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Questions tagged [poisson-process]

For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.

The Poisson process is one of the most widely used point processes, as well as one of the most important objects of study in the theories of point processes and of (more general) stochastic processes. Its name is derived from the fact that, for a Poisson point process, the number of points in a region of finite size is a random variable with a Poisson distribution.

The Poisson process can be defined on many different types of spaces. The simplest definition occurs on the real line, where the distance between two consecutive points of the process will have an exponential distribution. This implies that the points have the memoryless property: intuitively, the process "restarts afresh" at every point.

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Please explain the waiting paradox

A few years ago I designed a radiation detector that works by measuring the interval between events rather than counting them. My assumption was, that when measuring non-contiguous samples, on average I would measure half of the actual interval.…
Stephen Sackett
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Is there any gold standard for modeling irregularly spaced time series?

In field of economics (I think) we have ARIMA and GARCH for regularly spaced time series and Poisson, Hawkes for modeling point processes, so how about attempts for modeling irregularly (unevenly) spaced time series - are there (at least) any…
Qbik
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How to know if a data follows a Poisson Distribution in R?

I am an undergrad student and I have a project for my probability class. Basically, I have a dataset about the hurricanes that impacted my country for a series of years. In my probability Book, (Probability and Statistics with R) there is an (not…
Shariff
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Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

$\newcommand{\P}{\mathbb{P}}$We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides the probability of a number of events occurring…
MoonKnight
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How to estimate Poisson process using R? (Or: how to use NHPoisson package?)

I have a database of events (i.e. a variable of dates) and associated covariates. The events are generated by the non-stationary Poisson process with parameter being an unknown (but possibly linear) function of some covariates. I think the NHPoisson…
Adam Ryczkowski
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What are the differences between survival analysis and Poisson regression?

I'm working on a classical churn prediction problem using the number of visits of a given user to a site and I thought that Poisson Regression was the right tool for modelling the future engagement of that user. When then I came across a book about…
tonicebrian
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How do we predict rare events?

I am working on developing an insurance risk predictive model. These models are of "rare events" like airline no-show prediction, hardware fault detection, etc. As I prepared my data set, I tried to apply classification, but I couldn't obtain…
user3378649
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Can Negative Binomial parameters be treated like Poisson?

I have a count process that I'd like to model with a Poisson process. Data is measured every 30 minutes, and with a poisson distribution I can easily measure the probability of a given count of events being anomalous in different time periods using…
J Doe
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Help me understand poisson.test?

I want to understand the poisson.test() function: poisson.test(x, T = 1, r = 1, alternative = c("two.sided", "less", "greater"), conf.level = 0.95) I don't understand the parameters T, r and also what should be my…
Rohail
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Probability of an independent Poisson process overtaking another

I have asked this question before in another fashion on other stackexchanges, so sorry for the somewhat repost. I have asked my professor and a couple of PhD students about, without a definitive answer. I will first state the problem, then my…
no nein
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Total expectation theorem for Poisson processes

I have two independent Poisson processes $A$ and $B$ with arrival rates $\lambda_A$ and $\lambda_B$, respectively. Now, the expected time for the arrival of the next item for the merged process should be $\frac {1}{\lambda_A+\lambda_B}$. Assuming…
user90476
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Are there any alternatives to simulation for determining the distribution of number of events from two dependent non-homogeneous Poisson processes?

A "state of the art" model for the distribution of goals scored in a soccer match is that of Dixon and Robinson (1998) "A Birth Process Model for Association Football Matches" which accounts for two key phenomenon: 1) More goals are scored at the…
M. Berk
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Motivation for gamma distribution with a non-integer parameter

The Erlang distribution has a straightforward interpretation in terms of waiting time for the occurrence of a predefined number of events in a Poisson process or a sum of a predefined number of exponential random variables. The gamma distribution is…
macleginn
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Paradox of Poisson process with at least one event in the interval

Let $X_T$ is a number of events in Poisson process of unitary rate ($\lambda = 1$) within interval of length $T$. It is known that at least one event has been observed in the interval, I want to find probability that there is more events in the…
abukaj
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Poisson process and the memoryless property

I understand that inter-arrival times of a Poisson process are exponentially distributed and therefore the inter-arrival times are memoryless. However, how about the waiting times of Poisson process i.e wait time till $k$th arrival where $k \geq 2$.…
toing
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