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On beta distributed limits of iterated linear random functions

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  • McKinlay, Shaun

Abstract

We consider several special cases of iterations of random i.i.d. linear functions with beta distributed fixed points. When iterated in a backward direction we obtain a nested interval scheme, whilst the forward direction generates an ergodic Markov chain. Our approach involves relating the random equation satisfied by the beta distributed fixed point to a random equation with a gamma distributed fixed point. The paper extends many results available in the existing literature.

Suggested Citation

  • McKinlay, Shaun, 2017. "On beta distributed limits of iterated linear random functions," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 33-41.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:33-41
    DOI: 10.1016/j.spl.2017.03.021
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    References listed on IDEAS

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    1. Stoyanov, Jordan & Pirinsky, Christo, 2000. "Random motions, classes of ergodic Markov chains and beta distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 293-304, November.
    2. Pacheco-González, Carlos G., 2009. "Ergodicity of a bounded Markov chain with attractiveness towards the centre," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2177-2181, October.
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    6. Chen, Robert & Goodman, Richard & Zame, Alan, 1984. "Limiting distributions of two random sequences," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 221-230, April.
    7. Johnson, Norman L. & Kotz, Samuel, 1995. "Use of moments in studies of limit distributions arising from iterated random subdivisions of an interval," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 111-119, August.
    8. Stefano M. Iacus & Ilia Negri, 2003. "Estimating unobservable signal by Markovian noise induction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(2), pages 153-167, December.
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