Conditional Poisson Process

2022 ◽  
pp. 117-128
Author(s):  
Olga Korosteleva
Keyword(s):  
Poisson Process ◽  
Conditional Poisson

Conditional Poisson processes

1972 ◽  
Vol 9 (2) ◽  
pp. 288-302 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Poisson Processes ◽  
Random Time ◽  
Time Transformation ◽  
Limiting Behavior ◽  
Independent Increments ◽  
Conditional Poisson

A conditional Poisson process (often called a double stochastic Poisson process) is characterized as a random time transformation of a Poisson process with unit intensity. This characterization is used to exhibit the jump times and sizes of these processes, and to study their limiting behavior. A conditional Poisson process, whose intensity is a function of a Markov process, is discussed. Results similar to those presented can be obtained for any process with conditional stationary independent increments.

Conditional Poisson processes

1972 ◽  
Vol 9 (02) ◽  
pp. 288-302 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Poisson Processes ◽  
Random Time ◽  
Time Transformation ◽  
Limiting Behavior ◽  
Independent Increments ◽  
Conditional Poisson

A conditional Poisson process (often called a double stochastic Poisson process) is characterized as a random time transformation of a Poisson process with unit intensity. This characterization is used to exhibit the jump times and sizes of these processes, and to study their limiting behavior. A conditional Poisson process, whose intensity is a function of a Markov process, is discussed. Results similar to those presented can be obtained for any process with conditional stationary independent increments.

scholarly journals The Conditional Poisson Process and the Erlang and Negative Binomial Distributions

2017 ◽  
Vol 07 (01) ◽  
pp. 16-22
Author(s):  
Anurag Agarwal ◽  
Peter Bajorski ◽  
David L. Farnsworth ◽  
James E. Marengo ◽  
Wei Qian
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Binomial Distributions ◽  
Conditional Poisson

scholarly journals A Note on Embedding Certain Bernoulli Sequences in Marked Poisson Processes

2008 ◽  
Vol 45 (04) ◽  
pp. 1181-1185 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Poisson Process ◽  
Random Variables ◽  
Poisson Processes ◽  
Bernoulli Random Variables ◽  
Conditional Poisson

A sequence of independent Bernoulli random variables with success probabilities a / (a + b + k − 1), k = 1, 2, 3, …, is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.

scholarly journals A Note on Embedding Certain Bernoulli Sequences in Marked Poisson Processes

2008 ◽  
Vol 45 (4) ◽  
pp. 1181-1185 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Poisson Process ◽  
Random Variables ◽  
Poisson Processes ◽  
Bernoulli Random Variables ◽  
Conditional Poisson

A sequence of independent Bernoulli random variables with success probabilities a / (a + b + k − 1), k = 1, 2, 3, …, is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.

Lectures on the Poisson Process

2017 ◽  
Author(s):  
Günter Last ◽  
Mathew Penrose
Keyword(s):  
Poisson Process

Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽  
2013 ◽  
Vol 34 (6) ◽  
pp. 434-437 ◽  
Author(s):  
Donald W. MacKenzie
Keyword(s):  
Poisson Process ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Massachusetts Institute Of Technology ◽  
Homogeneous Poisson Process ◽  
Cornell University ◽  
The Difference ◽  
Suicide Clusters ◽  
Institute Of Technology ◽  
Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

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