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Question about marked poisson process

Let's say I have a Poisson point process on $\left[0,T\right]$ with rate $\lambda\left(t\right)=2t^2$. Suppose I attach a mark $m_t$ to each point $t$ of the process such that $m_t\sim ...
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0answers
10 views

Modeling Arrivals With a Time Limit

I have some data (sample here): ...
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1answer
45 views

Problem on Poisson Process

I am doing some problems related with the Poisson Process and i have a doubt on one of them. The problem is stated as follows: A doctor works in an emergency room. The emergencies arrive according a ...
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1answer
72 views

Find the distribution of $ N = \min \left\{k: \prod_{i = 1}^{k}U_i \lt .6\right\}. $

I'm cross-posting this from math.SE because it's not getting any love over there. However, if that's considered heresy, I can delete the posting over there. The Statement of the Problem: Let $ \{ ...
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1answer
30 views

Maximum value in Poisson process investigated using scan statistics

We have process where events are occurring at a rate of $B$, where the distribution of events in a fixed time frame can be described using Poisson statistics. Thus, the events can be modeled using a ...
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1answer
17 views

Decomposing multiple poisson process

Assume a time series composed by many recurring events coming from many different poisson process each with a different rate. Lets assume for simplicity no overlap between events. Is there any ...
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0answers
17 views

Testing for significant difference between two conditions for a poisson process with multiple replicates

I am a biologist rather than a statistician, so I apologise for any misuse of terminology. Happy to clarify if needed, and I am comfortable using R for statistical tests. I recently conducted an ...
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0answers
3 views

How to do regression on event density and size?

I have events with time and size. It might look like $(t_1, x_1), (t_2, x_2), \ldots $. What I really care about is average total size per time $\lambda =\frac{\sum_{k=i}^j x_k}{t_j-t_i}$. The $x_i$ ...
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1answer
78 views

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 ...
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0answers
42 views

Poisson process for queuing problem

I posted it incorrectly on a different thread so I'm reposting it here. I'm working on a problem and would love to get any advice - patients come into a clinic according to a Poisson process with ...
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0answers
55 views

R Poisson process simulation for a queuing problem [closed]

I'm working on the problem - patients come into a clinic according to a Poisson process with time parameter 10 minutes starting from 9 am until 4pm when the clinic stops admitting new patients. There ...
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0answers
202 views

How to Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides the probability of a number ...
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1answer
87 views

Probability of a rare event

Let's say I consider an event rare if it occurs no more than once in 90 days. Assuming everything is random and independent, If I see this event on day 3 of the observation, what is the probability ...
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60 views

Help with Poisson Process

I'm going to repost this here since my questions never get answered on mathstackexchange. It might be better suited to this location, as well. At the end of the workday, I add an amount between 0 and ...
5
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1answer
100 views

Exponentially decaying integral of a Poisson process

Suppose that $X_t$ is the set of times of the events of a Poisson process with unit rate after $t$ seconds. (In other words, $X_t$ is a set of $N$ uniformly distributed points over $[0,t]$ where $N$ ...
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1answer
28 views

Poisson distribution of rain storm arrival

I know what poisson distribution means.But I can not just understand how rain cells or rain storm arrivals is poisson process? looking for simple explanation. Thanks in advance
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1answer
15 views

Odds of specific generated population of exponential distributed stochast

I'm trying to generate a sequence of samples using an exponentially distributed stochast, i.e., making a Poisson arrival process. In my specific case I generate 337 samples using a mean inter-arrival ...
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0answers
21 views

Confidence interval for non-homogeneous Poisson process where lambda is fourier

I have a non-homogeneous Poison distribution $X = \{ x_1, x_2\, .., x_n\}$ where: $$\lambda(x) = \exp(a_0 + \sum_{z=1}^{Z}(b_z \sin(2 \pi x \frac{z}{Z}) + c_z \cos(2 \pi x \frac{z}{Z})))$$ ...
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1answer
54 views

