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The metalog distribution is a generalization of the logistic distribution, where the term "metalog" is short for "metalogistic".Starting with the logistic quantile function, = = + (), Keelin substituted power series expansions in cumulative probability = for the and the parameters, which control location and scale, respectively.
The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1]. The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1).
The metalog distribution is generalization of the logistic distribution, in which power series expansions in terms of are substituted for logistic parameters and . The resulting metalog quantile function is highly shape flexible, has a simple closed form, and can be fit to data with linear least squares.
Another generalized log-logistic distribution is the log-transform of the metalog distribution, in which power series expansions in terms of are substituted for logistic distribution parameters and . The resulting log-metalog distribution is highly shape flexible, has simple closed form PDF and quantile function , can be fit to data with linear ...
For other families of distributions that have also been called generalized logistic distributions, see the shifted log-logistic distribution, which is a generalization of the log-logistic distribution; and the metalog ("meta-logistic") distribution, which is highly shape-and-bounds flexible and can be fit to data with linear least squares.
The unbounded metalog distribution, which is a power series expansion of the and parameters of the logistic quantile function. The semi-bounded and bounded metalog distributions, which are the log and logit transforms, respectively, of the unbounded metalog distribution.
This category is collections of probability distribution that have been brought together for a similar usage in Statistics to the Pearson system of distributions, or the Burr system. That is to have distributions that between them cover a range of behaviour that is not covered by any single one, such that a statistical analysis would select a ...
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution.
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