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Large deviations for a class of counting processes and some statistical applications

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  • Macci, Claudio
  • Pacchiarotti, Barbara

Abstract

The aim of this paper is to prove results on large deviations for a class of counting processes, and to illustrate some statistical applications. We also present a generalization of the results for a class of compound processes. The statistical applications describe the asymptotic behavior of some issues concerning two hypothesis testing problems, and the logarithmic rates are expressed in terms of the large deviation rate functions.

Suggested Citation

  • Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    • Handle: RePEc:eee:stapro:v:104:y:2015:i:c:p:36-48
    DOI: 10.1016/j.spl.2015.04.028
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    References listed on IDEAS

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    1. Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
    2. de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    3. Leda Minkova & N. Balakrishnan, 2013. "Compound weighted Poisson distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 543-558, May.
    4. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    5. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.
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