Remove ChiSquared Distribution in favor of helper

[ricardoV94]

Description

It's just a Gamma(alpha=nu/2, beta=1/2). No point in having the extra code:

pymc/pymc/distributions/continuous.py

Lines 2378 to 2434 in ec4407d

	class ChiSquared(PositiveContinuous):
	r"""
	:math:`\chi^2` log-likelihood.
	The pdf of this distribution is
	.. math::
	f(x \mid \nu) = \frac{x^{(\nu-2)/2}e^{-x/2}}{2^{\nu/2}\Gamma(\nu/2)}
	.. plot::
	:context: close-figs
	import matplotlib.pyplot as plt
	import numpy as np
	import scipy.stats as st
	import arviz as az
	plt.style.use('arviz-darkgrid')
	x = np.linspace(0, 15, 200)
	for df in [1, 2, 3, 6, 9]:
	pdf = st.chi2.pdf(x, df)
	plt.plot(x, pdf, label=r'$\nu$ = {}'.format(df))
	plt.xlabel('x', fontsize=12)
	plt.ylabel('f(x)', fontsize=12)
	plt.ylim(0, 0.6)
	plt.legend(loc=1)
	plt.show()
	======== ===============================
	Support :math:`x \in [0, \infty)`
	Mean :math:`\nu`
	Variance :math:`2 \nu`
	======== ===============================
	Parameters
	----------
	nu : tensor_like of float
	Degrees of freedom (nu > 0).
	"""
	rv_op = chisquare
	@classmethod
	def dist(cls, nu, *args, **kwargs):
	nu = pt.as_tensor_variable(floatX(nu))
	return super().dist([nu], *args, **kwargs)
	def moment(rv, size, nu):
	moment = nu
	if not rv_size_is_none(size):
	moment = pt.full(size, moment)
	return moment
	def logp(value, nu):
	return _logprob_helper(Gamma.dist(alpha=nu / 2, beta=0.5), value)
	def logcdf(value, nu):
	return _logcdf_helper(Gamma.dist(alpha=nu / 2, beta=0.5), value)

class Chisquare:
  """docs"""

  def __new__(cls, name, nu, **kwargs):
    return Gamma(name, nu/2, 1/2, **kwargs)
  
  @classmethod
  def dist(cls, nu, **kwargs):
    return Gamma.dist(nu/2, 1/2, **kwargs)

Likewise, the ChiSquareRV in PyTensor can be removed in favor of a helper that just returns the right gamma:

https://github.com/pymc-devs/pytensor/blob/3169197c54e2cab7ba27c647c760b93e12abca5e/pytensor/tensor/random/basic.py#L490-L540

[williambdean]

I'll take this. I think I have it down 😃

Separate, documentation question: Is this generally recommended now? I see the contribution docs has the RV and Distribution recommendation still. Should this be suggested there too?

[ricardoV94]

We should add a pymc-examples using CustomDist first. That would be much more impactful if you want to contribute

[williambdean]

We should add a pymc-examples using CustomDist first. That would be much more impactful if you want to contribute

Sounds good. I will take a look at what exists and add something if needed

[ricardoV94]

Some nice examples that we have been meaning to illustrate involve simple timeseries: https://gist.github.com/ricardoV94/a49b2cc1cf0f32a5f6dc31d6856ccb63

We should however start with something simpler. The Maxwell distribution is a good example (as well as the two last examples in the docstrings).

This is a bit related to #6603

[williambdean]

Some nice examples that we have been meaning to illustrate involve simple timeseries: https://gist.github.com/ricardoV94/a49b2cc1cf0f32a5f6dc31d6856ccb63

We should however start with something simpler. The Maxwell distribution is a good example (as well as the two last examples in the docstrings).

This is a bit related to #6603

Sounds good. I see this current one (Notebook here) as the only one that touches this topic. Should I append to this or make something new?

I like your time series example and could work up to that. I can note distributions like skellam (difference of two distribution), BetaNegativeBinomial (compound distribution), and maxwell (scaled distribution) as they all small examples and touch some differences. I like your probabilities puzzles too which I would like to link.

I will open up an pymc-examples issue for this

[ricardoV94]

Closed via #7007

[ricardoV94]

Thanks @wd60622