Cumulative distribution function (CDF)


Cumulative distribution function is a function that given event $x$, returns the probability of observing a value equal to or lower than $x$. It is denoted as:

$$ \Phi(x) = F(x) = P(X\leq x) $$

Point percent function (PPF)


The percent-point function (PPF), also known as inverse of CDF, provides the value $x$ corresponding to a given $q-$th quantile, where $q$ percent of observations fall below it. It is often denoted as:

$$ \Phi^{-1}(q) = F^{-1}(q) = x $$

Software implementation


Use scipy.stats.norm.cdf and scipy.stats.norm.ppf to compute CDF and PPF of a normal distribution. Scipy also provides functions for other distribution as well, such as: scipy.stats.poisson, scipy.stats.chi.