This discussion paper resulted in a publication in the <I>Siam Journal on Matrix Analysis and Applications (2011). Volume 32, issue 3, pages 665-684.<P> A sequence of real numbers (<I>x_n</I>) is Benford if the significands, i.e. the fractionparts in the floating-point representation of (<I>x_n</I>), are distributed...</i></i></p></i>

This paper reports simulation experiments, applying the cross entropy method suchas the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failurebiasing schemes that have been proved to give...

A sequence of real numbers (<I>x_n</I>) is Benford if the significands, i.e. the fraction

A sequence of real numbers (xn) is Benford if the significands, i.e. the fractionparts in the floating-point representation of (xn), are distributed logarithmically.Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain withprobability transition matrix P and limiting...

There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state dependent importance sampling method which partitions the state space and applies the...

A sequence of real numbers (xn) is Benford if the significands, i.e. the fractionparts in the floating-point representation of (xn), are distributed logarithmically.Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain withprobability transition matrix P and limiting...