Beta Distribution
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Tap a term to see what it means, or .
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Example: before launching a page, you believed in a conversion rate near 10%, as if you had already seen 2 conversions in 20 visits: Beta(2, 18). In the first week, 3 of 20 visitors converted. What should you believe now? Change the values to work out your own case.
Step by step
What each term means
- Density (f(p))
- How plausible each value of the proportion p is, between 0 and 1. The area under the curve between two values is the probability that p lies between them.
- Weight of the Successes (p^(α−1))
- Grows with p: the larger α, the more the curve leans towards high proportions. α − 1 works like a count of successes.
- Weight of the Failures ((1 − p)^(β−1))
- Grows as p falls: β − 1 works like a count of failures. Adding k to α and n − k to β is the whole Bayesian update.
- Beta Function (B(α, β))
- The constant that makes the total area under the curve equal 1. It doesn't depend on p, only on the parameters.