Representation of multivariate Bernoulli distributions with a given set of specified moments

Fontana, Roberto; Semeraro, Patrizia

doi:10.1016/j.jmva.2018.08.003

Cited by 20 publications

(32 citation statements)

References 17 publications

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“…The class has 100 ray densities that we can find analitically and we found that all ray densities have different correlations. The bounds for the all moments of the distributions in the class are reached on the ray densities as proved in [9]. In this case the bounds for the second order moment and correlation are analytical, as proved in Section 3.1.1.…”

Section: Scenario 1: P = 03%mentioning

confidence: 87%

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Model Risk in Credit Risk

2019

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Section: Scenario 1: P = 03%mentioning

confidence: 87%

“…We build on the results in [9], where the authors represent the Fréchet class of multivariate d-dimensional Bernoulli distributions with given margins and/or pre-specified moments as the points of a convex hull. The generators of the convex hull are mass functions in the class and they can be explicitly found.…”

Section: Exchangeable Bernoulli Generatorsmentioning

confidence: 99%

Model Risk in Credit Risk

2019

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“…A proof of (2) can be found in the Appendix. See also [14]. Because blockages are uniformly distributed over A, the probability that a given blockage lands in a i is equal to a i /A, and hence the probability it is outside a i is 1 − a i /A.…”

Section: Sinr Outage Analysismentioning

confidence: 99%

“…By substituting (15) and (16) into (14) and solving for E[B 1 B 2 ], E[B 1 B 2 ] = p 1 p 2 + ρ √ p 1 p 2 q 1 q 2 = p 1 p 2 + ρh.…”

Section: Appendixmentioning

confidence: 99%

The Impact of Correlated Blocking on Millimeter- Wave Personal Networks

Hriba

Valenti

2018

MILCOM 2018 - 2018 IEEE Military Communications Conference (MILCOM)

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Due to its potential to support high data rates at low latency with reasonable interference isolation, millimeter-wave (mmWave) communications has emerged as a promising solution for wireless personal-area networks (WPAN) and an enabler for emerging applications such as high-resolution untethered virtual reality. At mmWave, signals are prone to blockage by objects in the environment, including human bodies. Most mmWave systems utilize directional antennas in order to overcome the significant path loss. In this paper, we consider the effects of blockage and antenna directivity on the performance of a mmWave WPAN. Similar to related work, we assume that the interferers are in arbitrary locations and the blockages are drawn from a random point process. However, unlike related work that assumes independent blocking, we carefully account for the possibility of correlated blocking, which arises when two interferers are close to each other and therefore an obstruction that blocks the first interferer may likely block the second interferer. Closed form expressions for the blockage correlation coefficient and the distribution of the SINR are provided for the case of two dominant interferers and a fixed number of blockages drawn from a binomial point process. Finally, the effects of antenna directivity and the spatial randomness of the interferers are taken into account, resulting in SINR curves that fully account for correlated blocking, which are compared against curves that neglect correlation. The results provide insight into the validity of the commonly held assumption of independent blocking and the improved accuracy that can be obtained when the blocking correlation is taken into account.

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“…Then, σ (M) = A −1 π (M) . Fontana and Semeraro [10] proposed a procedure based on this representation to construct a valid multivariate Bernoulli distribution for given marginal distributions, p i 's, and a correlation matrix, T = {τ i, j } as follows.…”

Section: Introductionmentioning

confidence: 99%