A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.

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Glmer model won't run all factor levels due to multicolinearity

I have a repeated measures design in which I test multiple individuals each with three different 20 second playback stimuli. I used 6 different playback orders in which each stimulus was played either ...
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26 views

what is the meaning and purpose of modeling a data?

Background: I collected a whole years access logs of my website, counted visit frequency for every user, and the numbers of user at each unique frequency, I got a distribution: $n_w \tilde\ D_w(f_w ; ...
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31 views

MonteCarlo simulations to test light curve variability

I have an average orbital light curve for a source, that is, binned count rate vs orbital phase, where the count rate are averaged over a number of orbit. I want to run MonteCarlo simulations to find ...
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11 views

Poisson regression with underdispersed and truncuated/censored upper bound

I'm analysing data from an experiment in which participants, over a number of trials, were presented with 8 boxes - 7 containing gold coins, and 1 containing a pirate. Their task was to open as many ...
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2answers
48 views

When is calculating probability based on a poisson distribution preferred over a binomial distribution?

I'm trying to understand why a poisson distribution may be preferred over a binomial one when modeling binary cases. Is there a case where you can't use a binomial distribution to solve a problem ...
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28 views

density function of the mixture of two NHPP

I'd like to know how can I calculate the density function of the mixture of two non-homogeneous Poisson process? I should mention that I have the kernel densities of those NHPP s. I can also describe ...
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25 views

ML classification problem for matrix and distribution estimate for each cell in the matrix

I am trying to think about a machine learning/statistical learning related problem. But would love to get idea from people in the forum about related problem/work/resource. So, the problem idea is ...
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99 views

What's the Mode of a Bivariate Poisson Distribution?

I have been looking at the bivariate Poisson distribution and I am wondering if there is close form expression for the mode of this distribution. I know the mode of the univariate Poisson distribution ...
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1answer
34 views

Poisson or Normal distribution?

In this problem: The respiratory disturbance index (RDI), a measure of sleep disturbance, for a specific population has a mean of 15 (sleep events per hour) and a standard deviation of 10. They ...
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45 views

Poisson distribution is a submartingale

Assuming that $s<t$, the poisson process is known to be a submartingale since only positive occurrence will happen as stating: $$E(X_t | \{ \mathcal{F}_s \}) = E(X_s | \{ \mathcal{F}_s \} ) + ...
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1answer
35 views

Overdispersion in poisson glm

When calculating the dispersion deviance/degrees freedom I get the value 1.8. Is it absolutly necessary to carry out the glm using quasipoisson? What is deemed 'significantly overdispersed' ?
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17 views

Distribution of “priority” emails among agents with different speeds (strange question)

but I figure if someone knows how to answer it, it may be someone here. Basically I have this weird distribution where the customer service agent speed (in terms of contacts per hour) is very ...
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2answers
33 views

Hierarchical Gamma-Poisson CDF?

What is the most computationally efficient way to evaluate the CDF $$P(X \leq x | r,v)$$ where $$ X \sim Poisson(\lambda)$$ and $$ \lambda \sim Gamma(r,v)$$ I can't see the next obvious step after ...
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2answers
47 views

Can categorical variables be treated as count data?

In a questionnaire study, I asked for the frequency of certain behaviors using a 5-point scale. Originally, I planned to treat it as categorical, however, distribution of the answers (N=1000) turns ...
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21 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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18 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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3answers
66 views

Negative Binomial Regression?

I have a dependent count variable that measures the number of days spent in a hospital (LOS) for a group of patients who received two different medical interventions upon hospitalization. I'm trying ...
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24 views

Zero-intercept poisson regression model predicts better than a model with an intercept?

