Convert between parametrizations of the Beta distribution

Given two shape parameters, calculate the mean and precision of the Beta distribution; or, given a mean and precision, calculate the corresponding shape parameters.

Usage

shapes_to_muphi(shape1, shape2)

muphi_to_shapes(mu, phi)

Arguments

shape1

The first shape parameter of the Beta distribution

shape2

The second shape parameter of the Beta distribution

mu

The mean of the Beta distribution

phi

The precision of the Beta distribution

Value

A list with two elements containing either the converted shape parameters or mean and precision values.

Details

The Beta distribution is defined by two shape parameters, α and β. Often it is desirable to parametrize the Beta distribution in terms of its mean and precision, rather than the shape parameters. Given, shape parameters, the mean (μ) and precision (φ) are calculated as:

$$\mu = \frac{\alpha}{\alpha + \beta}$$ $$\phi = \alpha + \beta$$

Similarly, given a mean and precision for the Beta distribution, the shape parameters can be calculated as:

$$\alpha = \mu\phi$$ $$\beta = (1 - \mu)\phi$$

For an intuitive introduction to the Beta distribution, see this post from Andrew Heiss.

Author

Andrew Heiss

Examples

shapes_to_muphi(6, 4)
#> $mu
#> [1] 0.6
#> 
#> $phi
#> [1] 10
#> 

muphi_to_shapes(0.6, 10)
#> $shape1
#> [1] 6
#> 
#> $shape2
#> [1] 4
#>