Cumulative Density Function
A Cumulative Density Function is a non-decreasing right-continuous unit function that returns the probability that a real-valued random variable X (with a given probability distribution) will be found at a value less than or equal to x
- AKA: CDF, Cumulative Continuous Probability, Cumulative Distribution Function.
- See: Continuous Random Variable, CDF Function Estimation.
- In probability theory and statistics, the cumulative distribution function (CDF), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
- (Dubnicka, 2006c) ⇒ Suzanne R. Dubnicka. (2006). “Random Variables - STAT 510: Handout 3." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- TERMINOLOGY : The cumulative distribution function (cdf) of a random variable X, denoted by FX(x), is given by FX(x) = P(X x), for all x 2 R.
- ALTERNATE DEFINITION: A random variable is said to be continuous if its cdf FX(x) is a continuous function of x.
- TERMINOLOGY : Let X be a continuous random variable with cdf FX(x). The probability density function (pdf) for X, denoted by fX(x), is given by fX(x) = d/dx FX(x),