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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Does this variable follow a poisson distribution or a binomial distribution?

I dance an average of 2/7 nights during a week. D = Number of nights dancing in one month/4 weeks. My first thought was Poisson, but am now unsure. Is it none of the above?
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29 views

Poisson Distribution - rpois - NAs produced [on hold]

I am new to R (a student) and running a Poisson distribution on football scores. head(results0910) works perfectly, showing me that my teams and scores are read in ...
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Zero-inflated Poisson and Gibbs sampling, proofs and sampling

I am trying to figure out zip-inflated Poisson (ZIP) model. In this model, random data $X_1, .., X_n$ are of the form $X_i=R_iY_i$, where the $Y_i$'s have Poisson distribution ($\lambda$) and the ...
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25 views

UMP test for poisson vs geometric

I have two hypotheses: $H_0\!: X\sim\rm{Pos}(1)$ $H_1\!: \rm{Geometric}(0.5)$ for any $\alpha$ in $(0,1)$ How can I construct a uniformly most powerful (UMP) test? I used the ratio under the $H_0$ ...
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80 views

Finding a UMVUE for a specific function

Let $X_1....X_n$ be a random sample from the Poisson distribution with parameter $\lambda$. Find the uniformly minimum-variance unbiased estimator of a) $\lambda^3$ b) $E(e^X)=e^{\lambda (e-1)}$ ...
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5 views

Poisson parameter lambda confidence interval [duplicate]

Based on x arrivals in time t, what is the alpha level Confidence interval for lambda?
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32 views

On deriving the Poisson distribution from the binomial distribution

My own personal understanding of modeling the number of independent uniformly distributed events occurring in a fixed time interval, is that we can first approximate this with a binomial distribution ...
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29 views

Compound Poisson Distributions: When, Why, and How To Split the Problem

I've just stumbled upon the Compound Poisson Distribution (CPD) and it seems to be precisely what I need. For the purposes of this post, let's suppose I have a store that sells many items of ...
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Is there a way to define a statistic similar to the z-score for the Poisson distribution?

Let's say I want to compare samples taken from Poisson distributions that have different values of lambda (rate). If the samples were from a normal distribution, I could convert each observation into ...
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63 views

Conditional Poisson Distribution

The number of claims, $N$, in a year on a portfolio of policies follows a Poisson distribution with parameter $λ$. Large claims have a probability $p$ and small claims $(1-p)$, independently of ...
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26 views

Difficult Counting problem

Just started a probability course and this problem is giving me a hard time A bookie offers two bets I and II on a soccer game I You win this bet if the total number of goals scored in the first half ...
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Predicted number of events from xtnbreg, fe make no sense

I am trying to compute the number of predicted events from a fixed effects negative binomial regression model in Stata. I run the model first using random effects, then using fixed effects, and ...
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37 views

What transformation should be carried out if the count is non-integer in poisson glm in r?

My data is like this: person final sex 1 34.20 1 2 2.00 0 3 15.58 0 4 18.00 1 5 50.06 1 I am fitting ...
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42 views

How to choose between poisson regression and zero inflated models

I have data on children visiting the A&E department. I want to see which variables are associated with the numbers of visits. For instance, if genetic factors are associated with more visits to ...
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17 views

Uncertainty on ratio of integrals (correlated)?

I have a histogram, and a quantity defined as the integral of a subrange of that histogram (int_sub) divided by the integral of the full range (...
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7 views

Approach to plotting a shock model with a Poisson parameter?

I know the shock model is defined as: $$ A(t) = \sum_{i=1}^{N(t)} A0\exp[-a(t-sn)] $$ where: $a = 0.5$ N(t) is Poisson ~ lambda, and lambda = 4 $t = 5$ $A0$ is given its own uniform ...
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28 views

Bypassing exponential waiting times for Poisson simulations?

Hello StackExchange users, I am trying to figure out how do I simulate a time dependent Poisson process through N(t). However, my main problem is having trouble understanding what N is and how to go ...
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134 views

Tricky Poisson distribution question

Am new to probability and have been struggling to solve the following question. Assume $X_1, \ldots,X_4$ are IID with $X_i ∼ \text{Po}(λ)$. Let $Y = \frac{1}{4} (X_1 + \ldots + X_4)$. Find ...
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Count Data Model, Poisson Distribution and Rounding?

In doing a count data model using a Possion distribution, should the estimate (output) be rounded (or the ceiling) if your target variable is always a whole number in the input training target data ...
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199 views

Which distribution to use for a probability problem?

In a food processing plant, on average, 2 packaging machines breakdown per week. I let x be the number of processing machine breakdowns in a week. So x is Poisson(2), but one part of the question ...
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6 views

GLM to asess differences between two treatments with only one IV

I have some data that I've collected in the field while running a trial where some sites (random 50%) received a treatment and the others did not. The dependent variable is the total number of baits ...
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1answer
36 views

Poisson for percentage data if values are low?

I have percentage data for diet per area (example here.....) I have no data on the individuals contributing to this diet, only for the population as a whole for each area. I want to assess ...
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13 views

variance of data of correlated poisson means?

