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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6 views

Find sufficient statistics for Poisson model with variable parameter

It might be an easy question, but the fact that the parameter is varying puzzled me. Here is the problem: In the Poisson model, where θ varies from zero (including) to infinity, we want to ...
0
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16 views

How to check if two results are consistent

I'm looking at an astronomical object. In one observation, it does something (not relevant what :) 2199 times out of a possible 2936. In another (later) observation, it occurred 2094 times out of a ...
0
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21 views

How to correctly standardize Poisson distriubuted variable? [on hold]

Is there any specific way how to standardize variable which comes from Poisson distribution? I've found that one way is the you can use same approach as for Gauss distributed variable. I've also ...
1
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0answers
9 views

Continuous, sometimes negative residuals from Poisson-distributed variable - how to analyze?

It's been years since I've taken my grad school stats courses, and it's a subject I struggle with, so bear with me. I am attempting to analyze a dataset containing two Poisson-distributed variables ...
0
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15 views

Comparing Two Count Variables Within-subjects

I have data where I asked participants to list 5 people that they thought fit a particular category. We then coded whether the people were men or women and counted the number of men and the number of ...
0
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2answers
41 views

Statistical test in R for count data

I am struggling with using the correct test for count data in r. The dataset I have is the number of nymphs produced by three aphid species on wheat. So this is count data with one response variable ...
0
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0answers
8 views

Probability of Pr(N=0) as function of Panjers (a,b) parameters

Is there a way to find the general formula for Pr(N=0) as the function of Panjers parameters a and b for Binomial, Negative Binomial and Poisson distributions? It is possible to show e.g. parameters ...
2
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1answer
45 views

Analysis of calls to a call center using Poisson distribution

I have a set of data from my workplace where we note how many support calls we receive. I have been playing around with it in my spare time just to see if I could predict anything interesting. I have ...
0
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1answer
19 views

Transformation of poisson distribution

Let's say you have a variable $X$ with a Poisson distribution ($Po( \lambda )$) and a variable $Y = 0.15 * X$. What is $EY$ and $Y$'s distribution? I'm almost certain that $EY = EX * 0.15$ but I'm ...
3
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19 views

Spatial Autoregressive Poisson model in R

I am estimating a gravity model of migration on cross-sectional data. The Moran I statistic indicates a positive and significant spatial autocorrelation in the residuals of the non-spatial model, and ...
0
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0answers
26 views

Forecast Daily Cash Flow

I am struggling with a forecast project. I have a time series of daily financial data for a personal account. The goal is to have a time series model for future daily cash flows. Right now,for better ...
0
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5 views

Compare related time-series count data before and after intervention

For a university library we did an intervention to create more free seating spots for students by introducing a way for students to temporarily give up their spot while away. They did this with an ...
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15 views

R hurdle and vuong tests giving strange results

So I'm trying to fit a hurdle model with the count distribution as negative binomial. I get the following outputs for assuming negative binomial and poisson: ...
3
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1answer
34 views

How to analyze this positively skewed data?

I am having trouble analyzing my dataset consisting of the sumscores of a questionnaire. For each item, subjects had to indicate whether they performed this behavior 'never', 'sometimes', or 'often', ...
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0answers
25 views

G test with small observed counts (~zero)

I have an experiments that counts how many events happened during a certain period of time. The experiments is repeated many times in different "runs" (I have 65 runs). Here for example the list of ...
1
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0answers
19 views

How to handle outliers in Poisson regression?

Consider the following count data: df <- data.frame( count=c(0,1,2,3,4,5,9,20), freq=c(1120,42,10,5,1,1,1,1) ) I want to use a quasi-poisson regression ...
0
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1answer
23 views

How does Anscombe transformation stabilize the variance of a Poisson R.V.?

