Length of stream for an independent events model
Michael F. Dacey · Water Resources Research · 1970
An independent events model is formulated for stream length. The stream is composed of links, where the number of links has the geometric distribution and link lengths are independently and identically distributed as the gamma variate with shape parameter α. This model is similar in all essential respects to the topologically random stream structure formulated by Shreve [1967; 1969]. This paper extends his results and shows that for α = 2 the distribution of stream length obeys a probability law defined by the modified Bessel function. It is also shown that when the expected number of links in a stream is large, stream length is approximated by the exponential distribution.