: Mathematics: Gauss-Kuzmin distribution

probability theory > probability distribution > Gauss-Kuzmin distribution

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mathematical analysis > real analysis > continued fraction > Gauss-Kuzmin distribution

Gauss-Kuzmin distribution

In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function
${\\displaystyle p(k)=-\\log _{2}\\left(1-{\ rac {1}{(1+k)^{2}}}\ ight)~.}$

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