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@ -110,6 +110,10 @@ class betaoddsrat_gen(stats.rv_continuous): |
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"""Construct a new beta_ratio distribution from two SciPy beta distributions""" |
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return self(*beta1.args, *beta2.args) |
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def set_cdf_terms(self, cdf_terms): |
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"""Set the number of terms to use when calculating CDF (see _cdf)""" |
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BETA_ODDSRATIO_CDF_TERMS[0] = cdf_terms |
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def _do_vectorized(self, func, x, a1, b1, a2, b2): |
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"""Helper function to call the implementation over potentially multiple values""" |
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@ -138,8 +142,39 @@ class betaoddsrat_gen(stats.rv_continuous): |
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def _pdf(self, w, a1, b1, a2, b2): |
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return self._do_vectorized(self._pdf_one, w, a1, b1, a2, b2) |
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def _cdf_one_infsum(self, w, a1, b1, a2, b2): |
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"""CDF for the distribution, by truncating infinite sum given by Hora & Kelly""" |
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if w <= 0: |
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return 0 |
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elif w < 1: |
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k = mpmath.beta(a1 + a2, b1 + b2) / (mpmath.beta(a1, b1) * mpmath.beta(a2, b2)) |
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inf_sum = 0 |
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for j in range(0, BETA_ODDSRATIO_CDF_TERMS[0]): |
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kj1 = mpmath.rf(a1 + b1, j) * mpmath.rf(a1 + a2, j) |
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kj2 = mpmath.rf(a1 + a2 + b1 + b2, j) * mpmath.factorial(j) |
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inf_sum += kj1/kj2 * mpmath.betainc(a1, j + 1, 0, w) |
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return k * inf_sum |
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else: |
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k = mpmath.beta(a1 + a2, b1 + b2) / (mpmath.beta(a1, b1) * mpmath.beta(a2, b2)) |
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inf_sum = 0 |
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for j in range(0, BETA_ODDSRATIO_CDF_TERMS[0]): |
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kj1 = mpmath.rf(a2 + b2, j) * mpmath.rf(a1 + a2, j) |
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kj2 = mpmath.rf(a1 + a2 + b1 + b2, j) * mpmath.factorial(j) |
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inf_sum += kj1/kj2 * mpmath.betainc(a2, j + 1, 0, mpmath.power(w, -1)) |
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return 1 - k * inf_sum |
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def _cdf(self, w, a1, b1, a2, b2): |
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"""CDF for the distribution, computed by integrating the PDF""" |
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""" |
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CDF for the distribution |
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If BETA_ODDSRATIO_CDF_TERMS = np.inf, compute the CDF by integrating the PDF |
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Otherwise, compute the CDF by truncating the infinite sum given by Hora & Kelley |
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""" |
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w = np.atleast_1d(w) |
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a1 = np.atleast_1d(a1) |
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@ -150,21 +185,26 @@ class betaoddsrat_gen(stats.rv_continuous): |
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if not ((a1 == a1[0]).all() and (b1 == b1[0]).all() and (a2 == a2[0]).all() and (b2 == b2[0]).all()): |
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raise ValueError('Cannot compute CDF from different distributions') |
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if w.size == 1: |
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if w <= 0: |
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return 0 |
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# Just compute an integral |
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if w < self.mean(a1, b1, a2, b2): |
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# Integrate normally |
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return integrate.quad(lambda x: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), 0, w)[0] |
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if BETA_ODDSRATIO_CDF_TERMS[0] == np.inf: |
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# Exact solution requested |
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if w.size == 1: |
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if w <= 0: |
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return 0 |
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# Just compute an integral |
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if w < self.mean(a1, b1, a2, b2): |
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# Integrate normally |
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return integrate.quad(lambda x: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), 0, w)[0] |
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else: |
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# Integrate on the distribution of 1/w (much faster) |
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return 1 - integrate.quad(lambda x: self._pdf_one(x, a2[0], b2[0], a1[0], b1[0]), 0, 1/w)[0] |
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else: |
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# Integrate on the distribution of 1/w (much faster) |
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return 1 - integrate.quad(lambda x: self._pdf_one(x, a2[0], b2[0], a1[0], b1[0]), 0, 1/w)[0] |
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# Multiple points requested: use ODE solver |
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solution = integrate.solve_ivp(lambda x, _: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), (0, w.max()), [0], t_eval=w, method='LSODA', rtol=1.5e-8, atol=1.5e-8) |
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return solution.y |
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else: |
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# Multiple points requested: use ODE solver |
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solution = integrate.solve_ivp(lambda x, _: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), (0, w.max()), [0], t_eval=w, method='LSODA', rtol=1.5e-8, atol=1.5e-8) |
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return solution.y |
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# Truncate infinite sum |
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return self._do_vectorized(self._cdf_one_infsum, w, a1, b1, a2, b2) |
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def _ppf_one(self, p, a1, b1, a2, b2): |
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"""PPF for the distribution, using Newton's method""" |
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@ -200,7 +240,10 @@ class betaoddsrat_gen(stats.rv_continuous): |
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def _munp(self, k, a1, b1, a2, b2): |
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return self._do_vectorized(self._munp_one, k, a1, b1, a2, b2) |
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beta_oddsratio = betaoddsrat_gen(name='beta_oddsratio', a=0) # a = lower bound of support |
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# See beta_oddsratio.cdf |
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BETA_ODDSRATIO_CDF_TERMS = [100] |
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beta_oddsratio = betaoddsrat_gen(name='beta_oddsratio', a=0, shapes='a1,b1,a2,b2') # a = lower bound of support |
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ConfidenceInterval = collections.namedtuple('ConfidenceInterval', ['lower', 'upper']) |
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