Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials

Abstract

Markov chain, Multistate trials, Runs, Moments, Enumeration schemes, Recursive scheme, Conditional distribution, Probability function, Probability generating function, Double generating function,

Bivariate Fibonacci polynomials of order k with statistical applications

“…Details of the derivation of the above formula can be found in Inoue and Aki (2007b) (see Balakrishnan and Koutras 2002). It is worth mentioning here that the generating function (k) (z) can be expressed in terms of bivariate Fibonacci polynomials of order k as (k) (z) = p 0 + ( p 1 p 10 z + B(z))P k−1 ( p 11 z) p 11 z · G (k+1) p 11 z; p 00 p 11 , p 01 p 10 p 2…”

On the Number of Event Appearances in a Markov Chain

“…The exact distributions of the numbers of runs in binary Markov chains were studied by Savelyev and Balakin [23,24], Antzoulakos [1], Inoue [11], and their limit distributions in Markov chains with any number of states were obtained by Tikhomirova [25], Chryssaphinou et al [5], and Fu et al [9]. The distribution of the length of the longest run was considered by Erdos and Revesz [6], Fu [8], and Lou [13] for a sequence of independent random variables and by Chryssaphinou and Vaggelatou [4,26] and Zhang [27] for a Markov chain.…”

On the Number of 1's Per Cycle of a Binary Random Multicyclic Sequence

“…In the future, it is also interesting to obtain limit distributions for the numbers of tuples and runs with a given structure in a sequence of the form (1) (see, e.g., [15,16,17,18,19]).…”