Recursive splitting of an interval when the proportions are identical and independent random variables (Q749006)

The authors study the distribution of the largest interval that is discarded in the process of randomly and recursively splitting the interval [0,1]. According to the scheme in the paper, at each stage of the process only the left-hand side interval is kept, while the right- hand side interval is discarded. For the case of the uniform distribution, a numerically approximated cumulative distribution function and the probability density function of the maximum discard are derived. Also, several moment relations for the distribution of the maximum discard are given.