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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributions. [ 1 ] It is closely related to the Bhattacharyya coefficient, which is a measure of the amount of overlap between two statistical samples or populations. It is not a metric, despite being named a "distance ...
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . 1. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is ...
Saddlepoint approximation method. The saddlepoint approximation method, initially proposed by Daniels (1954) is a specific example of the mathematical saddlepoint technique applied to statistics. It provides a highly accurate approximation formula for any PDF or probability mass function of a distribution, based on the moment generating function.
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. Given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is ...
As the number of discrete events increases, the function begins to resemble a normal distribution. Comparison of probability density functions, () for the sum of fair 6-sided dice to show their convergence to a normal distribution with increasing , in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the ...
In probability theory and statistics, the Weibull distribution / ˈwaɪbʊl / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables. The operation here is a special case of convolution in the ...