# Cumulative Distribution Function (CDF)

## Definition - What does Cumulative Distribution Function (CDF) mean?

Cumulative distribution function (CDF) can be defined as the probability that a random variable isn't greater than a given value. In a random trial the outcome of a random variable will be less than or equal to any specified value of X, as a function of X. It's plotted in a graph in which the horizontal axis is a variable X and the vertical axis ranges from 0-1. Oil and gas exploration and production is a risky industry where decisions are made based on representation of these risks and uncertainty.

CDF and probability density functions (PDF) convey information that will be useful in decision making.

## Trenchlesspedia explains Cumulative Distribution Function (CDF)

CDF are of two types. In the ascending CDF, a coordinate (x,y) indicates that the probability that the random variable X is less than or equal to x is y. In a descending CDF, a coordinate (x,y) indicates that the probability that a random variable X is greater than or equal to x is y. PDF can be integrated to yield the ascending CDF, i.e. for the random variable X, the derivative of an ascending CDF is the corresponding PDF. PDF's communicate the mode of distribution better than a CDF would do and gives lower variance in results for the mean.

CDF is beneficial for the purpose of communicating values like P10, P50 and P90 more accurately.