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A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
An alternative parameterization of the distribution gives the probability mass function (=) = () where = and =. [ 1 ] : 208–209 An example of a geometric distribution arises from rolling a six-sided die until a "1" appears.
The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a / base measure) for a random variable X for which E[X] = αθ = α/λ is fixed and greater than zero, and E[ln X] = ψ(α) + ln θ = ψ(α) − ln λ is fixed (ψ is the digamma function). [5]
In probability theory and statistics, the generalized extreme value (GEV) distribution [2] is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions.
In probability theory, Wald's equation, Wald's identity [1] or Wald's lemma [2] is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, describes the asymptotic behaviour of the empirical distribution function as the number of independent and identically distributed observations grows. [1]
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product = is a product distribution.