Runs in coin tossing: a general approach for deriving distributions for functionals

Lars Holst, Takis Konstantopoulos

Published 2014-07-25Version 1

We take a fresh look at the classical problem of runs in a sequence of i.i.d.\ coin tosses and derive a general identity/recursion which can be used to compute (joint) distributions of functionals of run types. This generalizes and unifies already existing approaches. We give several examples, derive asymptotics, and pose some further questions.