ccdf#
- Normal.ccdf(x, y=None, /, *, method=None)[source]#
- Complementary cumulative distribution function - The complementary cumulative distribution function (“CCDF”), denoted \(G(x)\), is the complement of the cumulative distribution function \(F(x)\); i.e., probability the random variable \(X\) will assume a value greater than \(x\): \[G(x) = 1 - F(x) = P(X > x)\]- A two-argument variant of this function is: \[G(x, y) = 1 - F(x, y) = P(X < x \text{ or } X > y)\]- ccdfaccepts x for \(x\) and y for \(y\).- Parameters:
- x, yarray_like
- The arguments of the CCDF. x is required; y is optional. 
- method{None, ‘formula’, ‘logexp’, ‘complement’, ‘quadrature’, ‘addition’}
- The strategy used to evaluate the CCDF. By default ( - None), the infrastructure chooses between the following options, listed in order of precedence.- 'formula': use a formula for the CCDF itself
- 'logexp': evaluate the log-CCDF and exponentiate
- 'complement': evaluate the CDF and take the complement
- 'quadrature': numerically integrate the PDF
 - The two-argument form chooses between: - 'formula': use a formula for the CCDF itself
- 'addition': compute the CDF at x and the CCDF at y, then add
 - Not all method options are available for all distributions. If the selected method is not available, a - NotImplementedErrorwill be raised.
 
- Returns:
- outarray
- The CCDF evaluated at the provided argument(s). 
 
 - Notes - Suppose a continuous probability distribution has support \([l, r]\). The CCDF \(G(x)\) is related to the probability density function \(f(x)\) by: \[G(x) = \int_x^r f(u) du\]- The two argument version is: \[G(x, y) = \int_l^x f(u) du + \int_y^r f(u) du\]- The CCDF returns its minimum value of \(0\) for \(x ≥ r\) and its maximum value of \(1\) for \(x ≤ l\). - The CCDF is also known as the “survival function”. - References [1]- Cumulative distribution function, Wikipedia, https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions - Examples - Instantiate a distribution with the desired parameters: - >>> import numpy as np >>> from scipy import stats >>> X = stats.Uniform(a=-0.5, b=0.5) - Evaluate the CCDF at the desired argument: - >>> X.ccdf(0.25) 0.25 >>> np.allclose(X.ccdf(0.25), 1-X.cdf(0.25)) True - Evaluate the complement of the cumulative probability between two arguments: - >>> X.ccdf(-0.25, 0.25) == X.cdf(-0.25) + X.ccdf(0.25) True