Abstract
The upper tail behaviour is explored for a stopped random product ∏j=1NXj, where the factors are positive and independent and identically distributed, andNis the first time one of the factors occupies a subset of the positive reals. This structure is motivated by a heavy-tailed analogue of the factorialn!, called the factoid ofn. Properties of the factoid suggested by computer explorations are shown to be valid. Two topics about the determination of the Zipf exponent in the rank-size law for city sizes are discussed.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability