python source code of f

Project: chaospy (GitHub Link)

chaospy-master
- .circleci
  - config.yml
- poetry.lock
- chaospy
  - spectral.py
  - descriptives
    - expected.py
    - kurtosis.py
    - correlation
      - pearson.py
      - auto_correlation.py
      - spearman.py
      - __init__.py
    - quantity_of_interest.py
    - skewness.py
    - percentile.py
    - standard_deviation.py
    - __init__.py
    - covariance.py
    - variance.py
    - conditional.py
    - sensitivity
      - main2.py
      - __init__.py
      - main.py
      - total.py
  - prange.py
  - basis.py
  - distributions
    - copulas
      - joe.py
      - clayton.py
      - __init__.py
      - gumbel.py
      - nataf.py
      - t_copula.py
      - archimedean.py
      - baseclass.py
    - constructor.py
    - operators
      - binary.py
      - logarithm.py
      - power.py
      - multiply.py
      - matmul.py
      - unary.py
      - __init__.py
      - negative.py
      - joint.py
      - addition.py
      - trunkation.py
    - evaluation
      - bound.py
      - parameters.py
      - forward.py
      - recurrence_coefficients.py
      - inverse.py
      - common.py
      - __init__.py
      - moment.py
      - density.py
      - dependencies.py
    - collection
      - f.py
      - beta.py
      - power_log_normal.py
      - anglit.py
      - power_normal.py
      - fisk.py
      - tukey_lambda.py
      - chi_squared.py
      - gompertz.py
      - uniform.py
      - logistic.py
      - chi.py
      - kumaraswamy.py
      - weibull.py
      - log_uniform.py
      - mv_log_normal.py
      - trunc_normal.py
      - normal.py
      - wrapped_cauchy.py
      - pareto1.py
      - wald.py
      - reciprocal.py
      - hyperbolic_secant.py
      - fatigue_life.py
      - mielke.py
      - log_weibull.py
      - burr.py
      - exponential_power.py
      - folded_normal.py
      - generalized_half_logistic.py
      - mv_normal.py
      - generalized_extreme.py
      - triangle.py
      - generalized_gamma.py
      - log_laplace.py
      - double_gamma.py
      - discrete_uniform.py
      - laplace.py
      - bradford.py
      - __init__.py
      - gamma.py
      - double_weibull.py
      - frechet.py
      - binomial.py
      - folded_cauchy.py
      - alpha.py
      - log_normal.py
      - cauchy.py
      - exponential_weibull.py
      - trunc_exponential.py
      - student_t.py
      - generalized_exponential.py
      - mv_student_t.py
      - pareto2.py
      - log_gamma.py
      - levy.py
      - nakagami.py
    - __init__.py
    - sampler
      - antithetic.py
      - latin_hypercube.py
      - generator.py
      - __init__.py
      - sequences
        van_der_corput.py
        chebyshev.py
        primes.py
        korobov.py
        grid.py
        hammersley.py
        __init__.py
        halton.py
        sobol.py
    - approximation.py
    - baseclass.py
  - external
    - scipy_stats.py
    - samples.py
    - openturns_.py
    - __init__.py
  - regression.py
  - example.py
  - orthogonal
    - frontend.py
    - three_terms_recursion.py
    - lagrange.py
    - gram_schmidt.py
    - __init__.py
    - cholesky.py
  - saltelli.py
  - __init__.py
  - chol
    - schnabel_eskow_.py
    - gill_murray_wright_.py
    - gill_king_.py
    - __init__.py
    - bastos_ohagen_.py
  - quadrature
    - recurrence
      - stieltjes.py
      - frontend.py
      - chebyshev.py
      - jacobi.py
      - lanczos.py
      - __init__.py
    - frontend.py
    - gauss_lobatto.py
    - gauss_radau.py
    - sparse_grid.py
    - gauss_patterson.py
    - newton_cotes.py
    - clenshaw_curtis.py
    - gauss_legendre.py
    - fejer.py
    - genz_keister
      - frontend.py
      - gk22.py
      - gk24.py
      - __init__.py
      - gk16.py
      - gk18.py
    - __init__.py
    - gauss_kronrod.py
    - combine.py
    - leja.py
    - gaussian.py
- polychaos.md
- codecov.yml
- tasks.rst
- .readthedocs.yaml
- README.rst
- CHANGELOG.rst
- poly
  - wrapper.py
  - variable.py
  - __init__.py
  - setdim.py
- tests
  - test_dist.py
  - test_orth.py
  - distributions
    - operators
      - test_multiply.py
      - test_matmul.py
  - quad
    - test_interface.py
  - poly
    - test_numpoly.py
  - test_pdf.py
  - test_stress.py
  - test_poly.py
- pyproject.toml
- docs
  - lagrange.rst
  - polynomial.rst
  - orthogonality.rst
  - Makefile
  - distributions
    - collection.rst
    - custom.rst
    - multivariate.py
    - multivariate.rst
    - index.rst
    - baseclass.rst
    - copulas.rst
  - sampling
    - introduction.rst
    - antithetic.rst
    - index.rst
    - sequences.rst
  - .static
    - chaospy_logo.svg
  - bibliography.bib
  - tutorials
    - polynomial
      - lagrange_polynomials.ipynb
      - wiener_askey_scheme.ipynb
      - polynomial_evaluation.ipynb
      - expansion_construction.ipynb
      - truncation_scheme.ipynb
    - README.rst
    - example_introduction.ipynb
    - introduction
      - monte_carlo_integration.ipynb
      - pseudo_spectral_projection.ipynb
    - advanced
      - intrusive_galerkin.ipynb
      - scikitlearn_regression.ipynb
  - quadrature.rst
  - fig
    - tutorial_figures.py
  - descriptives.rst
  - requirements.txt
  - index.rst
  - conf.py
  - installation.rst
- LICENSE.txt
- MANIFEST.in
- conftest.py

