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22 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
22 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
54 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
11 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 ...
2
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0answers
36 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
18 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
34 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
37 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 ...
2
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1answer
39 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
19 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
74 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 ...
1
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0answers
34 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
67 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 ...
2
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1answer
57 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
16 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
16 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
39 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
48 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
46 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
49 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
32 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 ...
0
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1answer
22 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
388 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
72 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
59 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 ...
3
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1answer
54 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
17 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
7k 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 ...
2
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0answers
78 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
26 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
45 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
votes
1answer
650 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 ...
2
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0answers
97 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
66 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 ...
2
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0answers
36 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 ...
4
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1answer
110 views

Test hypothesis point process is Poisson [duplicate]

I have some data and I would like to test the hypothesis that they come from a homogeneous Poisson process. I can of course look at the inter event times and test if these are exponentially ...
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0answers
29 views

Poisson counting process parameter

Two quick questions: What's the maximum likelihood estimator of the parameter of an homogeneous Poisson counting process? To estimate $\lambda$ I'm currently using number of events/total time, ...
1
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1answer
61 views

A modelling question about point processes with heavy tails

I am trying to model a number of point processes for which I have data. If I choose to model each one using a (different) homogeneous Poisson process and estimate the rate using MLE then for some of ...
2
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1answer
78 views

Given time series data, how to model the frequency of someone changes his job?

I am given a time series data vector (ordered by months and years),which contains only 0s and 1s. ...
4
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0answers
55 views

Detecting changepoint in ratio of rates of two Poisson processes

I'm interested in a changepoint detection problem of the following scenario: Consider two Poisson processes for which we have the event times. I'm interested in detecting a change in the relative ...
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1answer
102 views

Estimating Poisson process intensity using GLM

Suppose I want to build an explanatory model for events generated by an inhomogeneous Poisson process with unknown intensity $\lambda$. Each entry in my dataset represents the registration of an ...
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0answers
344 views

Fitting for a Poisson-Gaussian Mixture Distribution

First of all, I am rather new to statistics, so go easy on me. I am aware that the negative binomial distribution can be thought to arise as a result of letting the $\lambda$ parameter in a Poisson ...
6
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1answer
316 views

Total expectation theorem for Poisson processes

I have two independent Poisson processes $A$ and $B$ with arrival rates $\lambda_A$ and $\lambda_B$, respectively. Now, the expected time for the arrival of the next item for the merged process should ...
2
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2answers
110 views

Poisson arrival

Users arrive according to Poisson process with rate $\lambda$. If every third user is removed, then do the remaining users form a Poisson process with rate $2\lambda/3$? If every other user is ...
4
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1answer
1k views

How do we predict rare events?

I am working on developing an insurance risk predictive model. These models are of "rare events" like airline no-show prediction, hardware fault detection, etc. As I prepared my data set, I tried to ...
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0answers
68 views

Generalised (nonhomogeneous) Poisson process

Define a generalised Poisson process as an arrival process that begins at time 0 and that satisfies: The independence property: the number of arrivals during two non-overlapping intervals ...
3
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0answers
121 views

Non-parametric estimators for time-varying binomial proportion

I have a bunch of count data associated with time intervals (potentially overlapping and of variable lengths), say $(s_i, t_i, n_i, N_i)$ where $N_i$ is a count of the total number of events ...
0
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0answers
51 views

If Maria performs more observations per unit of time than Maximilien, how can he estimates the Maria's results from his own?

General problem Having a sequence of values $v_0, v_\Delta, v_{2\Delta}, \ldots, v_{N\Delta}$, which are measured every $\Delta$ units of time, usually we are interested in the prediction of the ...
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0answers
30 views

Mean length of time spent queueing in $M/E_2/1$ system?

Context: Consider a $M/E_2/1$ queueing system, where the customer arrival rate is $\lambda$ and the service time distribution has a gamma distribution with parameters $2$ and $\mu$, i.e. with p.d.f. ...
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1answer
147 views

Mean service time of a $M/E_2/1$ queueing system?

Consider a $M/E_2/1$ queueing system, where the customer arrival rate is $\lambda$ and the service time distribution has a gamma distribution with parameters $2$ and $\mu$, i.e. with p.d.f. ...