Cumulative density function

Cumulative density function is a self-contradictory phrase resulting from confusion between:

• probability density function, and
• cumulative distribution function.

The two words cumulative and density contradict each other. Given a graph of the probability density function $$y={P}(x),$$

$y$ is the probability of finding just the particular value of the variable corresponding to $x$ on the $x$-axis. It knows nothing about the probabilities to be found at other values of $x$, and therefore cannot be cumulative. The cumulative density function, by contrast is an accumulation of the probabilities of finding every value of $x$ up to and including the current value indicated on the $x$-axis.