added log-cauchy distribution

[mayankray2020]

• stats
  • implemented LogCauchy Distribution

[sympy-bot]

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• stats
  • implemented LogCauchy Distribution (#20632 by @mayankray2020)

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<!-- BEGIN RELEASE NOTES -->
* stats
  * implemented LogCauchy Distribution

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[czgdp1807]

Suggested change

	r"""
	Create a continuous random variable with a Log-Cauchy distribution.
	The density of the Log-Cauchy distribution is given by
	.. math::
	f(x) := \frac{1}{\pi x} \frac{\gamma}{(log(x)-\x0^2) + \gamma^2}
	Parameters
	==========
	x0 : Real number, the location
	gamma : Real number, `\gamma > 0`, a scale
	Returns
	=======
	RandomSymbol
	Examples
	========
	>>> from sympy.stats import LogCauchy, density, cdf
	>>> from sympy import Symbol, S
	>>> x0 = 2
	>>> gamma = S.One / 5
	>>> z = Symbol("z")
	>>> X = LogCauchy("x", x0, gamma)
	>>> density(X)(z)
	1/(5*pi*z*((log(z) - 2)**2 + 1/25))
	>>> cdf(X)(z)
	atan(5*log(z) - 10)/pi + 1/2
	References
	==========
	.. [1] https://en.wikipedia.org/wiki/Log-Cauchy_distribution
	"""
	r"""
	Create a continuous random variable with a Log-Cauchy distribution.
	The density of the Log-Cauchy distribution is given by
	.. math::
	f(x) := \frac{1}{\pi x} \frac{\gamma}{(log(x)-\x0^2) + \gamma^2}
	Parameters
	==========
	x0 : Real number, the location
	gamma : Real number, `\gamma > 0`, a scale
	Returns
	=======
	RandomSymbol
	Examples
	========
	>>> from sympy.stats import LogCauchy, density, cdf
	>>> from sympy import Symbol, S
	>>> x0 = 2
	>>> gamma = S.One / 5
	>>> z = Symbol("z")
	>>> X = LogCauchy("x", x0, gamma)
	>>> density(X)(z)
	1/(5*pi*z*((log(z) - 2)**2 + 1/25))
	>>> cdf(X)(z)
	atan(5*log(z) - 10)/pi + 1/2
	References
	=========
	.. [1] https://en.wikipedia.org/wiki/Log-Cauchy_distribution
	"""

[mayankray2020]

done

[czgdp1807]

Please add symbolic tests instead.

[mayankray2020]

added symbolic tests

[czgdp1807]

Suggested change

	return rv(name, LogCauchyDistribution, (x0, gamma))
	#-------------------------------------------------------------------------------
	return rv(name, LogCauchyDistribution, (x0, gamma))
	#-------------------------------------------------------------------------------

[mayankray2020]

done

[czgdp1807]

Suggested change

	set = Interval(0, oo)
	set = Interval.open(0, oo)

[mayankray2020]

done

[mayankray2020]

@czgdp1807 please review this

[czgdp1807]

Suggested change

	_value_check(sigma > 0, "Scale parameter Gamma must be positive.")
	_value_check((sigma > 0) != False, "Scale parameter Gamma must be positive.")

[mayankray2020]

done @czgdp1807

[czgdp1807]

LGTM. Will merge tomorrow if no objections raised.