Expected Value in Poisson Point Process with Prior Knowledge

I have a setup with a homogeneous Poisson Point Process (PPP) of intensity $\lambda$ in $W \subseteq \mathbb{R}^d$ and a set $A \subseteq W$. I'm looking for the expected value of points in set $A$, ...
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25 views

Question about M-step for bimodal Poisson Proces

all I have difficulty in deriving the result for the M-step of EM of the bimodal Poisson as shown in paper, Byers, Simon, and Adrian E. Raftery. "Nearest-neighbor clutter removal for estimating ...
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2answers
79 views

distribution of the last arrival in poisson process

Consider a Poisson process with rate $\lambda$ and let $L$ be the time of the last arrival in the interval $[0,t]$, with $L=0$ if there was no arrival. How can I prove that t-L has exponential ...
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32 views

How do we calculate this transition count probability?

Note: This is from the proof of prop 3.6 here. We want to calculate the probability of one transition between states $i$ and $j$, ending at state $r$, and starting at state $l$, in a time slice of ...
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0answers
32 views

Expected number of times two Poisson process events occur on the same day

So I have set up a Poisson Process N(t) with parameter L (events/year). I want to find the expected number of times over a 3 year period that 2 events occur on the same day. My approach: First ...
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1answer
20 views

Wait time for non-homogenous Poisson processes

Is the wait time between events for a non-homogenous Poisson process still exponentially distributed
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0answers
26 views

Transformation of growth function with two pulses

I'm trying to linearize the following exponential growth function: $$ y = ae^\frac{t}{b}+(1-a) e^\frac{t}{c} $$ To preempt any question regarding why I'm doing this: I'm trying to regress this ...
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0answers
35 views

Prediction Error for a Poisson Process

So I have a fleet of cars. I've sampled their breakdown rates (per hour driven) for the last 10 years. Their breakdown rate follows the gamma distribution. I am trying to do two things. Predict ...
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0answers
111 views

Autocorrelated Inter-arrival Times of Extreme Events

I'm using a bunch of techniques and methods from Extreme Value Theory to analyze my data. I have a time series representing the number of events happening in a given day. The time series is unequally ...
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0answers
15 views

Point process models

Two of the popular models for analyzing point process data are Cox and Hawkes processes. My question is how do we compare the statistical properties of these two processes as they both can be ...
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0answers
41 views

Estimate lambda for panel count data

I have panel count data for $F$ firms across $I$ years, so observe counts $C_{f,i}$ for $f \in \{1,...,F\}$, $i \in \{1,...,I\}$. I want to model the data as a poisson process. With increasing ...
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0answers
31 views

Pmf of compound Poisson process

Can I obtain an analytic expression for pmf of compound Poisson process? $Y_t = \sum \limits_{i=1}^{Xt} D_i$ where $X_t$ ~ Poisson($\lambda$) and $D$ ~ Geometric($\rho$)
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0answers
76 views

Implementing GLM for a poisson model using matlab function fminunc

I am trying to simulate a linear non-linear poisson model. The problem is that as far as I know, the log likelihood function in this case should be a convex one, but that does not seem to be true, ...
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0answers
42 views

Poisson vs. Gaussian in Geomagnetic Data

I've been studying geomagnetic signals using a threshold approach to detect pulse events in the data. The question here is what is the significance of the crossover of stddev and mean as the ...
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1answer
50 views

Alternatives to a one-dimensional Poisson process [closed]

Say I have "arrival" times in what may or may not be a Poisson process. I can think of at least three ways in which it can deviate from a Poisson process: Clumping. One arrival is likely to be near ...
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25 views