I want to find the mean and standard deviation for the data for the following question. We have 10 houses of known different sizes. The number of people living per square meter has a poisson ...
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55 views

How do I generate two correlated Poisson random variables?

How would I simulate observations from a bivariate Poisson distribution such that they have a nonzero covariance? The hint I was given is that I need to use the fact that the sum of two Poisson random ...
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96 views

hurdle model with negative binomial distribution of counts - error message and model selection

I'm working with over-dispersed count data, which is zero inflated (~2/3 zeros). I've fit a hurdle model using hurdle from ...
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52 views

Show posterior is proper for this poisson linear model

This question is 3.12 in Andrew Gelman's Bayesian Data Analysis 3rd edition. Let $y_i|\alpha,\beta \overset{iid}{\sim} \text{Poisson}$ with mean $\alpha+\beta t_i$. Find a prior distribution that ...
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Can I use glm with Poisson family if counts data are treated as density?

Imagine you have data of birds counted in an area - let's say, you count 18 birds in a surveyed area of 1,3 km^2. Imagine you relate this counts to 1km^2, so that you have 13.9 parrots per km^2. ...
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Since incidence rate ratios are always positive, how does one determine the sign of the effect?

I want the results from a Poisson regression to be comparable to previous OLS and Tobit regressions. To do this, I am utilizing the irr (incidence rate ratio) option in Stata. However, since all the ...
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Goodness of fit to poisson with unspecified mean

Is there a goodness of fit test for testing a series of counts against the whole family of poisson distributions? So, with the mean unspecified? Or does that not make any sense? Kinda related to ...
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Poisson convergences of series of random variable

Let $X_i$ be independent Poisson with mean $\lambda_i$. Show that i)$\sum_1^\infty\lambda_i<\infty$ implies $\sum_1^\infty X_i$ converges almost surely to a finite limit. ...
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How do I evaluate if an SIR model is consistent with a new-product diffusion model?

Background Susceptible-Infected-Recovered (SIR) models are used in epidemiology to determine the spread of disease. (link) The Bass models for new product diffusion are textbook in sales. (link) ...
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43 views

How to find the appropriate family for glm models?

As suggested over at stackoverflow I poste the question here instead: I have a data frame with three variables, where "Resp" is my response variable (count data), F1 is a categorical predictor (4 ...
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36 views

Relationship between Poisson generation and generalized Kullback-Leibler divergence

I have read that, in the context of matrix factorization, performing maximum likelihood estimation under the assumption that the entries are Poisson generated is equivalent to minimizing the ...
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Meta-analysis of skewed data with low event rate (single-arm studies)

I am trying to pool the data from several single-arm studies regarding the re-infection rate of a certain disease using STATA. From each study, I have obtained the no. of re-infections, and the ...
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Do the number of entries per bin of a histogram obtained out of a try and reject sampling of a pdf follow a Poisson distribution?

Imagine we have this pdf $\frac{3}{8}(1+x^2)+0.017x$ defined in $x\in[-1,1]$. Imagine we make a try and reject sampling and get many values of $x$. Imagine that with this variables we make a ...
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Approximation of “translated and scaled” Poisson distribution by normal distribution?

If I have a random variable $Y=a(\frac{b}{c}+\frac{X}{c})$, where $a,b,c$ are all integers and $X$ is Poisson distributed with a mean which is large enough to be approximated by the normal ...
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51 views

Distribution of ratio of Poisson distributed random variables

I am currently reading a paper and puzzling about a certain statement. I have a ratio ...
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45 views

Determine the mean and variance of X

Suppose that the number of customers who enter a post office in a 32-minute period is a Poisson random variable and that $P(X = 0) = 0.12$ How would I find the mean and variance in this case? I feel ...
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46 views

How to generate arrivals around a Poisson distribution

I'm interested in generating random arrivals that should simulate the call arrivals of a call center. I chose to use a Poisson distribution, but the greatest problem comes with the fact that it's a ...
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R glmer poisson for repeated measures - syntax correct?

I have for the past two days read all the questions and answers I could find regarding my problem, but as I got only more insecure, I finally decided to post a question on my own. I'd very much ...
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68 views

Poisson Regression Model - How to interpret the IRR and Base-Ratio?

By studying the Poisson regression model to analyze count data, I chanced upon the Incidence Rate Ratio (IRR). Browsing on the internet, I found different interpretations of that. For instance, ...
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38 views

Combining Poisson estimates

On average, 10 buses and 60 cars pass your house per hour. During one period of time, you count 11 buses and 40 cars passing your house. How long were you counting for? My first thought is to make ...
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748 views

Should the fumble rate of NFL teams be a normal distribution?

There's a lot of garbage statistics going around the internet regarding the Patriots, but I was just curious what the well-versed in statistics have to say about this. The main question is - in what ...
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Edited: Glmer model won't run all factor levels due to multicolinearity - can you have pseudo-multicolinearity?

I have a repeated measures design in which I have tested 112 individuals each with three different 20 second playback stimuli. I used a random block design where an individual was assigned to 1 of 6 ...
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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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55 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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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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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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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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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 ...