I have read some blogs/articles saying that intercept should not be suppressed. Recently, I used glmm.admb to model a ZIP (Zero-inflated Poisson) model which is giving better results without an ...
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16 views

Probability-generating function of two independent Poisson random variables [duplicate]

Let $X_1, X_2$ be two independent Poisson random variables with mean $\lambda_1, \lambda_2$, and $S_2 = a_1 X_1+a_2 X_2$, where the $a_1$ and $a_2$ are constants. Is it correct, that ...
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12 views

Poisson glm overdispersion. Calculating QAICc for model comparison

I'm having some difficulties with my glm . The models are overdispersed so I want to run them as quasipoisson. I would like to be able to compare the models using QAICc but the packages I have ...
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1answer
60 views

Mean of predictive distribution

I observe independent, Poisson-distributed data $ D = \{x_1, ... x_n \} $ with mean parameter $ \mu $, i.e., $$x_i\stackrel{\text{iid}}{\sim}\mathcal{P}(\mu)$$ Over $ \mu $ I assume $ Gamma(\alpha_0, ...
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1answer
50 views

Compare poisson and negative binomial regression with LR test

My question is related to the question Compare negative binomial models. I have some difficulties understanding UCLA guide in http://www.ats.ucla.edu/stat/r/dae/nbreg.htm (I am using ...
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1answer
103 views

Which of these distributions approximates better to a Poisson distribution?

Consider two Poisson binomial distributions (distributions of sums of independent Bernoulli variables) as below: The distribution of the sum of 99 variables with probability 0.01 (of taking the ...
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1answer
73 views

Maximize the profit of a product given a Gamma distribution

I'm having trouble translating this problem into a workable form: A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters ...
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1answer
17 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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17 views

Variance of the influence function of the parameters of an over-dispersed poisson model

Assume an over-dispersed Poisson model: \begin{align} E[C_ij] &= m_ij \quad\text{ and } \\ {\rm Var}[C_ij] &= ∅E[C_ij]= ∅m_ij \\ \log(m_{ij}) &= n_ij \\ n_{ij} &= c+ α_i + β_j ...
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1answer
25 views

How might I go about modeling the product of two random Poisson distributed variables that are not necessarily independent?

I think the title might capture the entire question but for clarity's sake let me expand here. I have several Poisson distributed random variables, and want to model the product of pairs of these ...
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1answer
21 views

Which distribution should I use when building a GAM in R?

What type of distribution would you consider this data to be? My first thought is an f-distribution, but I suppose it could also be a poisson distribution. I am trying to build a generalized additive ...
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11 views

Estimating a Poisson process when arrivals occur out of order?

TL;DR: Given a Poisson process with constant intensity $\lambda$, but you are hearing about arrivals out-of-order, how would you (sequentially/iteratively) estimate $\lambda$? What if the problem is ...
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37 views

How does one do a Post-hoc test for a Poisson glm in R?

My data consists of the following categories: Site - 3 sites - Boulder, Rubble and Cul-de-Sac Season - 4 types - warm1, warm2, cold1 and cold2 Behaviour - 6 behaviours scored - Basking, ...
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2answers
28 views

How to understand the “arriving rate” in a homogeneous Poisson process?

We know that when the arriving rate of a Poisson process $X(t)$ becomes constant, then the process becomes a homogeneous Poisson process. I have trouble understanding what "a constant arriving rate" ...
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31 views

individual level random effect for over dispersion

In glms we can use a quassipoison fudge factor to account for over dispersion in our poisson models. In glmms we can add an individual level random effect (e.g. ...
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24 views

Fast way to compute central moments of a Poisson random variable?

