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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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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15 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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6 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
36 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
78 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
51 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
13 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
23 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
20 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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10 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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29 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
24 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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18 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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20 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
39 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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19 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
66 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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47 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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18 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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132 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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63 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
37 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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24 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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24 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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30 views

Maximum Liklehood estimator of Poisson

I am trying to solve the following problem, I was able to solve first three bits of the problem but after that i am stuck and do not have clue to solve the (iv) bit. The local government has ...
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34 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 ...
2
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2answers
87 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
100 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
123 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 = ...
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1answer
28 views

The probability of a student getting a given question correct and the associated uncertainty (Item response theory)

I'm doing some statistics on multiple choice test scores (with item response theory, (http://en.wikipedia.org/wiki/Item_response_theory). I want to know the probability that a student with a certain ...
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11 views

How to determine CDF of Poisson function when only arrival time and service time are known?

If I can sample any given poisson arrival and service rate at any point and can sample any no of times. How just out of that sampling can I determine the CDF.
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37 views

to find the values of gamma distribution knowing the parameter value of a poisson

I have a variable X, and information available to me is that the parameter $\theta$ is around 2.2 $X\sim \mathbf{Poisson}(\theta)$ How can I determinate the value of the parameters $\alpha$ and ...
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2answers
49 views

Poisson as a limiting case of negative binomial

I was reading "Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter" by Walter W. Pieogorsch, and in the intro it says the Poisson distribution is a limiting case of negative ...
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32 views

Is there a Poisson-Gamma-Gamma model?

An example to elucidate my problem: The total claim amount can be modelled by a Poisson-Gamma model as it is assumed that the events (e.g. accidents) are Poisson distributed and the claims are Gamma ...
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1answer
158 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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2answers
34 views

Testing for independence between variables in poisson distribution

I'm trying to figure out how to test if variables that I think follow a Poisson distribution are independent (which is a requirement of the Poisson distribution) -- or it it matters. Let's assume I ...
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21 views

Values for the parameters of a Gamma in a Gamma-Poisson distribution

I need values for the parameters $ \alpha,\beta$ of a Gamma distribution that represent the parameter $\theta$ in a Poisson distribution,so its expected value. I'm using these distribution to ...
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81 views

Count data in a Structural Equation Model

I am currently trying to fit a structural equation model (SEM) on a certain dataset using R (lavaan package). Some of the most important variables in my model are count data (abundance of different ...
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1answer
36 views

Find out if I can ask for more

Scenario: I have a system that issues requests to another system. Each of these requests have a probability $p$ of requiring a specialized resource. The probability $p$ can be estimated using a ...
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1answer
31 views

Distribution of sum of two shifted Poisson

Suppose Y is shifted Poisson at "a", say Y -a ~Poisson (t) and X-b ~ Poisson (r), again a shifted Poisson at "b." Now what is the distribution of Z= X+ Y? Any idea? How to prove it?
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57 views

Poisson regression

I'm analyzing an article for my studies with the hypothesis if a change in work motivation is related with a change in mental well-being (http://www.sciencedirect.com/science...01879113001541). Sadly ...
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50 views

Glm with Poisson in R with no p-value?

I've been doing glm and thought I had it cracked but looking at some sites for interpreting results I realised R had displayed my results oddly. ...
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15 views

Poisson confidence interval that accounts for time?

I've gathered Poisson-distributed data and would like to compute a confidence interval, but the number of events and the amount of time are very small. Since standard CIs for rates aren't appropriate ...
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1answer
67 views

Correct Poisson Distribution Formulation

I have a Poisson formulation with the following parameters: I see 90 people in a city an hour 1.2% of people in the city are Indian How would I calculate: The maximum amount of time before I ...
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1answer
55 views

Use law of total variance to find unconditional variance of overdispersed Poisson?

First, I need to prove that the distribution of a RV X, where X|lambda ~ Pois(lambda), and lambda ~ gamma(a, B), is a negative binomial. I know that it is, but why negative binomial instead of another ...
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40 views

Can ayone help me in solving the below Problems of probability distribution?

Patients arrive randomly and independently at a doctor's surgery from 8·0 A.M. at an average rate of one in Five minutes.The waiting room holds 2 persons. What is the probability that the room will be ...