Python scipy.special.log1p() Examples

def _ppf(self, q, h, k):
        condlist = [np.logical_and(h != 0, k != 0),
                    np.logical_and(h == 0, k != 0),
                    np.logical_and(h != 0, k == 0),
                    np.logical_and(h == 0, k == 0)]

        def f0(q, h, k):
            return 1.0/k*(1.0 - ((1.0 - (q**h))/h)**k)

        def f1(q, h, k):
            return 1.0/k*(1.0 - (-np.log(q))**k)

        def f2(q, h, k):
            '''ppf = -np.log((1.0 - (q**h))/h)
            '''
            return -sc.log1p(-(q**h)) + np.log(h)

        def f3(q, h, k):
            return -np.log(-np.log(q))

        return _lazyselect(condlist,
                           [f0, f1, f2, f3],
                           [q, h, k],
                           default=np.nan) 

def _ppf(self, q, h, k):
        condlist = [np.logical_and(h != 0, k != 0),
                    np.logical_and(h == 0, k != 0),
                    np.logical_and(h != 0, k == 0),
                    np.logical_and(h == 0, k == 0)]

        def f0(q, h, k):
            return 1.0/k*(1.0 - ((1.0 - (q**h))/h)**k)

        def f1(q, h, k):
            return 1.0/k*(1.0 - (-np.log(q))**k)

        def f2(q, h, k):
            '''ppf = -np.log((1.0 - (q**h))/h)
            '''
            return -sc.log1p(-(q**h)) + np.log(h)

        def f3(q, h, k):
            return -np.log(-np.log(q))

        return _lazyselect(condlist,
                           [f0, f1, f2, f3],
                           [q, h, k],
                           default=np.nan) 

def _ppf(self, q, c):
        return sc.expm1(-sc.log1p(-q)/c) 

def _logcdf(self, x, c, d):
        return sc.log1p(-(1 + x**c)**(-d)) 

def _logpdf(self, x, c):
        cx = _lazywhere((x == x) & (c != 0), (x, c), lambda x, c: c*x, 0.0)
        logex2 = sc.log1p(-cx)
        logpex2 = self._loglogcdf(x, c)
        pex2 = np.exp(logpex2)
        # Handle special cases
        np.putmask(logpex2, (c == 0) & (x == -np.inf), 0.0)
        logpdf = np.where((cx == 1) | (cx == -np.inf),
                          -np.inf,
                          -pex2+logpex2-logex2)
        np.putmask(logpdf, (c == 1) & (x == 1), 0.0)
        return logpdf 

def _isf(self, q, c):
        x = -np.log(-sc.log1p(-q))
        return _lazywhere((x == x) & (c != 0), (x, c),
                          lambda x, c: -sc.expm1(-c * x) / c, x) 

def _loglogcdf(self, x, c):
        return _lazywhere((x == x) & (c != 0), (x, c),
                          lambda x, c: sc.log1p(-c*x)/c, -x) 

def _ppf(self, q, b):
        return pow(sc.log1p(-sc.log1p(-q)), 1.0/b) 

def _isf(self, x, b):
        return (sc.log1p(-np.log(x)))**(1./b) 

def _ppf(self, q, a, c):
        return (-sc.log1p(-q**(1.0/a)))**np.asarray(1.0/c) 

def _ppf(self, q, c, d):
        # The following is an implementation of
        #   ((1 - q)**(-1.0/d) - 1)**(1.0/c)
        # that does a better job handling small values of q.
        return sc.expm1(-1/d * sc.log1p(-q))**(1/c) 

def _ppf(self, q, c):
        return pow(-sc.log1p(-q), 1.0/c) 

def _pmf(self, k, p):
        # logser.pmf(k) = - p**k / (k*log(1-p))
        return -np.power(p, k) * 1.0 / k / special.log1p(-p) 

def _logsf(self, x, p):
        k = floor(x)
        return k*log1p(-p) 

def _ppf(self, q, b):
        return -sc.log1p(q*sc.expm1(-b)) 

def _ppf(self, q):
        return np.sqrt(-2 * sc.log1p(-q)) 

def _ppf(self, q, lambda_):
        vals = ceil(-1.0/lambda_ * log1p(-q)-1)
        vals1 = (vals-1).clip(self.a, np.inf)
        temp = self._cdf(vals1, lambda_)
        return np.where(temp >= q, vals1, vals) 

def _logsf(self, x, c):
        return -c*sc.log1p(x) 

def _sf(self, x, c):
        return np.exp(-c*sc.log1p(x)) 

def _logpdf(self, x, c):
        return np.log(c) - (c+1)*sc.log1p(x) 

def _logcdf(self, x, h, k):
        condlist = [np.logical_and(h != 0, k != 0),
                    np.logical_and(h == 0, k != 0),
                    np.logical_and(h != 0, k == 0),
                    np.logical_and(h == 0, k == 0)]

        def f0(x, h, k):
            '''cdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h)
               logcdf = ...
            '''
            return (1.0/h)*sc.log1p(-h*(1.0 - k*x)**(1.0/k))

        def f1(x, h, k):
            '''cdf = np.exp(-(1.0 - k*x)**(1.0/k))
               logcdf = ...
            '''
            return -(1.0 - k*x)**(1.0/k)

        def f2(x, h, k):
            '''cdf = (1.0 - h*np.exp(-x))**(1.0/h)
               logcdf = ...
            '''
            return (1.0/h)*sc.log1p(-h*np.exp(-x))

        def f3(x, h, k):
            '''cdf = np.exp(-np.exp(-x))
               logcdf = ...
            '''
            return -np.exp(-x)

        return _lazyselect(condlist,
                           [f0, f1, f2, f3],
                           [x, h, k],
                           default=np.nan) 

def _logpdf(self, x):
        return -x - 2. * sc.log1p(np.exp(-x)) 

def _logpdf(self, x):
        return np.log(2) - x - 2. * sc.log1p(np.exp(-x)) 

def _ppf(self, q):
        return np.log(-sc.log1p(-q)) 

def _ppf(self, q, c):
        return sc.log1p(-1.0 / c * sc.log1p(-q)) 

def _isf(self, q, c):
        x = -np.log(-sc.log1p(-q))
        return _lazywhere((x == x) & (c != 0), (x, c),
                          lambda x, c: -sc.expm1(-c * x) / c, x) 

def _logpdf(self, x, c):
        cx = _lazywhere((x == x) & (c != 0), (x, c), lambda x, c: c*x, 0.0)
        logex2 = sc.log1p(-cx)
        logpex2 = self._loglogcdf(x, c)
        pex2 = np.exp(logpex2)
        # Handle special cases
        np.putmask(logpex2, (c == 0) & (x == -np.inf), 0.0)
        logpdf = np.where((cx == 1) | (cx == -np.inf),
                          -np.inf,
                          -pex2+logpex2-logex2)
        np.putmask(logpdf, (c == 1) & (x == 1), 0.0)
        return logpdf 

def _loglogcdf(self, x, c):
        return _lazywhere((x == x) & (c != 0), (x, c),
                          lambda x, c: sc.log1p(-c*x)/c, -x) 

def _logpdf(self, x, c):
        return np.log(c) - x - (c+1.0)*sc.log1p(np.exp(-x)) 

def _ppf(self, q, c):
        return pow(-sc.log1p(-q), 1.0/c)