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 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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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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39 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 ...
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1answer
25 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
36 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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29 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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32 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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18 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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44 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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33 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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42 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 ...
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58 views

Choosing cutoffs in examining the Poisson distribution (an application to prime numbers)

I have observed a number ($n=6$) of events and want to test the null hypothesis that they are Poisson distributed with a known parameter $\lambda\approx1$. But I don't know exactly when I started and ...
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1answer
45 views

C-Test for comparing poisson means in Scipy

I'm relatively new to stats, and I have a large dataset of strings (n=114541) for which I'm interested in a binary event: whether X occurs or not (specifically, whether a specific language construct ...
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559 views

How odd is a cluster of plane accidents?

Original question (7/25/14): Does this quotation from the news media make sense, or is there a better statistical way of viewing the spate of recent plane accidents? However, Barnett also draws ...
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1answer
100 views

Particle filter (sequential Monte Carlo) for a non-Gaussian hierarchical model

I have the following, which I am attempting to model with a particle filter. \begin{align*} y_{i,t}&\sim\mathrm{Poisson}\left(\lambda_{i,j,t}\right)\\ ...
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3answers
396 views

How is the poisson distribution a distribution? It seems more like a formula

I just watched this video: https://www.youtube.com/watch?v=Fk02TW6reiA It shows a formula to calculate an answer for the following problem: There are 2 customers expected every 3 minutes in a store ...
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2answers
31 views

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
75 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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166 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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53 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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28 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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78 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 ...
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24 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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47 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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59 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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1answer
60 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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11 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
49 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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14 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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65 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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211 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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1answer
70 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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15 views

Module Updater Rejection

I was trying to build a Poisson model in OpenBUGS with the following codes: ...
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1answer
81 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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47 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
70 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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21 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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37 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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63 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
21 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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1answer
24 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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1answer
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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36 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
178 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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21 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 ...
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1answer
86 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 ...
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60 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 ...