cdf#
- Mixture.cdf(x, y=None, /, *, method=None)[source]#
- Cumulative distribution function - The cumulative distribution function (“CDF”), denoted \(F(x)\), is the probability the random variable \(X\) will assume a value less than or equal to \(x\): \[F(x) = P(X ≤ x)\]- A two-argument variant of this function is also defined as the probability the random variable \(X\) will assume a value between \(x\) and \(y\). \[F(x, y) = P(x ≤ X ≤ y)\]- cdfaccepts x for \(x\) and y for \(y\).- Parameters:
- x, yarray_like
- The arguments of the CDF. x is required; y is optional. 
- method{None, ‘formula’, ‘logexp’, ‘complement’, ‘quadrature’, ‘subtraction’}
- The strategy used to evaluate the CDF. By default ( - None), the one-argument form of the function chooses between the following options, listed in order of precedence.- 'formula': use a formula for the CDF itself
- 'logexp': evaluate the log-CDF and exponentiate
- 'complement': evaluate the CCDF and take the complement
- 'quadrature': numerically integrate the PDF
 - In place of - 'complement', the two-argument form accepts:- 'subtraction': compute the CDF at each argument and take the difference.
 - Not all method options are available for all distributions. If the selected method is not available, a - NotImplementedErrorwill be raised.
 
- Returns:
- outarray
- The CDF evaluated at the provided argument(s). 
 
 - Notes - Suppose a continuous probability distribution has support \([l, r]\). The CDF \(F(x)\) is related to the probability density function \(f(x)\) by: \[F(x) = \int_l^x f(u) du\]- The two argument version is: \[F(x, y) = \int_x^y f(u) du = F(y) - F(x)\]- The CDF evaluates to its minimum value of \(0\) for \(x ≤ l\) and its maximum value of \(1\) for \(x ≥ r\). - The CDF is also known simply as the “distribution function”. - References [1]- Cumulative distribution function, Wikipedia, https://en.wikipedia.org/wiki/Cumulative_distribution_function - Examples - Instantiate a distribution with the desired parameters: - >>> from scipy import stats >>> X = stats.Uniform(a=-0.5, b=0.5) - Evaluate the CDF at the desired argument: - >>> X.cdf(0.25) 0.75 - Evaluate the cumulative probability between two arguments: - >>> X.cdf(-0.25, 0.25) == X.cdf(0.25) - X.cdf(-0.25) True