The purpose of this paper is to investigate properties of the probability density function of the rank statistics for a Brownian motion. Fujita and Miura(2006)defined the rank statistics for a Brownian motion and derived closed form for its density function.However,since their density function includes multiple integrals, it is hard to imagine the shape of the density function. Thus we will evaluate the multiple integrals numerically to investigate the properties of the density function of the rank statistics.We also prove some properties of the distribution of the rank statistics mathematically.
On the Probability Density Function of the Rank Statistics
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19-1_⑦Kamimura&Miura
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