I was taught that a transformation f(X) is said to be a variance-stabilizing transformation if $[f'(E(X))]^2*Var(X)$ is independent of E(X). For a Poisson-distributed random variable X, E(X) = Var(X) ...
0
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1answer
24 views

Panel count data, choosing between xtpoisson cluster-robust versus negative binomial

I have a panel count data and I would like to estimate it with fixed effects. My data shows a little bit of overdispersion (when fitted with quasi-poisson the overdispersion parameter is 5.01 and the ...
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0answers
33 views

Bernoulli trial on Poisson random variable

I am trying to assess the sensitivity of an electronic system under alpha radiation. In "dynamic" mode, the system performs different kinds of operations (without any pause) which might fail due to ...
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18 views

Obtaining distribution function for positive linear combination of independent random variables with Poisson distribution [duplicate]

Let $X_1,X_2,...,X_n,Z$ be i.i.d poisson random variables,respectively with mean $\lambda_i$ and $\lambda$ where $"n"$ is definite, $c_i\geq 0$. Assume all the parameters $\lambda_i$'s and $\lambda$ ...
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0answers
28 views

The distribution of the positive linear combination of Poisson random variables [duplicate]

Let $X_1,X_2,...,X_n,Z$ be iid poisson random variables,respectively with mean $\lambda_i$ and $\lambda$ where $"n"$ is definite, $c_i\geq 0$. Assume all the parameters $\lambda_i$'s and $\lambda$ are ...
0
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0answers
12 views

Help with Power analysis with PASS

I'm putting together a Power analysis, which is not my strong suit. I'm using the Poisson Regression tool in PASS. My outcome variable is falls over a five year follow-up period. My exposure is a ...
3
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1answer
34 views

From the bivariate poisson to the Skellam (or Poisson Difference) distribution

I am looking at how to calculate the Skellam distribution (https://en.wikipedia.org/wiki/Skellam_distribution) from the bivariate poisson distribution. I understand that the Skellam comes from ...
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1answer
30 views

Difference between $\mathrm{Poisson}(x_1)$, $\mathrm{Poisson}(x_2)$ and $\mathrm{BPoisson}(x_1, x_2)$

I am trying to find out the difference between treating two random variables as poisson distributions, $\mathrm{Poisson}(x_1)$, $\mathrm{Poisson}(x_2)$, and using a bivariate poisson, ...
1
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1answer
39 views

Why is the Poisson distribution only defined for a positive rate

From wikipedia, a random variable $X$ is said to have the Poisson distribution if for $\lambda > 0$, $ \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!}$ Why can't the value $\lambda = 0$ be ...
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22 views

'Z-standardizing' data based on Poisson process

Hello all this is my first post on Cross Validated, so please let me know if it is not in an acceptable form. I have been attempting to analyze a data set where I have a Bernoulli process that is ...
3
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1answer
193 views

What distributions are possible for an arrival rate?

I'm really struggling to find a good statistical distribution. I've tried Poisson and Gamma so far, but without success (best I've got was a p-value of 0,00005 with a Pearson Chi-Square test). So I ...
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0answers
49 views

Specifying the priors for multivariate MCMCglmm mixed model in R (Poisson distribution)

I am trying to build a model using MCMCglmm. Ideally, I would use a negative binomial distribution for my response; however, this is not an option in MCMCglmm. I don't know of any open-source ...
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48 views

Using poisson distribution to model proportions

I have recently came across a number of articles that have used Poisson GLMs when modelling proportion data. For instance, one study modelled the proportion of pig mortality for each sow using a ...
0
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1answer
21 views

Count Models for Continuous variables

I want to analyze the effect of taxes on the amount of fixed assets an affiliate of an multinational capitalizes. Fixed assets are of course not a count variable. Can I anyway use a count model such ...
0
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0answers
17 views

Asymptotically exact confidence interval

I am trying to answer the following question: I have modeled it using a Poisson distribution, and from this calculated the Fisher information as $I(\lambda)= \frac{n}{\lambda}$. Then, when I ...
3
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1answer
49 views

Relationship between λ (or μ) in Poisson and Exponential distribution?

Is there any relationship between λ (or μ) in Poisson and Exponential distribution? In other words, if I know λ (or μ) for one of the distributions, is it possible to calculate the corresponding value ...
0
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1answer
14 views

Frequency Data, Model Choice (Poisson with Offset, Fractional Regression)

I have text data and am interested in estimating the effect of some covariate on word frequency. All the frequencies are very small. The unit of observation is a single document. I'm trying to think ...
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43 views

How to adapt standard Poisson model in Excel to account for excess zeros (zero-inflated Poisson in Excel)

I am trying to adapt the standard Poisson model in Excel to adjust for potential excess zeros. How would I do it with the following dataset? ...
1
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1answer
30 views

poisson random variable

I want to show that $\lim_{n\to\infty}e^{-n}\displaystyle\sum_{k=0}^n\frac{n^k}{k!}=\frac12$ hint = Let $X_n$ be poisson with mean n. Use the central limit theorem to show that P{$X_n\leq ...
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13 views

Is it ok to use the Poisson regression in cross sectional data?

