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Product-Type Estimator of Convolutions

In: Semi-Markov Models and Applications

Author

Listed:
  • Ilya Gertsbakh

    (Ben Gurion University of the Negev)

  • I. Spungin

    (Ben Gurion University of the Negev)

Abstract

An unbiased estimator of P(τ1 + … + τκ ≤ T) is suggested, where τ i , are independent random variables (r.v.) with density f i (t) and distribution function F i (t). This estimator is constructed sequentially. First, a r.v. X 1 with density f 1(x)/F 1(T) is generated. Its support is [0,T]. After observing X 1 = x 1, the second r.v. X 2 is generated from the density f 2(x)/F(T − x 1). Its support is [0,T − x 1], etc. The desired estimator has the form B(T) = Πψ i (X i ). We investigate the properties of this estimator and show how to use it to simulate the distribution function of the time to absorption for a Semi-Markov process.

Suggested Citation

  • Ilya Gertsbakh & I. Spungin, 1999. "Product-Type Estimator of Convolutions," Springer Books, in: Jacques Janssen & Nikolaos Limnios (ed.), Semi-Markov Models and Applications, chapter 0, pages 201-206, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3288-6_11
    DOI: 10.1007/978-1-4613-3288-6_11
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