### Table 1: Estimation of U Using Crude Monte Carlo and Balanced Failure Biasing

"... In PAGE 5: ... Assume that the network is functional if nodes 1 and 10 communicate (via a path with an operating component on each link). Table1 compares 90% confidence intervals for the limiting network unavailability from the crude Monte Carlo and BFB methods in regenerative simulations. The crude Monte Carlo simulation utilized 10,000,000 cycles to establish a benchmark.... ..."

### Table 8: Estimation of the variation of the Monte Carlo method.

2004

"... In PAGE 8: ... ^ (t) is used at the end for estimating P(Rn lt; t) and V ar(^ (t)) can be es- timated by ^ V ar(^ (t)) = ^ 2(t) B . Table8 gives the ^ (t) and a2 ^ V ar(^ (t)) based on n1 = 2000 and B = 200 samples. 8.... ..."

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### Table 5 Lognormal investigation

"... In PAGE 15: ...2. Monte Carlo simulation: non-normal mixture target density Table5 presents results from Monte Carlo simulations comparing the perfor- mance of AKM and R amp;W on the standard lognormal target density (E[log X ]= 0; Var[log X ] = 1) at sample sizes n = 100 and n = 1000. The results are based on 100 Monte Carlo replicates.... ..."

### Table 1: Comparison of Monte Carlo and quasi-Monte Carlo methods used to value a coupon bond

1998

"... In PAGE 21: ... For random Monte Carlo, the constant c is the standard deviation, and = :5. Table1 summarizes the results. For each method, the estimated size of the error at N = 10000 (based on the linear t), the convergence rate , and the approximate computation time for one run with this N are given.... In PAGE 25: ... Figure 2 displays these results in terms of the estimated computation time. In Table1 it can be seen that there is in fact a computational advantage to using quasi-random sequences over random for this problem. This is due to the time required for sequence generation.... ..."

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### Table 1: Prices computed by alternative methods under the 2-factor GBM model

2000

"... In PAGE 13: ... 4.2 Computational Results Table1 documents the spread option prices across a range of strikes under the two factor Geo- metric Brownian motion model [22], computed by three di erent techniques: one-dimensional integration (analytic), the fast Fourier Transform and the Monte Carlo method. The values for the FFT methods shown are the \lower quot; prices, computed over , regions that approach the the true exercise region from below and are therefore all less than the analytic price in the rst column.... ..."

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### Table 4 Monte Carlo Evidence

2005

"... In PAGE 14: ... The results of the six experiments are presented in Table 4. Table 4 Panel A of Table4 gives the actual quarterly IMRF where the underlying model is difference stationary and three FRFs derived from three alternative estimation strategies. For all three estimation strategies the resulting FRFs give large values of persistence that grow with the time horizon.... In PAGE 15: ... What do we make of these results? First, we may ask what these results imply about the estimation strategy employed by forecasters. From Table4 we see that the strategy of estimating low order ARMA models, omitting a time trend and leaving the largest root unconstrained yield very large and increasing FRFs. Because these estimates are much higher than any observed from the actual forecast revisions in Table 3, we may conclude that forecasters have not used this strategy.... In PAGE 15: ... Because these estimates are much higher than any observed from the actual forecast revisions in Table 3, we may conclude that forecasters have not used this strategy. Table4 indicates that the strategy of imposing a time trend yields moderate estimates of persistence when the underlying process is a unit root but very low estimates when the true process is trend stationary. The latter case is inconsistent with observed FRFs from Table 3.... In PAGE 15: ... Finally, the strategy of imposing a unit root on low order AR models yields FRFs somewhat higher than those actually observed in Table 3. More generally, the results in Table4 suggest that annual FRFs will tend to be substantially larger than underlying quarterly IMRFs. In that sense, annual FRFs provide very poor and upwardly biased estimates of the underlying quarterly IMRF.... In PAGE 15: ... If our interest is obtaining the underlying IMRF from quarterly data, we may conclude that the large estimates of persistence found in the previous section are merely artifacts of the estimation process and have little bearing on the question of whether shocks to output are persistent. An alternative interpretation of the results in Table4 is warranted. The FRFs represent how forecasters actually revise their forecasts in light of new information and ... In PAGE 16: ... In practice, forecasters, and presumably economic agents, do not have precise knowledge of the underlying model and will use new information to update their model specification. In that sense, the results of Table4 can be interpreted as implying that IMRFs provide a poor estimate of how shocks affect our forecasts of future levels of output and hence are poor measures of the persistence of shocks. ... ..."

### Table 2. Monte Carlo Uncertainties

2004

"... In PAGE 5: ... In the reference case, delivery, atmospheric and aerodynamic uncertainties were based on state of the art navigation, current knowledge of Neptune atmosphere and computational fluid dynamics analyses respectively. Table2 lists the uncertainties and dis- tribution types used in the Monte Carlo reference case. In the first sensitivity case study, the magnitudes of the high frequency random density perturbations were reduced by 50%.... ..."

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### Table 1 Monte Carlo results

2007

"... In PAGE 15: ... The nonparametric entropy estimate was obtained using cardinal B-spline wavelet functions. Table1 tabulates the empirical rejection rates of these 10,000 experiments. It is clear from the table that the empirical rejection rates are close to the ones predicted by the asymptotic theory.... ..."

### Table 3: Monte-Carlo results based on 1000 bootstrap replications Estimated Standard Errors of ^

1995

"... In PAGE 7: ...hese ratios range from 0.00012 up to 6.742 with arithmetic mean 1.246. In order to compare the bootstrap variance estimates of Table 2 with Monte-Carlo results we generate B = 1000 replications ^ of the maximum likelihood estimate ^ using all of the di erent resampling techniques. Consistent with the ndings from the previous sections the results in Table3 show no substantial di erences between the theoretical and the Monte-Carlo bootstrap results. Wu apos;s weighted bootstrap is based on generating ti variates from the N(0; 1) distribution.... ..."

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