"""(Non-central) F distribution."""
import numpy
from scipy import special

from ..baseclass import Dist
from ..operators.addition import Add


class f(Dist):
    """F distribution."""

    def __init__(self, dfn, dfd, nc):
        Dist.__init__(self, dfn=dfn, dfd=dfd, nc=nc)

    def _pdf(self, x, dfn, dfd, nc):
        n1, n2 = dfn, dfd
        term = -nc/2.+nc*n1*x/(2*(n2+n1*x)) + special.gammaln(n1/2.)+special.gammaln(1+n2/2.)
        term -= special.gammaln((n1+n2)/2.)
        Px = numpy.exp(term)
        Px *= n1**(n1/2.) * n2**(n2/2.) * x**(n1/2.-1)
        Px *= (n2+n1*x)**(-(n1+n2)/2.)
        Px *= special.assoc_laguerre(-nc*n1*x/(2.*(n2+n1*x)), n2/2., n1/2.-1)
        Px /= special.beta(n1/2., n2/2.)
        return Px

    def _cdf(self, x, dfn, dfd, nc):
        return special.ncfdtr(dfn, dfd, nc, x)

    def _ppf(self, q, dfn, dfd, nc):
        return special.ncfdtri(dfn, dfd, nc, q)

    def _lower(self, dfn, dfd, nc):
        return 0.


class F(Add):
    """
    (Non-central) F or Fisher-Snedecor distribution.

    Args:
        n (float, Dist):
            Degres of freedom for numerator
        m (float, Dist):
            Degres of freedom for denominator
        scale (float, Dist):
            Scaling parameter
        shift (float, Dist):
            Location parameter
        nc (float, Dist):
            Non-centrality parameter

    Examples:
        >>> distribution = chaospy.F(3, 3, 2, 1, 1)
        >>> distribution
        F(m=3, n=3, nc=1, scale=2, shift=1)
        >>> q = numpy.linspace(0, 1, 6)[1:-1]
        >>> distribution.inv(q).round(4)
        array([1.9336, 2.9751, 4.7028, 8.8521])
        >>> distribution.fwd(distribution.inv(q)).round(4)
        array([0.2, 0.4, 0.6, 0.8])
        >>> distribution.pdf(distribution.inv(q)).round(4)
        array([0.2277, 0.1572, 0.0837, 0.027 ])
        >>> distribution.sample(4).round(4)
        array([ 5.4212,  1.5739, 25.7656,  3.5586])
        >>> distribution.mom(1) > 10**8  # undefined
        True
    """

    def __init__(self, n=1, m=1, scale=1, shift=0, nc=0):
        self._repr = {"n": n, "m": m, "scale": scale, "shift": shift, "nc": nc}
        Add.__init__(self, left=f(n, m, nc)*scale, right=shift)