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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Predict number of users

I have a pretty basic question, but am pretty far removed from stats and modeling. I have historical data (daily, weekly, monthly, however I want to slice) for a few years and I want to predict the ...
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6 views

How can compare a Poisson model against a Quasipoisson model in GAM?

I have count data of species and I would like to fit a GAM model in mgcv with poisson distribution. The poisson model has overdispersion so I have read that is better to fit a quasipoisson ...
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11 views

What distribution is appropriate for length of a signal (in days)?

I have a vector of "signal lengths", which is the amount of days a signal lasts once initially activated. For the purpose of confidence intervals and hypothesis testing, do I want to use a Poisson ...
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1answer
55 views

Name of rv that results from integrating over gamma in gamma product prior on poisson

If $d$ is an arbitrary random variable with parameter(s) $\Psi$ and positive support, $g \sim \mathrm{Gamma}(\alpha, \beta)$, $x \sim \mathrm{Poisson}(gd)$, and $g$ and $d$ are independent, then ...
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25 views

Estimate lambda for panel count data

I have panel count data for $F$ firms across $I$ years, so observe counts $C_{f,i}$ for $f \in \{1,...,F\}$, $i \in \{1,...,I\}$. I want to model the data as a poisson process. With increasing ...
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2answers
49 views

How to sample a conditional PDF

Assuming I have two kind of balls, red and blue ones, and I pick randomly (with replacement) always a bunch of balls where the number of balls I pick is distributed according to the Poisson ...
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1answer
14 views

Poisson distribution exercises. Are my answers correct?

Suppose that a book contains an average of $\lambda$ misprints per page. (a) What is the probability that 10 pages will contain at most 1 misprint? (b) What is the probability that ...
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1answer
38 views

Simulation of Poisson data with a endogenous regressor

My simulation setup goes like this: I draw my dependend variable as $Y\sim \text{Poi}\left(\lambda\right)$ where $\lambda = \exp\left(\beta_0 + \beta_1x_1 + \beta_2z + u\right)$ and $z = \gamma_0 ...
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1answer
156 views

Sum of squared Poisson probability masses

Let $(p_k)_{k=0, \dots, \infty}$ denote the probability masses of a Poisson distribution with parameter $\lambda$. I'm looking for the sum of their squares, $$\sum_{k=0}^\infty p_k^2,$$ as a function ...
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2answers
70 views

How to fit a glm with sum to zero constraints in R (no reference level)

Question has been rewritten I am trying to fit a glm to find out how the rate of events happens (counts/exposure) related to some covariates, with Poisson error. Counts is the number of events ...
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1answer
32 views

Dealing with zero-inflation if the data are not count data type

In the literature I found that for the count data with a lot of zeros so-called zero-inflated distributions (models) and so-called hurdle-at-zero distributions (models) could be used. The differences ...
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19 views

Software or workarounds for vector autoregression on count data?

I have a research question that fits nicely in a VAR framework but my data are count data. They are much closer to a Poisson or negative binomial distribution than they are to a normal. This will ...
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13 views

Variable contribution in Poisson regression

I am trying to quantify a contribution of X on Y. Imagine I have a time series (per day) of the next variables: Y, X1, X2 Using a scatter plot on visits vs. each variable I have tested that the ...
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16 views

Best method to analyse longitudinal recurrent count data

I want to analyze count data, more specifically number of prescriptions over 10 years. My first idea was to use the GEE Poisson. However, after reading some papers about recurrent history analysis I ...
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19 views

Is data poisson distributed when comparing mean sample occurrences per area?

A question similar to this came up in a colleague's analysis and I cannot seem to decide the right way to think about this. The question is a moot point for her work, but I'm interested in the ...
2
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1answer
45 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
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25 views

Interpretation of coefficients from GLM (family Poisson) regression

I am running a GLM regression from the Poisson family. My dependent variable is the number of train accidents per month, and I define as offset variable the total number of train routes for that ...
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3answers
115 views

How large does a Poisson distribution's mean need to be to use normal distribution statistics?

