# 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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### Extension of Poisson Parameter for Different Temporal Interval

Suppose $Y$ follows a Poisson distribution with parameter $\lambda$ that explains a temporal Poisson process over an interval of 30 seconds. Now, it stands to reason that for an interval of 60 ...
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### What probability distribution would be suitable for modelling scores in a basketball match?

In football (not American football but what Americans call soccer), it is pretty clear: we may consider the difference of two independent Poisson variables. In basketball, in theory, we could increase ...
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### Conditional distribution of arrival times in Poisson process

Suppose I know over a window $[0, T)$ that I have observed $n$ samples from a poisson process $N_t \sim p(n|\lambda t) = \frac{1}{n!}(\lambda t)^{n}\exp(-\lambda t)$. What is the conditional ...
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### Modeling the number of corners in soccer

For a project, I am looking for idea to model for the distribution of corners in football matches. I know that the number of goals can be model by a Poisson distribution, but for the number of corners,...
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### Alternating between two states {A, B} each with exp distributed durations. What's the probability of state=A at time t?

Say I have a light bulb that can be on (A) or off (B). It alternates between being state A or B. It will be in state A for a duration a ~ exp(α), and in state B for duration b ~ exp(β), (...
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### 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 )...
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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 ...
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### Poisson Process With Two Different Rates

I am looking to investigate a Poisson Process that has two separate rates; essentially, there is a season of games that each have their own points rate (per minute). Comprehensively, over the season, ...
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### Overdispersion under different longitudinal constraints

I have panel data (police districts observed across many months) and I am modeling a count outcome. Fitting a Poisson model (simple pre/post comparison with 6 months of data) results in significantly ...
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### How to compute the expected number of events in the following conditional renewal process?

I have a stochastic point process with event times $\{x_1, x_2, ...\}$ and I want to compute the expected number of events $n(T)$ over the interval $[0,T]$. The point process is generated as follows: ...
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### How to show the inter-arrival time variance of a Cox process driven by a stationary Poisson process of constant intensity $\lambda$ is $3\lambda$

Ideas on how to show that the variance of a doubly-stochastic Poisson process(aka a Cox process) driven by a homogeneous(stationary) Poisson process of intensity $\lambda$ is $3\lambda$ ? I've come ...
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### To detect which of the three processes more-aptly fits Poisson process

There happens to be a type of generic poll, which can be described as:- A participant can vote only once and for only 1 of 3 running candidates - Red, Blue and Green. A random voter starts the ...
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### Solving an equation with logarithms of negative numbers

I'm modelling a bunch of non-homogeneous poisson processes. I'm impossing on them a linear-log functional form. you end up with two parameters, theta1 and theta0 for each estimated process. The ...
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### Correcting data using poisson-regression

I'm new to stats and I was wondering if anyone had any good resources that could explain to me: How one can correct their data (false-positives) using Poisson-regression. I've been looking for some ...
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### 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 ...
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### The probability distribution of waiting time until two exponentially distributed events with different parameters both occur

I am working on a problem related to the waiting time until a parking garage is empty. We are given that the cars independently spend an exponential distributed time in the parking garage, with ...