Prove that $N(\tau),V_t,Z_2,\ldots$ are independent in Poisson process

We define a Poisson process is a renewal process in which the interarrival intervals $X_n$'s have an exponential distribution with parameter $\lambda$. Denote $N(t)$ is the number of arrivals in ...
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142 views

estimate confidence interval for poisson process

I would like to know how I can estimate the confidence intervals for poisson process distributed variables. I have a pandas dataframe with a column of trials and a column of successes. I want to ...
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0answers
62 views

Fit to a non-homogeneous Poisson process

I have a sequence of event timings, $t_1, t_2, t_3, ..., t_n$ where there are a total number of $n$ events happening. For example, they are the timings when 911 was called in a city. I know these ...
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1answer
538 views

Poisson Process in R from exponential distribution

I am trying to simulate a poisson process sample path in R by starting off with exponentially distributed random variables. For example, for a value of $\lambda=0.5$, I can generate 500 samples and ...
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1answer
96 views

Using Poisson process model for prediction?

Suppose some event $X$ occurs on average $10$ times per minute. The events are independent of each other. Now, if I have understood correctly, this can be modeled as a Poisson process, and I can ask ...
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0answers
19 views

Overlapping interval of a Poisson arrival process

Calls arrives according to a Poisson arrival process with rate lambda = 15. Find E(N(2,4]N(3,5]) My thoughts: E(N(2,4]) = E(N(3,5]) = lambda * t = 15 * 2 = 30 However, I cannot figure out the next ...
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1answer
18 views

Is there a family of processes centred on the Poisson process?

I am looking for a model, characterized continuously by a single parameter, to describe the arrival times of buses with unit expected interarrival time. At one extreme of the parameter (say ...
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0answers
45 views

A math proof within a question about homogeneous Poisson process

We know that a homogeneous Poisson process is a process with a constant intensity $\lambda$. That is, for any time interval $[t, t+\Delta t]$, $P\left \{ k \;\text{events in}\; [t, t+\Delta t] \right ...
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0answers
51 views

Help me out with real-life Gamma distributions

I'm working with some data relating to maintenance and parts failures. I've got a pure math background with only a little bit of probability, and I'm currently learning by doing. I've got a list of ...
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0answers
73 views

Understanding Poisson Point Process [closed]

Could someone explain the Poisson Point Process? Is it simply an Integration over a Poisson Process for higher dimensions? If so, how do you derive the function, say in two-dimensional space, and ...
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0answers
38 views

Multiple poisson processes ?

I'm just trying to get my head around Poisson processes, as they're fairly new to me, and I've had a thought experiment that has been annoying me a little. Imagine a volume of some mixture hit by ...
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1answer
38 views

Is there a similarity between a jump process and a counting process since both follow a Poisson distribution

I read that a jump in a stock price can be modeled as a Poisson process. But I have also read that a Poisson process is a good model for a counting process (i.e. number of hits to a website per unit ...
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2answers
581 views

Expected value of a product of two compound Poisson processes

I'm working on my master thesis now and I've been struggling with a problem for some while now and no one seems to be able to help me or point me in any direction. So now I reach out to see if someone ...
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2answers
139 views

Uses of Poisson process in stock price models

If I want to find the probability that a stock is going to touch a support or resistance at least once in the next 5days, can I use a Poisson distribution? The textbook examples usually say that ...
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0answers
74 views

Split Poisson Process AND severity

I have a Poisson process whose statistics are interarrival times ($\bf X$), number of arrivals ($\bf N$), and arrival times ($\bf T$). Later, the process is split by a Bernoulli process that ...
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1answer
78 views

Comparing different poisson distributions with very variable sample sizes

I have data on around 50 different roads: The number of accidents and the volume of traffic on each. I'd like to compare these and estimate which is the most dangerous/safest, but the volumes (and ...
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19 views

What image registration metric should be employed to account for Poisson Noise?

I have a pair of adjacent frames (volumes) Xt and Xt+1 and I want to obtain a non rigid registration field relating the pixels (voxels) of Xt+1 to Xt. The intensities among the images are similar. If ...