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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Count event using Poisson random variable

An event occurs with a mean of 15 times per hour and a standard deviation of 10 times/h. From the population a sample of 100 individuals is drawn. What is the probability that the sample mean will be ...
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1answer
52 views

Is it Poisson distributed, and if so, what's its meaning?

I've collected data from my website. The website is about cars. The data are about user reviews and the cars. what we see in the graphs is the probability of some car type (Ford Focus 2008) to have X ...
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8 views

Graphical comparison of count models [on hold]

I need help on R codes to graphically compare possion regression, negative binomial regression, zero-inflated poisson regression, zero-inflated negative binomial regression models fitted to a count ...
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148 views

Deriving the bivariate Poisson distribution

I've recently encountered the bivariate Poisson distribution, but I'm a little confused as to how it can be derived. The distribution is given by: $P(X = x, Y = y) = ...
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1answer
38 views

Poisson Regression Residuals

I'm modeling the number of doctor visits (a count variable) on factors such as income, chronic condition, insurance, etc. I use the canned Stata command ...
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25 views

Estimating a distribution from a dataset with multiple parameters

How would you go about solving the following problem? You're an insurance company who writes workers compensation policies. You want to build a probability distribution for the number of annual ...
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68 views

Confidence interval for poisson distributed data

I'd like to calculate the confidence interval for a variable with a lower bound and I can't seem to figure out how to do so. I've seen several similar posts, but none answered my question, at least ...
2
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23 views

power of poisson test with large sample size

I would like to compute the power of two distributions which are poisson with $n_1$ being large and $n_2$ being medium sized. I have used the formula given by Krishnamoorthy and Thomson for the C-test ...
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36 views

Estimation parameters for latent (unobserved) variable

Here is my problem: I have 3 variables $X,Y,Z$ : $X$ is the number of clicks we observed on an web advertisement; $Y$ is the number of time a customer do a sign-up on the website after clicking ...
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54 views

Test for aggregation of binary events/successes (binomial/glm??)

this has been vexing me for a while and I can't seem to solidify an answer beyond vague thoughts about Poisson distributions. I think this is a simple problem and I'm missing something obvious. Any ...
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52 views

Problems with Poisson Regression

I have been studying a linguistic construction (let’s call it C) in a language L1 trying to individuate several factors (...
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7 views

Vanishing coefficients with poisson model in glmnet

The other day I made a poisson model in glmnet using the averages of observations over a 1 year period to predict a count. The result was pretty good, but I figured it could be made better by binning ...
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1answer
38 views

correct statistical test to compare 2 poisson distributions

I know there are similar posts, and I've read a few of them already, but none of them give explanations that I actually understand. I'm completely new to statistics and am finding it more difficult ...
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13 views

What approach to use for attrition analysis?

I am trying to perform an attrition analysis on a company with an average size fo around 250 to 300. I have monthly attrition data for the last 30 months or so. Now if i want to go for a predictive ...
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1answer
19 views

Simple approximation of tail surprisal of poisson distribution

I want to determine (in an algorithm) the approximate surprisal of getting an outcome "as extreme as $k$" from the $Poisson(\lambda)$ distribution. My original plan was to use ...
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59 views

Skew normal approximation of Poisson distribution

What is the skew normal approximation to Poisson($\lambda$)? Am I doing this wrong?
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2answers
202 views

Poisson probability of observing at least one zero out of k independent cases

I have a set of observations from a biological experiment. I have counted the occurrences of a particular event on each of the chromosome for $n$ cells and finally I have the final mean value for ...
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19 views

How to predict given Poisson regression?

I run some Poisson regressions with the following results: (with number of associations an individual belongs to as the dependent variable) ...
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22 views

Poisson autocorrelation function

I want to draw an autocorrelation function, call it, AC(tau) where tau is the offset in the autocorrelatin. The vector I'm feeding into the AC is the spike train of a neuron whose action potential ...
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0answers
53 views

Estimating adjusted risk ratios in binary data using Poisson regression

I am interested in estimating an adjusted risk ratio, analogous to how one estimates an adjusted odds ratio using logistic regression. Some literature (e.g., this) indicates that using Poisson ...
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10 views

Module Updater Rejection

I was trying to build a Poisson model in OpenBUGS with the following codes: ...
3
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1answer
70 views

Maximum likelihood estimation for mixed Poisson and Gaussian data

Background I've been doing a little bit of work lately on maximum likelihood estimation (MLE), for cases where the data is normally-distributed and also for cases where the data is Poisson ...
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45 views

Poisson regression on the means of count data

I just finished a small research project about hummingbirds and the effect of hummingbird feeders. I am a bit unsure about how to proceed with the statistics. We placed 15 points in a distance ...
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1answer
50 views

“Better” goodness-of-fit tests than chi squared for histogram modeling?

I work on data from a mass spectrometer that produces billions upon billions of count histograms, and I need a good way to test whether these histograms are consistent with one or several model ...
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18 views

GLM poisson regression and some independent variables are itself poisson distributed

How can we deal with in GLM regression, when some variables of the independent variables (the x) are itself poisson distributed? Suppose we have two random poisson distributed variables X,Y with ...
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34 views

How to Test Independence of Poisson Variables?

I have a data set of length $10,000$. Each entry, $e_i$, of my data set is associated with two values, $x_i$ and $y_i$. Let $X$ and $Y$ represent the random variables for which my data set is a ...
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60 views

Interpretation of two residual QQ plots from poisson regression

I have what I believe are an interesting QQ plot of the residuals of some sports data fitted using Poisson regression. My model is actually a live model to predict the number of remaining events in ...
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1answer
19 views

Literature for Cross Validation on Sparse Data?

