What is complementary cumulative distribution function?

The complementary cumulative distribution function (CCDF) is the probability that a random variable X is greater than or equal to a given value x, i.e. P(X >= x). It is also known as the tail distribution function or survival function.

It is complementary to the cumulative distribution function (CDF), which is the probability that X is less than or equal to a given value x, i.e. P(X <= x).

The CCDF is often used in reliability analysis, where it gives the probability that a system or component will survive beyond a certain time or number of cycles. It can also be used to estimate extreme events, such as the probability of a stock market crash or a natural disaster.

The CCDF can be represented graphically as a decreasing curve, starting from 1 at x = -∞ and approaching 0 at x = ∞. It is related to the probability density function (PDF) by the equation CCDF(x) = 1 - CDF(x) = ∫x to ∞ PDF(t) dt.