Product-Type Estimator of Convolutions

Ilya Gertsbakh and I. Spungin
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Ilya Gertsbakh: Ben Gurion University of the Negev
I. Spungin: Ben Gurion University of the Negev

Chapter Chapter 11 in Semi-Markov Models and Applications, 1999, pp 201-206 from Springer

Abstract: 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.

Keywords: Monte Carlo simulation; convolutions; product-type unbiased estimator; time to absorption; semi-Markov process (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3288-6_11

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DOI: 10.1007/978-1-4613-3288-6_11

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