# 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
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### Data of daily counts modelled as Poisson process: should it be compound?

I understand that one of the basic assumptions of a Poisson process is that in a small enough interval, the probability of more than one arrival is negligible. In my case, I have data that shows the ...
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### What to do with zero-counts when fitting Poisson distributions? [closed]

Suppose we have events that occur in time following some compound Poisson process. For example, let's say the rate parameter is such that an event occurs every 30 days, on average. If we have 10 years ...
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### MLE for a homogeneous Poisson process?

If we have a data set consisting of event times $\{t_1, t_2, \ldots, t_N\}$ and would like to model this as a Poisson process with intensity $\lambda$, how do we do it? Intuitively, I would expect ...
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### Parameter estimation for NHPP for arrival series

I have multiple data sets (about 15) that describe a process of arriving customers to a shop. When plotted it's pretty clear that over time the rate of customers arriving decreases. However the time ...
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### Poisson processes or regression for lambda

I am asked to solve a problem where I have a machine producing toys in tho slots and want to predict number of faulty toys. The data is like this: ...
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### What is mean by the term “constant rate” in Poisson distribution?

I have difficulty in understanding the assumptions of Poisson distribution, one assumption is the rate at which the events occur in the time interval is constant. What is the meaning of that phrase? ...
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### Help me understand poisson.test?

I want to understand the poisson.test() function: ...
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### How do I compare two event rates?

Say I have two event streams, modeled as Poisson processes. These streams omit events at rates $\lambda_1$ and $\lambda_2$ respectively, so the count of observed events in $t$ time is $\lambda_1t$ and ...
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### Compound Poisson process for demand

I have a demand pattern for a service part. Demand event rate of this part is Poisson distributed. Demand of the part is 3 times in a year. So the demand event rate is 0.25/Month. Each demand ...
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### Normal approximation on (what it looks like) a poisson

I am self-studying inferential statistics from Larson's introductory textbook named: "Introduction to Probability Theory and Statistical Inference" (1st edition John Wiley & Sons.). I came ...
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### Poisson Process - Determining Rainfall Accumulation

Disclaimer - I'm not a statistician. Most of my knowledge on the subject is self-taught. I'm trying to grasp how continuous random variables can be used in conjunction with a discrete Poisson process....
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### Poisson Process: Probability of 2 arrivals by time 1 given that there are 6 arrivals by time 4?

Let $(N_t)_{t \ge 0}$ be a Poisson process with parameter $\lambda = 1.5$. Find the following: (c) $P(N_1 = 2 | N_4 = 6)$ I know how to do it if the times are reversed (it simply uses the ...
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### Poisson Process: In a small parliamentary election, votes are counted according to a Poisson process at the rate of 60 votes per minute

In a small parliamentary election, votes are counted according to a Poisson process at the rate of 60 votes per minute. There are six political parties, whose popularity among the electorate is shown ...
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### Poisson Process: Computers in a lab fail, on average, twice a day, according to a Poisson process

Computers in a lab fail, on average, twice a day, according to a Poisson process. Last week, 10 computers failed. Find the expected time of the last failure, and give an approximate time of day when ...
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### Histogram for a compound poisson process

Would a compound poisson process result in a histogram that isn't the same as that of a regular poisson process? How would I fit such a histogram without knowing the rate?
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### Inter-arrival time of Poisson arrivals?

Assume a Poisson process with rate $\lambda$. Let $T_{1}$,$T_{2}$,$T_{3}$,.... be the time until the first, second, third,......(so on) arrivals following exponential distribution. If I consider ...
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### Derivation of probability under assumption of Poisson process

Poisson process start with certain assumption about the how process govern in short interval of time $\Delta t$. The first assumption about the Poisson process is that the probability of occurrence ...
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### Compound Poisson Process with Weibull jumps

I need to simulate a compound Poisson Process in R, however I am not clear with the algorithm to generate it. I have conceptual gaps. I know by definition that: A compound Poisson process is the ...
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### zero inflated poisson model, how to choose “inflate” variables

I am trying to run a zero-inflated Poisson regression. The data I have are number of West Nile Virus cases NoCases (dependent var), and my independent variables are AvgTemp, AvgPrecipitaion, Region (*...
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### Poisson Process Intensity Function

I'm working through Kingman's Poisson Processes and have a question about defining the mean measure. Why is it that in most cases we specify an intensity function $\lambda(x)$, where the mean measure ...
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### How to quantify the reliablility of an estimate

Lets say I inspect two workers. Worker A works one hour and produces 2 goods. Worker B works 100 hours and produces 180 goods. So, on average, worker A produces 2 goods per hour and worker B 1.8 ...
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### 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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### Poisson: Probability it will take less than x time for more than y to occur

I am able to answer a poisson question where say: expected value = 2 per week, whats the probability greater than 7 in 3 weeks. But how would I answer a question where, for example expected value = ...
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### Poisson distribution inside-out: estimate the beginning of the period based on first occurrence time

If a Fisherman catches his first fish of the day at 10am, when is he more likely to have started fishing given that in average he catches 1 fish/hour? In other words: Let's assume a Poisson process ...
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### Equation for Inverse Poisson CDF

I am attempting to calculate quantile probabilities. I.e., the value above which there is only a 1% chance occurrence for an arrival process. The R code is pretty straight forward with say a lambda = ...
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### How should I smooth / average semi-sparse service usage data used in a time series regression?

I am using time series regression and survival models to predict future user outcomes based on past usage trends. I am dealing with a data set of daily service usage per user which, on a given day ...
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### Poisson process: getting a poisson from an exponential assumption

In a poisson process, getting an exponential distribution from a poisson assumption (for eg. in a given period of time $t$, if number of books that arrive is given by a Poisson, then the time until ...