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Super-Poissonian Distribution
In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a smaller variance. An example of super-Poissonian distribution is negative binomial distribution. The Poisson distribution is a result of a process where the time (or an equivalent measure) between events has an exponential distribution, representing a memoryless process. Mathematical definition In probability theory it is common to say a distribution, ''D'', is a sub-distribution of another distribution ''E'' if ''D'' 's moment-generating function, is bounded by ''E'' 's up to a constant. In other words : E_ exp(t X)\le E_ exp(C t X) for some ''C > 0''. This implies that if X_1 and X_2 are both from a sub-E distribution, then so is X_1+X_2. A distribution is ''strictly sub-'' if ''C ≤ 1''. From this definition a distribution, ''D'', is sub-Poissonian if : E_ exp(t X)\le E_ exp(t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