I have a cross-sectional database (n=500) and I am exploring the association between a number of factors (5) and one outcome, the number of accesses to a service (count of data). I was wondering if ...
3
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1answer
32 views

Poisson glm for rank or score data?

I have a question about analyzing a dataset that I'm currently working with. Each row of the dataset represents an individual songbird, and its reproductive success over the course of a breeding ...
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9 views

Counts vs. percentage of predictor variables in the presence of an offset

The case: I am using negative binomial models to predict the number of deaths per household for four African countries. I am using an offset (log number of household members) to obtain estimates of ...
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2answers
57 views

How can the Poisson GLM be used instead of logistic regression for the Titanic survival data?

I have a professor who made a very good point about the data titanic analysis during a lecture this week. I am still however trying to better understand. He argued that it is also possible to have a ...
3
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1answer
31 views

How to account for a lack of fit using a quasi-poisson on non-integer, overdispersed data

I am trying to run a mixed model on over-dispersed non-integer data. My data are not counts, but are zero-inflated and over dispersed. The variable is distance (how far a gps point is from a central ...
3
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1answer
41 views

Does this scaled version of a Poisson distribution have a name?

I have this probability distribution: $$P(\{X=x\})=\frac{\lambda^x\exp(-\lambda)}{x!(1-\exp(-\lambda))}$$ where $x\in \mathbb{N}$. If not for this factor $\frac{1}{1-\exp(-\lambda)}$, this would be ...
5
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3answers
200 views

What sort of GLM should I use if my response variable is colony size?

I want to model mean colony size as a function of predator density. Within each treatment level the smaller colonies (3-5 individuals) are a lot more common than the large ones (up to 600 ...
0
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2answers
43 views

Whats is the probability generating function of Poisson varied with parameter lambda

I have a question which says: "Show that the probability generating function of Poisson varied with parameter $\lambda$ is $e^{-\lambda(1-t)}$. I am not quite sure about the question because the ...
0
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0answers
15 views

How to set up data to run a model with poisson distribution and temporal autocorrelation

So I have GoPRO video data where we measured fish abundance and fish bites per minute. We had 4 videos total (2 for each treatment) and we took still frames every 5 minutes to capture the abundance ...
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45 views

Expected value of a censored poisson

I have the following density (it's a censored model): $$f(y) = \begin{cases} e^{-\lambda}(1+\lambda), & \text{if }y^*=0,1 \\ \frac{\lambda^{y^*}e^{-\lambda}}{y^*!}, & \text{if }y^*=2,3.... ...
3
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1answer
41 views

Confidence interval for population mean when sample is a series of counts?

I have count data for each of a sample of individuals (it's the number of times each independent individual performed a certain behaviour during a standardised observation of that individual). How can ...
2
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30 views

How can I deal with overdispersed count data if I have a nested design?

I am trying determine whether pollen tube counts differ between nectar-robbed and un-robbed flowers. Pollen tube counts are nested within plant (multiple flowers of each type sampled from each plant) ...
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1answer
44 views

Related to Poisson distribution

Suppose that internet users access a particular website according to a Poisson process with rate $\lambda$ per hour, but $\lambda$ is unknown. The website maintainer believes that $\lambda$ has a ...
3
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19 views

MGF of chi-squared distribution with n+2M freedom, where M is poisson distribution with parameter t [closed]

What is the Moment-generating function (MGF) of chi-squared distribution with n+2M freed, where M is poisson distribution with parameter t. Why?
2
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1answer
140 views

Convergence to normal distribution

Let $X_{1},X_{2},...$ be independent random variables such that $X_{k}$ is Po(k)-distributed for k=1,2... Show that: $$Z_{n}=\frac{1}{n}\sum_{k=1}^{n}\left(X_{k}-\frac{n^{2}}{2}\right)$$ ...