arc-sine transformation

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For a random variable X, having a binomial distribution with parameters n and p, a transformation that stabilizes the variance and produces a variable with an approximate normal distribution whose variance is almost independent of p is An improvement suggested by Anscombe in 1948 is Both transformed variables have expectation and variance given approximately by sin−1√p and 1/(4n), respectively. See also Freeman–Tukey transformation.

Subjects: Probability and Statistics.

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