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The geometric distribution, a discrete distribution which describes the number of attempts needed to get the first success in a series of independent Bernoulli trials, or alternatively only the number of losses before the first success (i.e. one less). The Hermite distribution; The logarithmic (series) distribution; The mixed Poisson distribution
v. t. e. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1][2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).
The cumulative distribution function of a real-valued random variable is the function given by [2]: p. 77. (Eq.1) where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore [2]: p. 84.
Furthermore, it covers distributions that are neither discrete nor continuous nor mixtures of the two. An example of such distributions could be a mix of discrete and continuous distributions—for example, a random variable that is 0 with probability 1/2, and takes a random value from a normal distribution with probability 1/2.
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/ n. Intuitively, a discrete uniform distribution is "a known, finite number ...
Continuous uniform distribution. One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc.
The reciprocal 1/ X of a random variable X, is a member of the same family of distribution as X, in the following cases: Cauchy distribution, F distribution, log logistic distribution. Examples: If X is a Cauchy (μ, σ) random variable, then 1/ X is a Cauchy (μ / C, σ / C) random variable where C = μ2 + σ2. If X is an F (ν1, ν2) random ...
The above can be extended in a simple way to allow consideration of distributions which contain both discrete and continuous components. Suppose that the distribution consists of a number of discrete probability masses p k ( θ ) {\textstyle p_{k}(\theta )} and a density f ( x ∣ θ ) {\textstyle f(x\mid \theta )} , where the sum of all the p ...