# 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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### 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) ...
21k views

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 ...
51k views

### 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, (...
12k views

### 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 ...
2k views

### Help me understand poisson.test?

I want to understand the poisson.test() function: ...
2k views

### Testing for Poisson process

I have some discrete times of events and I would like to do a test to see if they are likely to have come from a homogeneous Poisson process. From this pdf, I see: REMARK 6.3 ( TESTING POISSON )...
403 views

### Poisson processes

I have two realizations of a poisson stochastic process, they are over the same space with rate $\lambda_{1}$ and $\lambda_{2}$. What is the probability that N elements in both sequences are the same, ...
2k views

### Nonhomogeneous poisson process simulation

I've been looking at ways to generate a Nonhomogeneous Poisson Process (NHPP) including the nonlinear time transformation (using a rate-1 process and inverting the cumulative rate function). I've also ...
92 views

### Any expression for the probability of a hard sphere in Boolean model

I am working hard on a problem of Boolean model. In a example of Boolean model, points are scattered in the plane according to a homogeneous Poisson process of intensity λ. On each of these points a ...
8k views

### 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) ...
2k views

### Bayesian parameter estimation of a Poisson process with change/no-change observations at irregular intervals

Consider a Poisson process with unknown parameter $\lambda$. We perform a sequence of $n$ observations at intervals $\overline{t}=t_1,\,t_2,\,\dots,\,t_n$. Each observation is a binary variable $x_i$ ...
3k views

### Simulation of a Poisson Process

I am trying to simulate the compound Poisson process using the next algorithm that I found in a textbook on stochastic processes. Let $S_0 = 0$. Generate i.i.d. exponential random ...
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### Time up to $n$th event in Poisson process distributed as $\frac{1}{2\lambda} \chi^2_{2n}$

Let's assume that a number X of some events over time $t$ is modeled by Poisson distribution with rate $\lambda$ (here, it's rate, not mean):  X \sim Poisson(\lambda \cdot t) ~~~~ (\lambda t ~\text{...