# 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.

243 questions
10k views

### 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 ...
163 views

### Generalised (nonhomogeneous) Poisson process

Define a generalised Poisson process as an arrival process that begins at time 0 and that satisfies: The independence property: the number of arrivals during two non-overlapping intervals ...
169 views

### Non-parametric estimators for time-varying binomial proportion

I have a bunch of count data associated with time intervals (potentially overlapping and of variable lengths), say $(s_i, t_i, n_i, N_i)$ where $N_i$ is a count of the total number of events ...
88 views

414 views

### Estimate of censored poisson process

I have a set of processes, each of which has number of events and the total length of time. I'm trying to model them as independent Poisson processes with there own rates. The rate of the ith process ...
2k views

### Maximum likelihood for number of events in Poisson process

I have a Poisson process with parameter $\lambda$ known. How do I compute the maximum-likelihood estimator for $N$, ie. the number of events over a specific time spell $T$. To repeat, I know $\lambda$...
223 views

### Expected waiting time

The following is a worked example found in past papers of my university, but haven't been able to figure out to solve it (I have the answer, but do not understand how to get there). Any help in ...
151 views

### Poisson Process arrivals

This is a homework problem. Between 10 AM and 6 PM visitors arrive at the Tate Modern Gallery in accordance with a Poisson process at the rate of 6 per minute. Determine the probability that 10 ...
936 views

### Poisson and Exponential Distribution- Is the following question correct?

Accidents occur with a Poisson distribution at an average of 4 per week. i.e., $\lambda= 4$. Calculate the probability of more than 5 accidents in any one week. What is the probability that at least ...
50k 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, (...
59 views

163 views

### Compound poisson process: Average size of claim will exceed £110

"An insurance company receives claims at a rate of two per week, the size of a claim in pounds having mean 100 and standard deviation 50. Assuming the compound Poisson process as a model, and using ...
378 views

1k views

### Distribution of arrival times to server for an M/M/1 queue (what the server experiences)

In an M/M/1 queue, we know that inter-arrival times are exponentially distributed, and that service times are the same. What is the distribution of to-server inter-arrival times (aka service start ...
11k 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 ...
1k views

### Poisson process thinning females and males arriving

Rock tickets are sold at a ticket counter. Females and males arrive at times of independent Poisson processes with rates 30 and 20. What is the probability that the first three customers are ...
679 views

### No-simultaneous-events assumption of the Poisson process

I am checking the description of Poisson process from Wikipedia. The Poisson process is based on four assumptions, but I am not clear this: No counted occurrences are simultaneous. Can you explain ...
268 views

### What are finite window effects?

I'm reading a paper that uses a Poisson process to model real world events. The authors mention "finite window effects". What are finite window effects? Here is quote from the paper where the ...
14k views

### 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) ...
3k views

### Can I estimate the parameter of a Poisson arrival process from a low-incidence observation period?

If I know only that the arrival process is Poisson, and I observe it for a pre-chosen (say, unit) period of time, observing $k$ arrivals, is it meaningful to describe an estimate of its time parameter ...
Take an event to be a set $E \subseteq {\mathbb R}^{\ge 0}$. We want to estimate the duration of the event (the measure of $E$) by sampling using a Poisson process $N$. That is, for some experiment ...