I am looking for a way to quickly compute the central moments of a Poisson random variable. I've found a couple of resources on how to compute the central moments, but I'm still trying to figure out ...
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1answer
54 views

Type of inference to use with log-linear Poisson glm on contingency table frequency counts

I was doing some log-linear models to test for interactions/associations in multiway contingency tables (based on the tutorial here, http://ww2.coastal.edu/kingw/statistics/R-tutorials/loglin.html). I ...
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33 views

Measure of explained variance for Poisson GLM (log-link function)

I am looking for an appropriate measure of the "explained variance" of a Poisson GLM (using a log-link function). I have found a number of different resources (both on this site and elsewhere) that ...
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1answer
77 views

Need help calculating poisson posterior distribution given prior

I have been attempting to figure this out for hours, but gamma distribution is somehow beyond me. I have a question where we are given α=5 and ...
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52 views

Poisson GLM,Hessian matrix = the observed Hessian matrix

Assume a simple Poisson model with 2 unknown parameters (the intercept and the slope) Show that the expectation of the Hessian matrix = the observed Hessian matrix or equivalently the observed ...
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1answer
44 views

What is the statistical distribution of a Poisson process when the windows size is different?

I have a discreet random variable X known to be Poisson distributed. This represents the number of observations in a certain time window, day one day. Assuming there are no other factors dependent on ...
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27 views

Probability generating function of poisson point process

Assume you have a 1D non homogenous PPP $\Xi$ with intensity $$\lambda(x)=\lambda x^{\frac{2}{\alpha}-1} \ x \in \mathbb{R}^+$$ where $\alpha$ is positive integer. Now define $$\gamma_k = ||x_k||$$ ...
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1answer
136 views

Simulating the waiting paradox

After seeing this question, I thought I would try to simulate the bus waiting time paradox to help my understanding. However, what I got was the "intuitive" result, rather than that predicted by the ...
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2answers
65 views

Occurrences of two independent Poisson processes

I am trying to prove the result that exactly k occurrences of a Poisson process before the first occurrence of another independent Poisson process is a geometric random variable. $$P(k\text{ events ...
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16 views

Source of least square estimator of Poisson parameter

I have $X \sim \text{Poisson}(\theta)$ I need to see how least square estimator of $\theta$ is obtained. Is there anything online showing that?
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1answer
40 views

is the sum of a poisson process a poisson process?

I would like to write an application that emits events distributed by a Poisson process with some $\lambda$ I need to separate the generation of these events in multiple processes, but I only have a ...
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2answers
82 views

Expectation of $(X + Y)^2$ where $X$ and $Y$ are independent Poisson random variables

I would really appreciate anyone's help with this problem: (let $E$ denote expectation) Suppose $X$ and $Y$ are independent Poisson random variables, each with mean $1$. Find: $E[(X + ...
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0answers
25 views

Distribution of a binary matrix times a Bernoulli vector

Suppose we have the vector $\mathbf{Y} = (Y_{1},\ldots,Y_{n})$ where $Y_{i} \sim \textrm{Bernoulli}(p_{i})$ independently. For the applications I have in mind, $n$ will typically be several thousand, ...
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25 views

Understanding the variance to mean power function in Poisson gamma models

I have a biology background and try to understand what it means that the distribution of snps over the genome follows a Poisson gamma (PG) model. It is accepted that each chromosome contains Poisson ...
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40 views

Can we use the AIC values to compare a hurdle poisson model to a multinomial logit model?

I estimated two different models using an SP survey: Hurdle poisson and multinomial logit with 5 alternatives. My dependent variable is the number of weekly trips (0,1,2,3,4,5 trips) that students ...
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2answers
88 views

Suppose that $X\sim\text{Poisson}(\lambda)$, find $E[X(X-1)(X-2)(X-3)]$

Hint: do not use linearity, use definition of expectation. i have a rough idea that we turn the inside into g(x), but not sure how to proceed from there.
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1answer
140 views

Convert Poisson distribution to normal distribution

I primarily have a computer science background but now I am trying to teach myself basic stats. I have some data which I think has a Poisson distribution I have two questions: Is this a Poisson ...
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1answer
125 views

Find the parameter of a Poisson, given the distribution function at a known value

Assuming a Poisson distribution, the probability ($\alpha$) that the result will fall within the range $0\ldots k$ is given by the following expression: \begin{equation} \alpha = ...