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1-Dependent Stationary Sequences for Some Given Joint Distributions of Two Consecutive Random Variables

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  • George Haiman

    (Université de Lille 1, UFR de Mathématiques, Cité Scientifique)

Abstract

We provide a method to construct a 1-dependent stationary sequence provided some mixing condition on the joint distribution of two consecutive random variables. Two illustrations of computational benefits of the method are given. We obtain analytical formulas to compute the expectation and variance of the number of occurrences of a word in a sequence of letters from a finite alphabet generated by the 1-dependent model.We also obtain an approximation formula for the distribution of the longest success run in a Bernoulli sequence generated by our model.

Suggested Citation

  • George Haiman, 2012. "1-Dependent Stationary Sequences for Some Given Joint Distributions of Two Consecutive Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 445-458, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9234-y
    DOI: 10.1007/s11009-011-9234-y
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    References listed on IDEAS

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    1. Vaggelatou, Eutichia, 2003. "On the length of the longest run in a multi-state Markov chain," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 211-221, April.
    2. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
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    Cited by:

    1. Haiman, George & Preda, Cristian, 2013. "One dimensional scan statistics generated by some dependent stationary sequences," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1457-1463.

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