Search results
Results from the WOW.Com Content Network
The probability density function of the four parameter beta distribution is equal to the two parameter distribution, scaled by the range (c − a), (so that the total area under the density curve equals a probability of one), and with the "y" variable shifted and scaled as follows:
The beta family includes the beta of the first and second kind [7] (B1 and B2, where the B2 is also referred to as the Beta prime), which correspond to c = 0 and c = 1, respectively. Setting =, = yields the standard two-parameter beta distribution.
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
It is a transformation of the four-parameter beta distribution with an additional assumption that its expected value is μ = a + 4 b + c 6 . {\displaystyle \mu ={\frac {a+4b+c}{6}}.} The mean of the distribution is therefore defined as the weighted average of the minimum, most likely and maximum values that the variable may take, with four ...
This particular distribution is known as the flat Dirichlet distribution. Values of the concentration parameter above 1 prefer variates that are dense, evenly distributed distributions, i.e. all the values within a single sample are similar to each other. Values of the concentration parameter below 1 prefer sparse distributions, i.e. most of ...
What is now known as the beta distribution had been used by Thomas Bayes as a posterior distribution of the parameter of a Bernoulli distribution in his 1763 work on inverse probability. The Beta distribution gained prominence due to its membership in Pearson's system and was known until the 1940s as the Pearson type I distribution. [1 ...
The beta distribution is a continuous probability distribution defined over the interval . It is characterised by a couple of parameters, namely α {\displaystyle \alpha } and β {\displaystyle \beta } according to:
The compound gamma distribution [3] is the generalization of the beta prime when the scale parameter, q is added, but where p = 1. It is so named because it is formed by compounding two gamma distributions :