Fast and accurate computation of the distribution of sums of dependent log-normals

Botev, Zdravko I.; Salomone, Robert; MacKinlay, Daniel

doi:10.1007/s10479-019-03161-x

Cited by 9 publications

(8 citation statements)

References 27 publications

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“…The matrix C is taken as exchangeable, meaning that all off-diagonal elements are the same ρ, and various values of ρ are considered. Similar examples produced with somewhat different methods are in Botev et al (2017).…”

Section: Søren Asmussenmentioning

confidence: 77%

Conditional Monte Carlo for sums, with applications to insurance and finance

Asmussen

2018

Ann. actuar. sci.

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Section: Søren Asmussenmentioning

confidence: 77%

Conditional Monte Carlo for sums, with applications to insurance and finance

Asmussen

2018

Ann. actuar. sci.

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“…The signal-to-interference-plus-noise ratio (SINR) is expressed in this case as a ratio of the desired power signal and the sum of interfering power signals plus noise. Thus, in this case the OP computation is equivalent to evaluating the complementary CDF of sums of RVs [4], [5].…”

Section: Index Termsmentioning

confidence: 99%

“…This includes the CDF of sums of Log-normal, Rayleigh, Nakagami, Rice, etc. The calculation of has been extensively investigated in the literature through either approximation methods [13]- [16] or efficient simulation techniques [3], [5], [17]- [20].…”

Section: A Cdf Of the Sum Of Independent Rvsmentioning

confidence: 99%

A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

Rached

MacKinlay

Botev

et al. 2020

IEEE Trans. Wireless Commun.

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We propose a unified rare-event estimator for the performance evaluation of wireless communication systems. The estimator is derived from the well-known multilevel splitting algorithm. In its original form, the splitting algorithm cannot be applied to the simulation and estimation of time-independent problems, because splitting requires an underlying continuous-time Markov process whose trajectories can be split.We tackle this problem by embedding the static problem of interest within a continuous-time Markov process, so that the target time-independent distribution becomes the distribution of the Markov process at a given time instant. The main feature of the proposed multilevel splitting algorithm is its large scope of applicability. For illustration, we show how the same algorithm can be applied to the problem of estimating the cumulative distribution function (CDF) of sums of random variables (RVs), the CDF of partial sums of ordered RVs, the CDF of ratios of RVs, and the CDF of weighted sums of Poisson RVs. We investigate the computational efficiency of the proposed estimator via a number of simulation studies and find that it compares favorably with existing estimators.

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“…2009) fail to be accurate when the tail of the CDF is considered. The literature is rich in works in which variance reduction techniques were developed to efficiently estimate rare event probabilities corresponding to the lefttail of the CDF of sums of random variables, see Asmussen et al (Sep. 2016, Botev et al (2019), Gulisashvili and Tankov (Feb. 2016), Alouini et al (2018) and Beaulieu and Luan (2019) and the references therein. For instance, the authors in Asmussen et al (Sep. 2016) used exponential twisting, which is a popular importance sampling (IS) technique, to propose a logarithmically efficient estimator of the CDF of the sum of i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Efficient importance sampling for large sums of independent and identically distributed random variables

et al. 2021

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We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $$\mathbb {P}(\sum _{i=1}^{N}{X_i} \le \gamma )$$ P ( ∑ i = 1 N X i ≤ γ ) , via importance sampling (IS). We are particularly interested in the rare event regime when N is large and/or $$\gamma $$ γ is small. The exponential twisting is a popular technique for similar problems that, in most cases, compares favorably to other estimators. However, it has some limitations: (i) It assumes the knowledge of the moment-generating function of $$X_i$$ X i and (ii) sampling under the new IS PDF is not straightforward and might be expensive. The aim of this work is to propose an alternative IS PDF that approximately yields, for certain classes of distributions and in the rare event regime, at least the same performance as the exponential twisting technique and, at the same time, does not introduce serious limitations. The first class includes distributions whose probability density functions (PDFs) are asymptotically equivalent, as $$x \rightarrow 0$$ x → 0 , to $$bx^{p}$$ b x p , for $$p>-1$$ p > - 1 and $$b>0$$ b > 0 . For this class of distributions, the Gamma IS PDF with appropriately chosen parameters retrieves approximately, in the rare event regime corresponding to small values of $$\gamma $$ γ and/or large values of N, the same performance of the estimator based on the use of the exponential twisting technique. In the second class, we consider the Log-normal setting, whose PDF at zero vanishes faster than any polynomial, and we show numerically that a Gamma IS PDF with optimized parameters clearly outperforms the exponential twisting IS PDF. Numerical experiments validate the efficiency of the proposed estimator in delivering a highly accurate estimate in the regime of large N and/or small $$\gamma $$ γ .

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Fast and accurate computation of the distribution of sums of dependent log-normals

Cited by 9 publications

References 27 publications

Conditional Monte Carlo for sums, with applications to insurance and finance

Conditional Monte Carlo for sums, with applications to insurance and finance

A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

Efficient importance sampling for large sums of independent and identically distributed random variables

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