] student's t
- [ ] tracy–Widom
- [ ] variance-gamma
- [ ] voigt

**with support whose type varies**

- [ ] generalized chi-squared
- [ ] generalized extreme value
- [ ] generalized Pareto
- [ ] marchenko–Pastur
- [ ] kaniadakis κ-exponential
- [ ] kaniadakis κ-Gamma
- [ ] kaniadakis κ-Weibull
- [ ] kaniadakis κ-Logistic
- [ ] kaniadakis κ-Erlang
- [ ] q-exponential
- [ ] q-Gaussian
- [ ] q-Weibull
- [ ] shifted log-logistic
- [ ] tukey lambda

### Discrete distributions

**with finite support**

- [ ] benford
- [X] bernoulli
- [ ] beta-binomial
- [X] binomial
- [ ] categorical
- [X] hypergeometric
- [ ] negative hypergeometric
- [ ] poisson binomial
- [ ] rademacher
- [ ] soliton
- [X] discrete uniform
- [ ] zipf
- [ ] zipf–Mandelbrot

**with infinite support**

- [ ] beta negative binomial
- [ ] borel
- [ ] conway–Maxwell–Poisson
- [ ] discrete phase-type
- [ ] delaporte
- [ ] extended negative binomial
- [ ] flory–Schulz
- [ ] gauss–Kuzmin
- [x] geometric
- [ ] logarithmic
- [ ] mixed Poisson
- [X] negative-binomial
- [ ] panjer
- [ ] parabolic fractal
- [X] poisson
- [ ] skellam
- [ ] yule–Simon
- [ ] zeta

### Mixed distributions

- [ ] rectified Gaussian

### Multivariate(joint) distributions

**Discrete:**

- [ ] ewens
- [ ] multinomial
- [ ] dirichlet multinomial
- [ ] negative multinomial

**Continuous:**

- [ ] Dirichlet
- [ ] generalized Dirichlet
- [ ] multivariate Laplace
- [ ] multivariate normal
- [ ] multivariate stable
- [ ] multivariate t
- [ ] normal-gamma
- [ ] normal-inverse-gamma

### Related Issues

None.

### Questions

No.

### Other

No.

### Checklist

- [X] I have read and understood the [Code of Conduct](https://github.com/stdlib-js/stdlib/blob/develop/CODE_OF_CONDUCT.md).
- [X] Searched for existing issues and pull requests.
- [X] The issue name begins with `RFC:`.

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