Binomial Distribution Handbook for Scientists and Engineers

Collani, Elart von; Dräger, Klaus

doi:10.1007/978-1-4612-0215-8

Cited by 41 publications

(19 citation statements)

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“…2 can be obtained by where [⋅] represents expectation operation. Recall that the moment-generating function of the binomial random variable, , is given by [24] ( ) = ( ) = (1 − + ) .…”

Section: Appendix a Derivation Ofmentioning

confidence: 99%

Spatial spectrum holes for cognitive radio with relay-assisted directional transmission

Zhao

et al. 2009

IEEE Trans. Wireless Commun.

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Spectrum hole (SH) is defined as a spectrum band that can be utilized by unlicensed users, which is a basic resource for cognitive radio (CR) systems. Most of existing contributions detect SHs by sensing whether a primary signal is present or absent and then try to access them so that the CR and primary users use the spectrum band either at different time slots or in different geographic regions. In this paper, we propose a novel scheme with relays or directional relays for CR users to exploit new spectrum opportunity, called spatial SH. It can provide higher spectrum efficiency by coexistence of primary and CR users at the same region, time, and spectrum band. In particular, when the spectrum opportunity of a direct link from a CR transmitter to a CR receiver does not appear, our scheme may still establish the communication through indirect links, i.e., other CR users act as relay stations to assist the communication by using other spatial domains. Furthermore, we analyze the successful communication probabilities of CR users and demonstrate that the spectrum efficiency can be considerably improved by our scheme.

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“…2 can be obtained by where [⋅] represents expectation operation. Recall that the moment-generating function of the binomial random variable, , is given by [24] ( ) = ( ) = (1 − + ) .…”

Section: Appendix a Derivation Ofmentioning

confidence: 99%

Spatial spectrum holes for cognitive radio with relay-assisted directional transmission

Zhao

et al. 2009

IEEE Trans. Wireless Commun.

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show abstract

“…For example, handbook [13] is directed at scientists and engineers who need to estimate and test hypotheses about the probability of an event. According to the authors, "The purpose of the book is twofold: it aims at providing practitioners with refined and easy-to-use techniques as well as initiating a new field of research in theoretical statistics.…”

Section: Elart Von Collani German Engineering Educatormentioning

confidence: 99%

In Memoriam: Elart von Collani

Dimitrov

2017

Stochastics and Quality Control

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“…However, because of the different wind conditions, the Bernoulli experiments are not identical. Therefore, the overall recurrence time T r must be partitioned in times for the different operating wind analogous to the derivation of equation (9). In contrast, in IEC 61400-1 Edition 3, Annex F, identical Bernoulli experiments are assumed, yielding a simple binomial distribution for the number of exceedances with parameters n = m and p = P e (F, T).…”

Section: Characteristic Load Of Annex F Iec 61400-1 Editionmentioning

confidence: 99%