I've read a lot about Cross Validation to estimate prediction error, specifically for selecting the number of components in a PCA model (I'm not doing SVD/PCA, but it's very similar), but I can't find ...
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23 views

How to calculate the MGF for a poisson random variable

$\phi (t)=\sum_{n=0}^{\infty}e^{tn}\cdot \frac{\lambda^{n}}{n!}e^{-\lambda}$ $=e^{-\lambda}\sum_{n=0}^{\infty}\frac{(e^{t}\lambda)^{n}}{n!}$ $=e^{-\lambda+\lambda e^{t}}$ I'm confused here as how ...
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39 views

Is the information matrix equality valid for the Poisson distribution?

As far as I know it should, since the support of the Poisson is independent of its lambda parameter. The negative of the expected Hessian equals $\frac{n}{\hat{\lambda}}$, where $\hat{\lambda}$ is ...
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28 views

Stata's -margins- shows negative predicting value for count model

I am modeling "Innovation" counts over "HHI" and "squared HHI" with fixed effect poisson model. (My sample is unbalanced, small & wide one.) I am aware of that I can use Stata's -margins- command ...
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1answer
155 views

How does glmnet handle overdispersion?

I have a question about how to model text over count data, in particular how could I use the lasso technique to reduce features. Say I have N online articles and ...
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17 views

How to calculate the average selling period from inventory list (uneven intervals)?

Will I be able to calculate the average sales time (number of days) for an item, simply from the following 6 data points? Or will I need to repeatedly collect data, such that I for each day (say in ...
6
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1answer
77 views

In a Poisson process measured with some efficiency, is the measured count still Poisson?

Situation: Say I have a Poisson process, like radioactive decay, producing R particles per second. I measure with a detector. There is a probability P that a particle will be detected by the ...
2
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1answer
58 views

How to express a Poisson regression as an equation

I have a Poisson regression where I regress a counts variable (called $H(x)$) on one covariate (called $x$) and one factor (categorical) variable (called $s$), which can take one of three values ...
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54 views

Outlier detection with ROBPCA for multivariate poisson/non-normal data

It is stated here[1] that we can use ROBPCA to detect outliers for multivariate data. After reading the manual ([2] page 12 : "multivariate normal model etc."), I think the ROBPCA method is also ...
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1answer
111 views

How to find lambda in R, if other parameters are known

I am solving some problems on Poisson distribution and I have come across a problem where in I need to check the rate (lambda) of a particular thing with a probability of 0.001 (1 in 1000) of p(4). ...
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15 views

Confidence interval on Poisson distributed data

We have events which has different durations. I'm now computing confidence interval on defective events, meaning the ratio of events having encountered an issue. I consider this problem as counting ...
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18 views

How to choose response of Poisson GLM

I am trying to model a system using a Poisson regression for date time, I don't want to use Classical timeseries models like ARIMA, because we have a discrete time series. I want to do a 3-years case ...
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10 views

Distribution for time between arrivals at the same location by the same entity

Given a sample of inter arrival times for an entity at the same location, is there a distribution that can fit such a sample?. I was thinking about poisson, but was concerned about the independence, ...
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21 views

P(no collision) with Poisson arrivals and exponential packet length

The Aloha scheme is a time-division multiple random access scheme used in networking, developed at the University of Hawaii by Norm Abrahamson for their network, ALOHAnet to deal with the fact that it ...
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28 views

Probability of Confidence Interval Missing: Why Non-smooth w.r.t. Theta?

See this: http://ms.mcmaster.ca/peter/s743/poissonalpha.html The probability that a Confidence Interval will "miss the mark", or fail to contain its target parameter's true value $\theta$, is often a ...
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2answers
63 views

Why does Poisson GLM fit better to non-integer data?

Let's assume that I have a set of predictors and a non-negative integer resulting variable (number of events). All observations are repeated few times (it means that all predictors have the same ...
3
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1answer
42 views

Can Poisson regression be run with a small sample?

I am just a beginner. I have a sample of 71. I wish to do a Poisson regression. Is this sufficient for estimating a Poisson model? Should I use only counts as $Y$ variable or should I use percentages ...
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38 views

Is there a better test than chi-2 to determine plausibility of a distribution?

So, I'm trying to determine what's the best distribution to use to analyze my data. Previous authors suggest using a chi-2 test to determine whether the data is Poisson or Gaussian distributed. All ...
2
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2answers
85 views

Poisson arrival

Users arrive according to Poisson process with rate $\lambda$. If every third user is removed, then do the remaining users form a Poisson process with rate $2\lambda/3$? If every other user is ...
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25 views

Trying to find chi2 values to see if a dataset is Poisson or Gaussian distributed using matlab

I'm trying to check whether my data is poisson or normally distributed. The normal distribution works okay, but the poisson I'm having trouble with. My problem is when I try the template matlab gives ...
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28 views

Normal distribution is better than Poisson for large sample set?

I'm at a beginner level, so please bear with me. This is a call center use case. For every week, certain number of calls are received. The average is about 20. This seemed like a Poisson distribution ...
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1answer
21 views

Difference between hazard function and intensity function?

I'm reviewing a paper whereby the nonhomogeneous poisson process is explored. I'm familiar with the intensity function, but the idea of the hazard function is throwing me off. Especially, I cannot ...
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1answer
136 views

Zero-inflation on steroids: choose among Poisson, negative binomial and zero-inflated regressions

I am struggling to fit alternative count models into my data. I guess my problem is just too many zeros. This is my data ...