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The metalog PDF converges to the standard normal PDF as the number of terms increases. With two terms, the metalog approximates the normal with a logistic distribution. With each increment in number of terms, the fit gets closer. With 10 terms, the metalog PDF and standard normal PDF are visually indistinguishable.
The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
A quantile-parameterized distribution (QPD) is a probability distributions that is directly parameterized by data. They were created to meet the need for easy-to-use continuous probability distributions flexible enough to represent a wide range of uncertainties, such as those commonly encountered in business, economics, engineering, and science.
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 ...
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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.
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. [1] Note that such factors may well be functions of the parameters of the
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 ...