The poisson-process tag has no wiki summary.
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1answer
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Ripley's K Function and L Function for Point Patterns
The following is a spatial point pattern:
and these are the corresponding Ripley's K function and L function for this data:
How are these functions interpreted?
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1answer
83 views
Prior for Bayesian Inference on Failure Rate in Poisson Distribution
I'm trying to derive the posterior distribution for the failure rate (lambda) of a process with poisson distribution.
I have tried the use of an improper uniform distribution on lambda by letting the ...
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2answers
156 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 $x_i$ ...
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1answer
85 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, ...
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1answer
248 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) ...
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0answers
55 views
singularity of the Poisson counting process for non-statistician
I would like to explain to non-statisticians the singularity of the Poisson counting process over others (if possible, in a simple sentence). Simply translating in non-mathematical terms its formal ...
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1answer
46 views
Instantaneous Event Probability in Poisson Process
In a homogeneous Poisson process with rate $\lambda$, what is the probability of observing an event in an "instant," that is, an infinitesimally small interval of length dt? I have read that the ...
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1answer
146 views
Expectation and confidence intervals of a Poisson process
A Poisson process has PDF
$$P(X=k)=\frac{e^{-\lambda t}(\lambda t)^k}{k!}$$
I'm trying to find an expression for:
$E[X | \lambda, t]$
Confidence intervals (i.e. find $\delta$ such that ...
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0answers
69 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 ...
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1answer
87 views
Regression for poisson process in R
I have a series of samples of varying length, and the number of bugs created in those time samples. Reading the literature, this is often modeled as a Poisson process. If you write it like:
...
2
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1answer
76 views
Finding the PMF of conditional probability, poisson process. Don't understand where $10^6$ goes
"Customers arrive at a bank according to a Poisson process with rate 6 per hour.
State (together with a proof) clearly the (conditional) probability mass function of the numbers of customers arrived ...
2
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1answer
64 views
Let $\{N(t), t \geq 0 \}$ be a $PP(\lambda)$. Compute $P(N(t) = k | N(t + s) = k + m)$
The question is:
" Let $ \{N(t) , t \geq 0 \} $ be a $PP(\lambda)$. Compute
$$P(N(t) = k | N(t = s) = k + m), $$
where k and m are non-negative integers and $ t, s \geq 0 $ are any real numbers".
...
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1answer
159 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 ...
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1answer
354 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 ...
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1answer
101 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 ...
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1answer
79 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 ...
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1answer
126 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 ...
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5answers
625 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) ...
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3answers
313 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 ...
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1answer
188 views
Estimating event duration by sampling with a Poisson process
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 ...
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1answer
137 views
Number of events of type B given n events of type A in a Poisson process
I have a simple probability calculation I was working on that I came up with an answer for, but a question a colleague asked me led me to come up with a second approach - and a different answer. I put ...
