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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Can you show that $\bar{X}$ is a consistent estimator for $\lambda$ using Tchebysheff's inequality?

This question was taken from a practice exam in my statistics course. Given a random sample $X_1, X_2, ... X_n$ from a Poisson distribution with mean $\lambda$, can you show that $\bar{X}$ is ...
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14 views

Identify deviations from trend

I have a panel with individuals $i$ measured at time $t$ (the date). The outcome is a count, which we can call $C$. There's some general time trend $g$ affecting all individuals. $E[C_{it}] = ...
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18 views

Relationship between Poisson and Exponential distribution problem

I'm struggling to understand why I can't use an exponential distribution to solve this question: Astronomers treat the number of stars in a given volume of space as a Poisson random variable. On ...
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15 views

How to model the following dependent variable? [on hold]

If I got a dataset which the (count data) dependent variable has the following distribution, how should I model it? I am aware of the zero inflated model and the negative binomial model, but are ...
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40 views

How can we find $Cov(X(s), X(t))$ for a compound poisson process?

If I assume that $X(t)$ is a compound poisson process, how can it be found what $Cov(X(s), X(t))$ is? I have seen this over and over in books, but they only state it as fact. It is stated to be ...
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15 views

Cameron and Trivedi overdispersion test-Eviews 7

I would be glad for explanation about the Overdispersion test (Cameron and Trivedi,1990). I am working with Eviews 7, and i needed to obtain the fitted and the forecast values of the dependent ...
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15 views

implementation of Poisson regression [duplicate]

I am trying to work with Poisson regression. I came across this video which is very helpful - https://www.youtube.com/watch?v=HntUY8SsYZg. In the video one of parameters (Race) is categorical and ...
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Poisson Hypothesis Testing for Two Parameters

So, for fun, I am taking some of the data of calls from the call center I work at and trying to do some hypothesis testing on them, specifically the number of calls received in a week, and using a ...
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9 views

retrospective kpi study

I have data about a business that looks like: actions: <timestamp, # responses, cat1, cat2> where each action can generate 0 up to perhaps 20 responses. ...
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19 views

How to transform counts for correlation?

I have averaged counts (>= 0, so poisson-like distributed) and need to correlate them (for the purpose of cross-validation, but this is not important I believe). Should I transform them before ...
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14 views

Skellam Distribution with Dummies (Difference of two Poisson RV)

The difference of two Poisson distributed random variables follows a Skellam distribution. We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
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27 views

Probability of obtaining a greater-than or equal set of observations from a Poisson RV

I have a suspicion this might be fairly trivial, but for some reason I cannot obtain a satisfiable answer today. Assume a Poisson random variable $X$ with known parameter $\lambda$ (though I suspect ...
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16 views

Two rate chi squared tests infection rate

We would just like to display a crude statistic to compare infection rate pre/post intervention. Based on a paper I read the statistical test I need to apply is a 2 rate chi squared test. I've been ...
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28 views

Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
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26 views

Tree model with poisson distributed response variable

If I understand correctly the R tree model - library(tree) - can only be used if the response variable is normally distributed. Is there a way to create a tree model with poisson distributed response ...
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38 views

Auto insurance claim modelling

I am really struggling with finding the best model for predicting claims with my third party motor insurance data. First of all, I am not sure whether I have done correctly with the grouping of ...
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1answer
28 views

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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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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32 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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108 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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33 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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31 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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74 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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27 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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39 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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53 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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31 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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139 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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205 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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43 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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1answer
57 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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112 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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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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31 views

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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22 views

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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48 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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1answer
43 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 ...