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A numbered list:
An unordered list:
A mixture of the two:
A Variable List
The definition of term 1
The definition of term 2
The definition of term 3
Here's a big table with code and other tricky things:
Table 1. Notes on the Implementation of the Beta Distribution
Function |
Implementation Notes |
---|---|
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f(x;α,β) = xα - 1 (1 - x)β -1 / B(α, β) Implemented using ibeta_derivative(a, b, x). |
cdf |
Using the incomplete beta function ibeta(a, b, x) |
cdf complement |
ibetac(a, b, x) |
quantile |
Using the inverse incomplete beta function ibeta_inv(a, b, p) |
quantile from the complement |
ibetac_inv(a, b, q) |
mean |
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variance |
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mode |
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skewness |
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kurtosis excess |
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kurtosis |
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parameter estimation |
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alpha from mean and variance |
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beta from mean and variance |
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The member functions from cdf and probability x
and either |
Implemented in terms of the inverse incomplete beta functions ibeta_inva, and ibeta_invb respectively. |
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