A cumulative distribution function (CDF) is a mathematical concept used in probability theory and statistics to describe the probability distribution of a random variable. It provides a way to determine the probability that a random variable takes a value less than or equal to a given point.
The CDF is defined as a function that assigns a probability to each possible value of the random variable. It represents the cumulative sum of all the probabilities up until a specific value. In other words, it calculates the cumulative probability of observing a value less than or equal to a given value.
The CDF is a monotonically increasing function that ranges from 0 to 1. At the lower end, it starts at 0 because the probability of getting a value less than the smallest possible value is zero. At the upper end, it approaches 1 since the probability of obtaining a value greater or equal to the largest possible value is one.
The CDF can be represented mathematically as P(X ≤ x), where X is the random variable and x is a given value. It is commonly used in statistical analysis to calculate important statistical measures such as the mean, median, and percentile values of a random variable.
By examining the CDF, one can gather insights about the distribution of the random variable, including characteristics such as skewness, kurtosis, and symmetry. Additionally, it provides a useful tool for making predictions and analyzing the behavior of data in various fields such as finance, economics, biology, and engineering.
