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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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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10 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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1answer
8 views

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

We know that when the arriving rate of a Poisson process $X(t)$ becomes constant, then the process becomes a homogenous Poisson process. I have trouble understanding what "a constant arriving rate" ...
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12 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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18 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
30 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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14 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
46 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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43 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
43 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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12 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
129 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
60 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
36 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
78 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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21 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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19 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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28 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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31 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
76 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
74 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
121 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
26 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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9 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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1answer
36 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
48 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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31 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
138 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
27 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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19 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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70 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
30 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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56 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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43 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
65 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
54 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 ...
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35 views

R: Is it possible to estimate the poisson noise?

I have a dataset of many discrete counts (RNAseq read counts per base), which contain both real signals and background noise. The noise is random, and should be poisson distributed. What I would ...
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2answers
60 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 ...
3
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1answer
41 views

Credit Risk and Concentration

I am working with a UK credit-union and we are looking to build a model to assess our credit risk and changes to this over time. We have a number of loans to borrowers who each have a credit rating ...
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2answers
51 views

Call Centre Models

Can anyone suggest me, which Mathematical(Statistical) methods can be used to predict incomingcalls by a given time interval at a call centre? Please cite any ...
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48 views

Bivariate Poisson regression: Error: “in `contrasts<-`(…): contrasts can be applied only to factors with 2 or more levels ”

I realize this error message has been posted before, but the solutions previously provided does not work for me, so here goes: I am working with a data.frame, which looks like this: ...
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80 views

Analysis of Split (A/B) tests using Poisson and/or Binomial Distribution

I've seen this question asked before, but I have yet to come across a definitive source answering the specific questions: What's the most appropriate statistical test to apply to a small A/B test? ...
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24 views

Using glm(family = guassian) on data that is actually Poisson. Strange non-symmetrical bias

Let's say I want test the consequences of assuming a normally distributed response variable in a glm model when it is really Poisson. I simulate some data with some quadratic terms. ...
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67 views

Statistic for count process and measurements

I am facing some problems concerning which statistical approach to use for my measurements. I have a sensors which counts how many times an events occured. I had to characterize two lots of sensors, ...
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109 views

Count data correlation

My dataset is basically a time series - each case is a one day and several events are being observed for each case. I am not experienced in time series analysis but I still would like to get at least ...
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63 views

Basic idea of zero inflated two part models(hurdel) and application to big data (machine learning)

I'm currently working on the data which has 90% 0s in response variable. Based on my research, it seems zero inflated models could be a solution to this. However, while I was reading related ...