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A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. [1] It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process.
The discrete phase-type distribution is a probability distribution that results from a system of one or more inter-related geometric distributions occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process .
The Pareto distribution, or "power law" distribution, used in the analysis of financial data and critical behavior. The Pearson Type III distribution; The phase-type distribution, used in queueing theory; The phased bi-exponential distribution is commonly used in pharmacokinetics; The phased bi-Weibull distribution
The law of a stochastic process or a random variable is also called the probability law, probability distribution, or the distribution. [ 133 ] [ 142 ] [ 144 ] [ 145 ] [ 146 ] Finite-dimensional probability distributions
The rule can then be derived [2] either from the Poisson approximation to the binomial distribution, or from the formula (1−p) n for the probability of zero events in the binomial distribution. In the latter case, the edge of the confidence interval is given by Pr( X = 0) = 0.05 and hence (1− p ) n = .05 so n ln (1– p ) = ln .05 ≈ −2.996.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
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 statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
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