# Ascending and descending cumulative plots

There are two ways one can plots a cdf. The vertical axis can be either the probability of being less than (less than or equal to for a discrete variable) the x-axis value, or the probability of being greater than (greater than or equal to for a discrete variable) the x-axis value:

Obviously, the plots contain the same information. The most common form of the cdf is the ascending cumulative, which equates to the very commonly used probability distribution function F(x). It allows us to directly read off answers to the question 'What is the probability of being less than X?'. The question is most natural for variables where we are happier the large the value of X, for example: life of a person or machine, profit of a project, or time until supplies run out.

The descending cumulative plot is used where we want to answer the question: 'What is the probability of exceeding X?' which is most natural for variables we want to be small, for example: cost and completion time of a project, number of disease outbreaks, or number of people dying from cancer. In reliability engineering, the time cumulative probability P(X>=x) is called the survival function.

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