Generalized beta distribution

In probability and statistics, the generalized beta distribution is a continuous probability distribution with four shape parameters (however it's customary to make explicit the scale parameter as a fifth parameter, while the location parameter is usually left implicit), including more than thirty named distributions as limiting or special cases. It has been used in the modeling of income distribution, stock returns, as well as in regression analysis. The exponential generalized beta (EGB) distribution follows directly from the GB and generalizes other common distributions. A generalized beta random variable, Y, is defined by the following probability density function: and zero otherwise. Here the parameters satisfy , and , , and positive. The function B(p,q) is the beta function. The parameter is the scale parameter and can thus be set to without loss of generality, but it is usually made explicit as in the function above (while the location parameter is usually left implicit and set to as in the function above). It can be shown that the hth moment can be expressed as follows: where denotes the hypergeometric series (which converges for all h if c

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (5)

Related concepts (1)

Related lectures (5)

Shape parameter

In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributions that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter). Such a parameter must affect the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). For example, "peakedness" refers to how round the main peak is.

Improved modelling of a monomorph piezoelectric actuator for linear self-sensing applications

Yves Perriard, Louis Antoine Masson

Based on a previous approach for the modelling of piezoelectric monomorph benders, a new, more complete, analytical model is proposed. Some previously neglected features of the actuator stack, notably the thickness of the electrodes and the presence of iso ...

IEEE2019

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high t ...

Springer2016

Mapping extreme snowfalls in the French Alps using max-stable processes

Johan Alexandre Philippe Gaume

The evaluation of extreme snowfalls is an important challenge for hazard management in mountainous regions. In this paper, the extreme snowfall data acquired from 40 meteorological stations in the French Alps since 1966 are analyzed using spatial extreme s ...

2013

Exploration vs. Exploitation: Softmax Policy Quiz CS-456: Artificial neural networks/reinforcement learning

Presents a quiz on the exploration vs. exploitation dilemma using the softmax policy.

Extreme Value Theory: Maximum Distribution MATH-447: Risk, rare events and extremes

Explores extreme value theory, focusing on maximum distribution and different types of distributions based on shape parameters.

Basics of Risk Analysis and Management CIVIL-438: Risk analysis and management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.