A Review of Results on Sums of Random Variables

Nadarajah, Saralees

doi:10.1007/s10440-008-9224-4

Cited by 116 publications

(62 citation statements)

References 26 publications

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“…The exact distribution of the sum of independent and non-identically distributed Gamma random variables can be found in [50], however, it will not yield a mathematically tractable expression. Therefore, we employ the second-order matching technique shown in the following lemma to obtain an approximation distribution.…”

Section: B Isotropic Approximation For Channel Vectorsmentioning

confidence: 99%

Downlink Spectral Efficiency of Distributed Massive MIMO Systems With Linear Beamforming Under Pilot Contamination

Wang

Zhu

et al. 2018

IEEE Trans. Veh. Technol.

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Abstract-In this paper, the downlink spectral efficiency of multi-cell multi-user distributed massive MIMO systems with linear beamforming is studied in the presence of pilot contamination. According to the levels of effective channel gain information at user side, we provide the lower bound and upper bound on user ergodic achievable downlink rate. Due to the different access distance from each user to different remote antenna units, the entries of user channel vectors are no longer identically distributed in distributed massive MIMO systems, which makes the spectral efficiency analysis challenging. Using the properties of Gamma distributions together with the approximate methods for non-isotropic vectors, we derive tractable but accurate closed-form expressions for the rate bounds with maximum ratio transmission (MRT) and zero-forcing (ZF) beamforming in distributed massive MIMO systems. Based on these expressions, user ultimate achievable rates are also given when the ratio of the total number of transmit antennas to the number of users goes to infinity. It is shown that MRT and ZF beamforming achieve the same ultimate rate no matter what levels of effective channel gain information at user side. Numerical results show that ZF achieves better performance gain and faster convergence speed than MRT. When the coherence interval is large, the downlink beamforming training scheme is more preferable for the distributed massive MIMO systems.

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Section: B Isotropic Approximation For Channel Vectorsmentioning

confidence: 99%

Downlink Spectral Efficiency of Distributed Massive MIMO Systems With Linear Beamforming Under Pilot Contamination

Wang

Zhu

et al. 2018

IEEE Trans. Veh. Technol.

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“…I find that the share of traded goods sector in GDP is 0.25 which implies that ρ is 0.75. Following Alvarez and Lucas (2007), θ, which controls the variability of the national idiosyncratic component of productivity, is 0.15, which lies well within the range of values estimated by EK for the OECD countries (values range 10 Even though the distribution of equilibrium prices in country i is a Weibull, the density function of Q mi is not tractable because no results (not even approximations) have been known for sums of Weibull random variables (see Nadarajah (2008)). As a result there is no analytical expression for the distribution of σ(x).…”

Section: Model Solution and Simulation Of Pricesmentioning

confidence: 53%

Local Costs of Distribution, International Trade Costs and Micro Evidence on the Law of One Price

Giri

2009

SSRN Journal

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This paper connects trade flows to deviations from the law of one price (LOOP) in a structural model of trade and retailing. It accounts for the observed cross-country dispersion in prices of goods, based on retail price survey data, by focusing on two sources of goods market segmentation -(i) international trade costs, and (ii) non-traded input costs of distribution. I find that a multi-sector Ricardian trade model, ala Eaton-Kortum, augmented with a distribution sector, can account for the average price dispersion for a basket of goods fully and generates 70 percent of the variation in price dispersion across goods within the basket. While tradability of goods is important in explaining the average price dispersion for the basket of goods, distribution costs are important in explaining why, within the basket, some goods show more price dispersion than others.

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“…Then τ = E 1 + E 2,4 + E 3 + E 5 and we use the results from [28] to show that Pr [τ ≤ 240 sec] = 99.9 %.…”

Section: F Modeling Of Decision Maker Notification Timementioning

confidence: 99%

An Open-System Transportation Security Sensor Network: Field-Trial Experiences

Fokum

Frost

Kuehnhausen

et al. 2010

IEEE Trans. Veh. Technol.

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Cargo shipments are subject to hijack, theft, or tampering. Furthermore, cargo shipments are at risk of being used to transport contraband, potentially resulting in fines to shippers. The Transportation Security Sensor Network (TSSN), which is based on open software systems and Service Oriented Architecture (SOA) principles, has been developed to mitigate these risks. Using commercial off-the-shelf (COTS) hardware, the TSSN is able to detect events and report those relevant to appropriate decision makers.However, field testing is required to validate the system architecture as well as to determine if the system can provide timely event notification. Field experiments were conducted to assess the TSSN's suitability for monitoring rail-borne cargo. Log files were collected from these experiments and postprocessed. We present the TSSN architecture and results of field experiments, including the time taken to report events using the TSSN as well as on the interaction between various components of the TSSN. These results show that the TSSN architecture can be used to monitor rail-borne cargo.ii

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A Review of Results on Sums of Random Variables

Cited by 116 publications

References 26 publications

Downlink Spectral Efficiency of Distributed Massive MIMO Systems With Linear Beamforming Under Pilot Contamination

Downlink Spectral Efficiency of Distributed Massive MIMO Systems With Linear Beamforming Under Pilot Contamination

Local Costs of Distribution, International Trade Costs and Micro Evidence on the Law of One Price

An Open-System Transportation Security Sensor Network: Field-Trial Experiences

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