On the ratios for extreme value distributions with application to rainfall modeling

Nadarajah, Saralees; El‐Shaarawi, A. H.

doi:10.1002/env.758

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Thus, in order to determine the secrecy rate behavior, as K and M grow, one needs to address the ratio of Gumbel random variables. However, the ratio distribution of Gumbel random variables is not known to have a closed-form [21]. Thus, we first express it as an infinite sum of Gamma functions, then provide tight bounds on the obtained distribution, from which we can infer the outage probability.…”

Section: Asymptotic Secrecy Outagementioning

confidence: 99%

On secrecy rates and outage in multi-user multi-eavesdroppers MISO systems

Kampeas

Cohen

Gurewitz

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-In this paper, we study the secrecy rate and outage probability in Multiple-Input-Single-Output (MISO) Gaussian wiretap channels at the limit of a large number of legitimate users and eavesdroppers. In particular, we analyze the asymptotic achievable secrecy rates and outage, when only statistical knowledge on the wiretap channels is available to the transmitter.The analysis provides exact expressions for the reduction in the secrecy rate as the number of eavesdroppers grows, compared to the boost in the secrecy rate as the number of legitimate users grows.

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Section: Asymptotic Secrecy Outagementioning

confidence: 99%

On secrecy rates and outage in multi-user multi-eavesdroppers MISO systems

Kampeas

Cohen

Gurewitz

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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“…24,25 In our case, we have to consider the ratio of two independent, exponentially distributed variables. In general, the ratio of two random variables also represents a random variable.…”

Section: Looks Likementioning

confidence: 99%

Statistical analysis of time resolved single molecule fluorescence data without time binning

Hinze

Basché

2010

The Journal of Chemical Physics

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We depict two algorithms to calculate correlation functions from two different time resolved single molecule fluorescence experiments without the need of time binning. Our first procedure allows to calculate the reduced linear dichroism from polarization resolved fluorescence data. Since we process single photon counts instead of time binned data, considerably faster fluctuations of the dichroism can be analyzed than with conventional methods. With our second procedure time resolved fluorescence obtained with a time correlated single photon counting setup can be analyzed with respect to fluorescence lifetime fluctuations. Again this new algorithm processes single photon events making time binning of photon counts obsolete. Both methods presented are characterized by enhanced time resolution thus allowing to study fast fluctuations of either single molecular orientation or fluorescence life times, respectively.

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Extreme Value Modeling and Prediction of Extreme Rainfall: A Case Study of Penang

Hasan¹,

Yeong²

2010

AIP Conference Proceedings

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On the ratios for extreme value distributions with application to rainfall modeling

Abstract: SUMMARYThe exact distributions of the ratio X=Y are derived when X and Y are independent random variables and come from type I, type II or type III extreme value distributions. A detailed application of the results is provided to extreme rainfall data from Korea.

Cited by 3 publications

References 14 publications

On secrecy rates and outage in multi-user multi-eavesdroppers MISO systems

On secrecy rates and outage in multi-user multi-eavesdroppers MISO systems

Statistical analysis of time resolved single molecule fluorescence data without time binning

Extreme Value Modeling and Prediction of Extreme Rainfall: A Case Study of Penang

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