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Generates a beta distribution based on a specified mean and variance, and returns a density estimate as a data frame.

Usage

beta_dist(mean, variance, samples = 1000, variance_factor = 0.1)

Arguments

mean

Numeric scalar. Desired mean of the beta distribution. Must be between 0 and 1 (exclusive).

variance

Numeric scalar. Desired variance of the beta distribution. Will be constrained by variance_factor.

samples

Integer. Number of samples to draw from the beta distribution. Default is 1000.

variance_factor

Numeric scalar. Limits the allowed variance as a fraction of the theoretical maximum variance. Default is 0.1.

Value

A tibble with columns x and y representing the smoothed density estimate of the sampled beta distribution.

Details

The shape (i.e., skew and peak) of a Beta distribution is driven by the ratio alpha / (alpha + beta) (which controls the mean), and the sum alpha + beta (which controls the concentration/peakedness).

Examples

beta_dist(mean = 0.4, variance = 0.01)
#> # A tibble: 512 × 2
#>         x        y
#>     <dbl>    <dbl>
#>  1 0.0891 0.000358
#>  2 0.0905 0.000431
#>  3 0.0918 0.000517
#>  4 0.0931 0.000620
#>  5 0.0944 0.000743
#>  6 0.0957 0.000886
#>  7 0.0971 0.00105 
#>  8 0.0984 0.00124 
#>  9 0.0997 0.00147 
#> 10 0.101  0.00174 
#> # ℹ 502 more rows