我们从Python开源项目中，提取了以下12个代码示例，用于说明如何使用scipy.special.betainc()。
def compHistDistance(h1, h2): def normalize(h): if np.sum(h) == 0: return h else: return h / np.sum(h) def smoothstep(x, x_min=0., x_max=1., k=2.): m = 1. / (x_max - x_min) b = - m * x_min x = m * x + b return betainc(k, k, np.clip(x, 0., 1.)) def fn(X, Y, k): return 4. * (1. - smoothstep(Y, 0, (1 - Y) * X + Y + .1)) \ * np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) \ + 2. * smoothstep(Y, 0, (1 - Y) * X + Y + .1) \ * (1. - 2. * np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) - 0.5) h1 = normalize(h1) h2 = normalize(h2) return max(0, np.sum(fn(h2, h1, len(h1)))) # return np.sum(np.where(h2 != 0, h2 * np.log10(h2 / (h1 + 1e-10)), 0)) # KL divergence
def my_t1cdf(x): ''' cumulative distribution function of a t-dist. with 1 degree of freedom function p=my_t1cdf(x) input x = point output p = cumulative probability see also: tcdf ''' xsq=x*x; p = betainc(1/2, 1/2,1 / (1 + xsq)) / 2 p[x>0]=1-p[x>0] return p
def cdf(self, x): """Evaluates the CDF along the values ``x``.""" y = .5 * betainc(self.m / 2., .5, np.sin(np.pi * x) ** 2) return np.where(x < .5, y, 1 - y)
def MakeCdf(self, steps=101): """Returns the CDF of this distribution.""" xs = [i / (steps - 1.0) for i in range(steps)] ps = [special.betainc(self.alpha, self.beta, x) for x in xs] cdf = Cdf(xs, ps) return cdf
def ttest_1samp(population_mean, a, axis=0): """ Calculates the T-test for the mean of ONE group of scores. Parameters ---------- a : array_like sample observation population_mean : float or array_like expected value in null hypothesis, if array_like than it must have the same shape as `a` excluding the axis dimension axis : int or None, optional Axis along which to compute test. If None, compute over the whole array `a`. Returns ------- statistic : float or array t-statistic pvalue : float or array two-tailed p-value Notes ----- For more details on `ttest_1samp`, see `stats.ttest_1samp`. """ a, axis = _chk_asarray(a, axis) if a.size == 0: return 'Empty Array' sample_mean = a.mean(axis=axis) sample_var = a.var(axis=axis, ddof=1) sample_count = a.count(axis=axis) # force df to be an array for masked division not to throw a warning df = ma.asanyarray(sample_count - 1.0) svar = ((sample_count - 1.0) * sample_var) / df with np.errstate(divide='ignore', invalid='ignore'): t = (sample_mean - population_mean) / ma.sqrt(svar / sample_count) prob = special.betainc(0.5 * df, 0.5, df / (df + t * t)) return Ttest_1sampResult(t, prob)
def MakeCdf(self, steps=101): """Returns the CDF of this distribution.""" xs = [i / (steps - 1.0) for i in range(steps)] ps = special.betainc(self.alpha, self.beta, xs) cdf = Cdf(xs, ps) return cdf
def log_sf(self,x): scalar = not isinstance(x,np.ndarray) x = np.atleast_1d(x) errs = np.seterr(divide='ignore') ret = np.log(special.betainc(x+1,self.r,self.p)) np.seterr(**errs) ret[x < 0] = np.log(1.) if scalar: return ret[0] else: return ret
def resid_anscombe(self, endog, mu): ''' The Anscombe residuals Parameters ---------- endog : array-like Endogenous response variable mu : array-like Fitted mean response variable Returns ------- resid_anscombe : array The Anscombe residuals as defined below. Notes ----- sqrt(n)*(cox_snell(endog)-cox_snell(mu))/(mu**(1/6.)*(1-mu)**(1/6.)) where cox_snell is defined as cox_snell(x) = betainc(2/3., 2/3., x)*betainc(2/3.,2/3.) where betainc is the incomplete beta function The name 'cox_snell' is idiosyncratic and is simply used for convenience following the approach suggested in Cox and Snell (1968). Further note that cox_snell(x) = x**(2/3.)/(2/3.)*hyp2f1(2/3.,1/3.,5/3.,x) where hyp2f1 is the hypergeometric 2f1 function. The Anscombe residuals are sometimes defined in the literature using the hyp2f1 formulation. Both betainc and hyp2f1 can be found in scipy. References ---------- Anscombe, FJ. (1953) "Contribution to the discussion of H. Hotelling's paper." Journal of the Royal Statistical Society B. 15, 229-30. Cox, DR and Snell, EJ. (1968) "A General Definition of Residuals." Journal of the Royal Statistical Society B. 30, 248-75. ''' cox_snell = lambda x: (special.betainc(2/3., 2/3., x) * special.beta(2/3., 2/3.)) return np.sqrt(self.n) * ((cox_snell(endog) - cox_snell(mu)) / (mu**(1/6.) * (1 - mu)**(1/6.)))
def ttest_ind(a, b, axis=0, equal_var=True): """ Calculates the T-test for the means of two independent samples of scores. Parameters ---------- a, b : array_like The arrays must have the same shape, except in the dimension corresponding to `axis` (the first, by default). axis : int or None, optional Axis along which to compute test. If None, compute over the whole arrays, `a`, and `b`. equal_var : bool, optional If True, perform a standard independent 2 sample test that assumes equal population variances. If False, perform Welch's t-test, which does not assume equal population variance. .. versionadded:: 0.17.0 Returns ------- statistic : float or array The calculated t-statistic. pvalue : float or array The two-tailed p-value. Notes ----- For more details on `ttest_ind`, see `stats.ttest_ind`. """ a, b, axis = _chk2_asarray(a, b, axis) if a.size == 0 or b.size == 0: return 'One of the vector is empty' (mean1, mean2) = (a.mean(axis), b.mean(axis)) (var1, var2) = (a.var(axis=axis, ddof=1), b.var(axis=axis, ddof=1)) (n1, n2) = (a.count(axis), b.count(axis)) if equal_var: # force df to be an array for masked division not to throw a warning df = ma.asanyarray(n1 + n2 - 2.0) svar = ((n1 - 1) * var1 + (n2 - 1) * var2) / df denom = ma.sqrt(svar * (1.0 / n1 + 1.0 / n2)) # n-D computation here! else: vn1 = var1 / n1 vn2 = var2 / n2 with np.errstate(divide='ignore', invalid='ignore'): df = (vn1 + vn2) ** 2 / (vn1 ** 2 / (n1 - 1) + vn2 ** 2 / (n2 - 1)) # If df is undefined, variances are zero. # It doesn't matter what df is as long as it is not NaN. df = np.where(np.isnan(df), 1, df) denom = ma.sqrt(vn1 + vn2) with np.errstate(divide='ignore', invalid='ignore'): t = (mean1 - mean2) / denom probs = special.betainc(0.5 * df, 0.5, df / (df + t * t)).reshape(t.shape) return Ttest_ind(t, probs.squeeze())
