Difference between revisions of "Renewal"

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[[File:lighterstill.jpg]][[File:Renewal.jpg|right|frame]]
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[[File:lighterstill.jpg]][[File:Hornbill_Renewal.jpg|right|frame]]
  
==Pronunciation==
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*Pronunciation - \ri-ˈnü-əl, -ˈnyü-\
\ri-ˈnü-əl, -ˈnyü-\
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*Origins - circa 1686
==Function==
 
noun
 
==Date==
 
circa 1686
 
 
==Definitions==
 
==Definitions==
 
# : the [[act]] or [[process]] of renewing : repetition
 
# : the [[act]] or [[process]] of renewing : repetition
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# : the rebuilding of a large area (as of a city) by a [[public]] [[authority]]
 
# : the rebuilding of a large area (as of a city) by a [[public]] [[authority]]
  
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----
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<center>For lessons on the [[topic]] of '''''Renewal''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Renewal this link].</center>
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==Poisson Process==
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A '''Poisson process''', named after the French mathematician [https://en.wikipedia.org/wiki/Sim%C3%A9on-Denis_Poisson Siméon-Denis Poisson]  (1781–1840), is a [https://en.wikipedia.org/wiki/Stochastic_process stochastic] [[process]] in which [[events]] occur continuously and [[independently]] of one another (the word [[event]]  used here is not an instance of the [[concept]] of event frequently used in [[probability]] [[theory]]). Examples that are well-[[modeled]] as Poisson processes include the radioactive decay of [[atoms]], telephone calls arriving at a switchboard, page view requests to a website, and rainfall.
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The Poisson process is a collection {N(t) : t ≥ 0} of [https://en.wikipedia.org/wiki/Random_variable random variables], where N(t) is the [[number]] of [[events]] that have occurred up to time t (starting from time 0). The number of events between time a and time b is given as N(b) − N(a) and has a [https://en.wikipedia.org/wiki/Poisson_distribution Poisson distribution]. Each [[realization]] of the [[process]] {N(t)} is a non-negative integer-valued step function that is non-decreasing, but for [[intuitive]] [[purposes]] it is usually easier to think of it as a point [[pattern]] on [0,∞) (the points in time where the step function jumps, i.e. the points in time where an event occurs).
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The Poisson process is a continuous-time process: its discrete-time [[Complement|counterpart]] is the [https://en.wikipedia.org/wiki/Bernoulli_process Bernoulli process]. Poisson processes are also examples of [https://en.wikipedia.org/wiki/Continuous-time_Markov_process continuous-time Markov processes]. A Poisson process is a [[pure]]-[[birth]] [[process]], the [[simplest]] example of a birth-[[death]] process. By the aforementioned [[interpretation]] as a [[random]] point pattern on [0, ∞) it is also a point process on the real half-line.[https://en.wikipedia.org/wiki/Poisson_process]
  
 
[[Category: General Reference]]
 
[[Category: General Reference]]

Latest revision as of 02:37, 13 December 2020

Lighterstill.jpg

Hornbill Renewal.jpg
  • Pronunciation - \ri-ˈnü-əl, -ˈnyü-\
  • Origins - circa 1686

Definitions

  1. : the act or process of renewing : repetition
  2. : the quality or state of being renewed
  3. : something (as a subscription to a magazine) renewed
  4. : something used for renewing; specifically : an expenditure that betters existing fixed assets
  5. : the rebuilding of a large area (as of a city) by a public authority



For lessons on the topic of Renewal, follow this link.

Poisson Process

A Poisson process, named after the French mathematician Siméon-Denis Poisson (1781–1840), is a stochastic process in which events occur continuously and independently of one another (the word event used here is not an instance of the concept of event frequently used in probability theory). Examples that are well-modeled as Poisson processes include the radioactive decay of atoms, telephone calls arriving at a switchboard, page view requests to a website, and rainfall.

The Poisson process is a collection {N(t) : t ≥ 0} of random variables, where N(t) is the number of events that have occurred up to time t (starting from time 0). The number of events between time a and time b is given as N(b) − N(a) and has a Poisson distribution. Each realization of the process {N(t)} is a non-negative integer-valued step function that is non-decreasing, but for intuitive purposes it is usually easier to think of it as a point pattern on [0,∞) (the points in time where the step function jumps, i.e. the points in time where an event occurs).

The Poisson process is a continuous-time process: its discrete-time counterpart is the Bernoulli process. Poisson processes are also examples of continuous-time Markov processes. A Poisson process is a pure-birth process, the simplest example of a birth-death process. By the aforementioned interpretation as a random point pattern on [0, ∞) it is also a point process on the real half-line.[1]