icdf#
- Uniform.icdf(p, /, *, method=None)[source]#
- Inverse of the cumulative distribution function. - The inverse of the cumulative distribution function (“inverse CDF”), denoted \(F^{-1}(p)\), is the argument \(x\) for which the cumulative distribution function \(F(x)\) evaluates to \(p\). \[F^{-1}(p) = x \quad \text{s.t.} \quad F(x) = p\]- icdfaccepts p for \(p \in [0, 1]\).- Parameters:
- parray_like
- The argument of the inverse CDF. 
- method{None, ‘formula’, ‘complement’, ‘inversion’}
- The strategy used to evaluate the inverse CDF. By default ( - None), the infrastructure chooses between the following options, listed in order of precedence.- 'formula': use a formula for the inverse CDF itself
- 'complement': evaluate the inverse CCDF at the complement of p
- 'inversion': solve numerically for the argument at which the CDF is equal to p
 - Not all method options are available for all distributions. If the selected method is not available, a - NotImplementedErrorwill be raised.
 
- Returns:
- outarray
- The inverse CDF evaluated at the provided argument. 
 
 - Notes - Suppose a continuous probability distribution has support \([l, r]\). The inverse CDF returns its minimum value of \(l\) at \(p = 0\) and its maximum value of \(r\) at \(p = 1\). Because the CDF has range \([0, 1]\), the inverse CDF is only defined on the domain \([0, 1]\); for \(p < 0\) and \(p > 1\), - icdfreturns- nan.- The inverse CDF is also known as the quantile function, percentile function, and percent-point function. - References [1]- Quantile function, Wikipedia, https://en.wikipedia.org/wiki/Quantile_function - 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 inverse CDF at the desired argument: - >>> X.icdf(0.25) -0.25 >>> np.allclose(X.cdf(X.icdf(0.25)), 0.25) True - This function returns NaN when the argument is outside the domain. - >>> X.icdf([-0.1, 0, 1, 1.1]) array([ nan, -0.5, 0.5, nan])