Normal approximation to the Beta distribution

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The Beta distribution is difficult to calculate, involving a Beta function in its denominator, so an approximation is often welcome. A Taylor series expansion of the Beta distribution probability density function shows that the Beta(a1, a2) distribution can be approximated by the Normal distribution when a1 and a2 are sufficiently large. More specifically, the conditions are:

          and         

A pretty good rule of thumb is that a1 and a2 are both equal to 10 or more, but they can be as low as 6 if a1 » a2. In such cases, an approximation using the Normal distribution works well where we use the mean and standard deviations from the exact Beta distribution:

Beta(a1, a2)» Normal

Examples of a Normal approximation to a Beta distribution