The Distribution Function of the Longest Head Run

2020/07/13 by Dennis Koh, Koh, Dennis
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #Advanced Queuing Theory Analysis #Complex Systems and Time Series Analysis #Stochastic processes and financial applications #math.PR #math.ST #msc:60-02 #msc:60J10 #stat.TH

paper · pdf · doi:10.48550/arxiv.2007.06735

Due to an error in Theorem 4.3 on page 4. The proof does not work

arxiv created 2020/07/21 · arxiv updated 2020/07/22

Abstract

In this paper, the open problem of finding a closed analytical expression for the distribution function of the length of the longest pure head run in coin tosses of a possibly biased coin is solved by studying the closely related Markov chain of current head runs.

Related

• Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs
• On the length of the longest consecutive switches
• Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials
• A note on the closed-form solution for the longest head run problem of Abraham de Moivre
• How many coin tosses would you need until you get n Heads or m Tails?