Nonhomogeneous geometric distributions with relations to birth and death processes

Mandelbaum, Marvin; Hlynka, Myron; Brill, Percy H.

doi:10.1007/s11750-007-0018-z

Cited by 16 publications

(9 citation statements)

References 3 publications

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“…Olsen et al (1998) has been unnoticed in the water resources literature (e.g., El Adlouni et al 2007;Sivapalan and Samuel 2009;Walter and Vogel 2010;Obeysekera et al 2012;Gilroy and McCuen 2012). Subsequently, Mandelbaum et al (2007) developed the basis of nonhomogeneous geometric random variables, which paves the way for extending the concepts of return period and risk for nonstationary conditions. More recently, Cooley (2013) reviewed and compared the return period definitions suggested by Olsen et al (1998) and Parey et al (2007).…”

Section: Brief Review Of Existing Concepts and Methodsmentioning

confidence: 99%

Revisiting the Concepts of Return Period and Risk for Nonstationary Hydrologic Extreme Events

2014

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Current practice using probabilistic methods applied for designing hydraulic structures generally assume that extreme events are stationary. However, many studies in the past decades have shown that hydrological records exhibit some type of nonstationarity such as trends and shifts. Human intervention in river basins (e.g., urbanization), the effect of low-frequency climatic variability (e.g., Pacific Decadal Oscillation), and climate change due to increased greenhouse gasses in the atmosphere have been suggested to be the leading causes of changes in the hydrologic cycle of river basins in addition to changes in the magnitude and frequency of extreme floods and extreme sea levels. To tackle nonstationarity in hydrologic extremes, several approaches have been proposed in the literature such as frequency analysis, in which the parameters of a given model vary in accordance with time. The aim of this paper is to show that some basic concepts and methods used in designing flood-related hydraulic structures assuming a stationary world can be extended into a nonstationary framework. In particular, the concepts of return period and risk are formulated by extending the geometric distribution to allow for changing exceeding probabilities over time. Building on previous developments suggested in the statistical and climate change literature, the writers present a simple and unified framework to estimate the return period and risk for nonstationary hydrologic events along with examples and applications so that it can be accessible to a broad audience in the field. The applications demonstrate that the return period and risk estimates for nonstationary situations can be quite different than those corresponding to stationary conditions. They also suggest that the nonstationary analysis can be helpful in making an appropriate assessment of the risk of a hydraulic structure during the planned project-life.

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Section: Brief Review Of Existing Concepts and Methodsmentioning

confidence: 99%

Revisiting the Concepts of Return Period and Risk for Nonstationary Hydrologic Extreme Events

2014

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“…where F X (1) = p 1 and F X (x max ) = 1. Mandelbaum et al (2007) introduced nonhomogeneous geometric random variables, which are similar to the above and provided a convenient recursive formula for computing f(x).…”

Section: Expected Waiting Time (Ewt)mentioning

confidence: 99%

Techniques for assessing water infrastructure for nonstationary extreme events: a review

Salas

Obeysekera

Vogel

2018

Hydrological Sciences Journal

193

110

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Statistical and physically-based methods have been used for designing and assessing water infrastructure such as spillways and stormwater drainage systems. Traditional approaches assume that hydrological processes evolve in an environment where the hydrological cycle is stationary over time. However, in recent years, it has become increasingly evident that in many areas of the world the foregoing assumption may no longer apply, due to the effect of anthropogenic and climatic induced stressors that cause nonstationary conditions. This has attracted the attention of national and international agencies, research institutions, academia, and practicing water specialists, which has led to developing new techniques that may be useful in those cases where there is good evidence and attribution of nonstationarity. We review the various techniques proposed in the field and point out some of the challenges ahead in future developments and applications. Our review emphasizes hydrological design to protect against extreme events such as floods and low flows.

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“…Based on Equ. (16), the number of times (i.e., trials) a packet is required to be decoded until it is recovered has a nonhomogeneous geometric distribution (denoted by G) [16] given that the length (i.e., number of symbols) of predetermined parity code equals m t at the t th trial. Lemma 3.2: We use f t G (n) to denote the probability of successful decoding on the t th decoding trial for one packet going through n hops.…”

Section: B Probability Of Successful Decodingmentioning

confidence: 99%

CEDAR: An optimal and distributed strategy for packet recovery in wireless networks

Qiu

Shen

Soltani

et al. 2013

2013 Proceedings IEEE INFOCOM

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Underlying link-layer protocols of wireless networks use the conventional "store and forward" design paradigm cannot provide highly sustainable reliability and stability in wireless communication, which introduce significant barriers and setbacks in scalability and deployments of wireless networks. In this paper, we propose a Code Embedded Distributed Adaptive and Reliable (CEDAR) link-layer framework that targets low latency and high throughput. CEDAR is the first comprehensive theoretical framework for analyzing and designing distributed and adaptive error recovery for wireless networks. It employs a theoretically-sound framework for embedding channel codes in each packet and performs the error correcting process in selected intermediate nodes in packet's route. To identify the intermediate nodes for the en/decoding for minimizing average packet latency, we mathematically analyze the average packet delay, using Finite State Markovian Channel model and priority queuing model, and then formalize the problem as a non-linear integer programming problem. Also, we propose a scalable and distributed scheme to solve this problem. The results from real-world testbed "NESTbed" and simulation with Matlab prove that CEDAR is superior to the schemes using hop-by-hop decoding and destination-decoding not only in packet delay but also in throughput. In addition, the simulation results show that CEDAR can achieve the optimal performance in most cases.

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Nonhomogeneous geometric distributions with relations to birth and death processes

Abstract: Nonhomogeneous, Geometric distribution, Queueing, Birth-and-death processes, 60E05, 60K25, 90B22,

Cited by 16 publications

References 3 publications

Revisiting the Concepts of Return Period and Risk for Nonstationary Hydrologic Extreme Events

Revisiting the Concepts of Return Period and Risk for Nonstationary Hydrologic Extreme Events

Techniques for assessing water infrastructure for nonstationary extreme events: a review

CEDAR: An optimal and distributed strategy for packet recovery in wireless networks

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