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27 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
36 views

R Poisson process simulation for a queuing problem [on hold]

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
83 views

Model a Process using 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
79 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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0answers
51 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
96 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
25 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
13 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
18 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
48 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 $A$, ...
2
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0answers
22 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
76 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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0answers
27 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
30 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
19 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
25 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
29 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
97 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
14 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
39 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
26 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
65 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
41 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
49 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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0answers
23 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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0answers
125 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
52 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
214 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
84 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
18 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 ...
1
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1answer
17 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
44 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
56 views

Proof about an Inhomogeneous Poisson Process

We know that an inhomogeneous Poisson process is a process with a rate function $\lambda(t)$. 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
50 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
69 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
34 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
484 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
97 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
69 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
74 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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0answers
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 ...
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3answers
8k views

Please explain the waiting paradox

A few years ago I designed a radiation detector that works by measuring the interval between events rather than counting them. My assumption was, that when measuring non-contiguous samples, on ...
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0answers
90 views

Mean and variance of Cox process

Consider the (doubly-stochastic) Poisson point process with rate $ \lambda(t) = \rho e^{-t/\tau} $ where $\rho\sim\Gamma(\alpha,\beta)$ is a Gamma-distributed random variable. I require the mean ...
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0answers
29 views

A union bound on a continuous variable

Assume a continuous point process (say Poisson) in [0,t]. Assume that it is given that only three jumps occurred in [0,t], however, their exact time coordinate is unknown. In addition, it is known ...
0
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1answer
50 views

Binsize for Compound Poisson Gamma Distribution

Having data of a (putative) Poisson-Gamma process I am looking for a method to define the correct binsize for analysing my data. I need a certain range (!) of binsizes (for instance starting with ...
2
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1answer
2k views

Poisson process and the memoryless property

I understand that inter-arrival times of a Poisson process are exponentially distributed and therefore the inter-arrival times are memoryless. However, how about the waiting times of Poisson process ...
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0answers
107 views

Estimating parameters and latent variables in a split Poisson distribution using R and JAGS

I am trying to estimate parameters and latent variables in a split Poisson model that describes observable and unobservable counts in time assuming the split probability is $\pi$. An observable event ...
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2answers
70 views

Mean of Poisson distribution experimentally

Suppose I approximate a variable (events of certain type) by a Poisson distribution and I would like to write a program and measure the mean experimentally. The idea is that I have an algorithm which ...
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0answers
39 views

Testing if points on a line are over/under dispersed

I have a series of about 1000 points on a chromosome and I want to know if they are clumped, over-dispersed, or neither. The chromosome can be viewed as a 1-dimensional. I've looked over some ...