# 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.

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### Burke's Theorem for rejection from Erlang-B loss queue

I have some general uncertainties regarding the rejection process from an Erlang-B loss queue ($M/M/c/c$), where the total capacity of the queue is equal to the number $c$ of servers. Consider the ...
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### Marking a hard core poisson process

A hard core process (HCP) deals with the deposition of hard spheres, generally of the same radius, that are forbidden to overlap. Suppose instead that the identical spheres are replaced with distinct ...
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### Proof for the distribution of the increments of Gaussian and Poisson processes?

What is analytic proof for the fact that increments of a Gaussian process are again Gaussian? How could I apply that to increments of Poisson process? Maybe do I multiply characteristic function ...
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### Characteristic Function of a Compound Poisson Process

The definition of a compound Poisson process and its characteristic function I have are the following: Let $\lambda>0$ and $N\sim\text{Poisson}(\lambda T)$. Also, $\{X_i\}_{i=1}^N$ are i.i.d. ...
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### How do I check whether a series of time events does not show acclimatization? And test it for several animals. R

I am studying animal behavior and I want to know whether the frequency of a specific behavior changes with time. I thought it was a common and simple problem but I cannot find papers with examples ...
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### Poisson Distribution: Estimating rate parameter and the interval length

Here is the motivation for my question. I have a sensor that reports data to me. The occurrence of the reports from the sensor follows a Poisson process (so, obviously, the inter-event times are ...
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### Conditional distribution (on N) of arrival times in a nonhomogenous poisson process

Conditional on $N(t)$, given some $\lambda(t)$ characterizing some Nonhomogenous poisson point process, the distribution of an arrival time $t_i$ is $\lambda(t_i)/\int_{A}\lambda\left(t\right)dt$ ...
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### Probability Distribution for Inter-arrival Time

I'm trying to build a simulation for a quality control process, where quality analysts inspect the product and report faults if they found any. I have a dataset of this bug reports, so I'm trying to ...
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In Garman's inventory model (http://www.sciencedirect.com/science/article/pii/0304405X76900064), buying order and selling order are Poisson processes with order size = 1. Buying price and selling ...
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### Modeling Arrivals With a Time Limit

I have some data (sample here): ...
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### Problem on Poisson Process

I am doing some problems related with the Poisson Process and i have a doubt on one of them. The problem is stated as follows: A doctor works in an emergency room. The emergencies arrive according a ...
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### Pmf of compound Poisson process

Can I obtain an analytic expression for pmf of compound Poisson process? $Y_t = \sum \limits_{i=1}^{Xt} D_i$ where $X_t$ ~ Poisson($\lambda$) and $D$ ~ Geometric($\rho$)
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### Poisson vs. Gaussian in Geomagnetic Data

I've been studying geomagnetic signals using a threshold approach to detect pulse events in the data. The question here is what is the significance of the crossover of stddev and mean as the ...
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### Alternatives to a one-dimensional Poisson process [closed]

Say I have "arrival" times in what may or may not be a Poisson process. I can think of at least three ways in which it can deviate from a Poisson process: Clumping. One arrival is likely to be near ...
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### Help me out with real-life Gamma distributions

I'm working with some data relating to maintenance and parts failures. I've got a pure math background with only a little bit of probability, and I'm currently learning by doing. I've got a list of ...
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### Multiple poisson processes ?

I'm just trying to get my head around Poisson processes, as they're fairly new to me, and I've had a thought experiment that has been annoying me a little. Imagine a volume of some mixture hit by X-...
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### Is there a similarity between a jump process and a counting process since both follow a Poisson distribution

I read that a jump in a stock price can be modeled as a Poisson process. But I have also read that a Poisson process is a good model for a counting process (i.e. number of hits to a website per unit ...
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### Expected value of a product of two compound Poisson processes

I'm working on my master thesis now and I've been struggling with a problem for some while now and no one seems to be able to help me or point me in any direction. So now I reach out to see if someone ...
I have a Poisson process whose statistics are interarrival times ($\bf X$), number of arrivals ($\bf N$), and arrival times ($\bf T$). Later, the process is split by a Bernoulli process that ...