2010
DOI: 10.1007/s10700-010-9082-1
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Poisson process with fuzzy rates

Abstract: In a stochastic homogeneous Poisson process, interarrival times are independent and identically distributed (iid) exponential random variables whose parameter is called the rate of the process. By using fuzzy variables to describe the parameter, a Poisson process whose rates are fuzzy variables is established. Based on the random fuzzy theory, relationship between the renewal number and fuzzy rates is discussed. As an application, a random fuzzy compound Poisson process is investigated.

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Cited by 4 publications
(3 citation statements)
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References 17 publications
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“…They predict the data arrival rate to resize the buffer to minimize the information loss. For the calculation of data arrival rate they utilize Poisson probability model [41] by assuming the data streams as a sequence of events occurred in a fixed time interval.…”
Section: Related Work a Data Stream Anonymizationmentioning
confidence: 99%
“…They predict the data arrival rate to resize the buffer to minimize the information loss. For the calculation of data arrival rate they utilize Poisson probability model [41] by assuming the data streams as a sequence of events occurred in a fixed time interval.…”
Section: Related Work a Data Stream Anonymizationmentioning
confidence: 99%
“…3: Screenshot of our Crime Reporting Application of success that occurs within a given unit of measure. This property of the Poisson distribution makes viewing the arrival rate of the reported crime data as a series of events occurring within a fixed time interval at an average rate that is independent of occurrence of the time of the last event [6]. Only one parameter needs to be known, the rate at which the events occur which in our case is the rate at which crime reporting occurs.…”
Section: Anonymization Layer: Data Stream Anonymizationmentioning
confidence: 99%
“…They predict the data arrival rate to resize the buffer to minimize the information loss. For the calculation of data arrival rate they utilized Poisson probability model [37] by assuming the data streams as a sequence of events occurred in a fixed time interval.…”
Section: Introductionmentioning
confidence: 99%