As the mean of a Poisson distribution increases, the Poisson distribution approximates a normal distribution. I assume that once the Poisson mean becomes large enough, we can use normal distribution ...
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1answer
62 views

Use of Poisson distribution to analyse distribution of individuals in space

Dytham 2010 suggests using the Poisson distribution to establish whether individuals are evenly distributed in space. Say we end up with a map of individuals in a study site that looks like the ...
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2answers
114 views

Am I breaking the assumptions of the Poisson distribution?

The Poisson distribution arises when events are counted within a specified interval. I've recorded the number of events each month (I'll not discuss what these events represent). This appears to meet ...
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46 views

Do I have enough information to answer this question?

On average, five calls per hour made to a call center will not be answered within the target time set. What is the probability of: Six calls not being answered within the target time during one hour? ...
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1answer
38 views

Poisson goodness-of-fit of small sample

Please note that I have no background in statistics - this is for personal interest. The post is inspired by a question at work. We were given data by another department asserting that for a ...
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1answer
32 views

Inference of user activity on binary condition variable

I recently ran a test on our application that models a fairly contrived example: Users are expected to add things to a bucket. We count the things in this bucket. A binary condition variable exists ...
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24 views

Cell count distribution assumption in loglinear modelling

In relation to loglinear analysis, SPSS gives two options for "Distribution of Cell Counts". The SPSS User Manual states: Assumptions. Two distributions are available in General Loglinear ...
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14 views

Difference between queuing delay and service time in queuing theory

I am reading a paper that uses queuing theory to model a network. The paper defines two metrics : queuing delay and mean service time for a packet . My question is : What is the difference between ...
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1answer
85 views

Using Poisson distribution to evaluate summations

I'm interested in how to use a Poisson distribution to evaluate $\sum\limits_{x=0}^\infty \frac{(x^2-x+1)(2^x)}{x!}$ I see that this is similar to the general pmf form of $\frac{2^{x}}{x!}$. My ...
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45 views

Estimating probability of observing greater than X events based on a current population and historical rates

Let's say I have a population that varies from month to month, and per month, there are X number of failures. Based on historical rates, I am trying to find the probability of observing Y or greater ...
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15 views

using mgfs to find limiting distribution

Can someone help me out with proving that the limiting distribution of a negative binomial (k,p) distributed variable is poisson if we let k -> infinity and p->1. I am just learning about limiting ...
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1answer
36 views

Likelihood ratio test in Poisson distribution

I have a dataset that describe the number of passengers that fly with an airline per day. The airline guesses that on average 1300 passengers fly per day and I want to test this hypothesis using a ...
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1answer
73 views

Dealing with outliers in simple linear regression

I want to perform a simple linear regression in R. However, the plot of fitted and residual values has outliers. Transformations (ie log, square root) did not solve this problem. Removing these ...
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15 views

3 groups, 3 measurement points, poisson distribution, baseline difference: GLMM or RM ANCOVA?

I have a small experimental data set. 3 group (n's = 12, 12, 16). T1 is baseline before intervention. T2 post-intervention, T3 follow-up (times between testing vary). The DV is count data that fits a ...
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22 views

What is the difference between residual and null deviance?

I applied poisson regresson on count data. In the model summary I got NULL deviance and residual deviance. I understood that residual deviance is the part which accounts for what is not explained by ...
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22 views

Combined likelihood of multiple counting experiments

I have two counting experiments, each experiment is an independent detector (A and B) which detects some events (photons). Detector A has frequency resolution - it measures that a count occurred at a ...
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1answer
81 views

Poisson Distribution Problem

I need to derive an approximate $100(1 − α)$ percent confidence interval for $\lambda$ given data $X_1, X_2, \ldots, X_n$ from a Poisson distribution with parameter $\lambda$, I should use the ...
4
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1answer
79 views

Poisson regression for count data - predictions

This is probably an elementary error in either my understanding or my R implementation: I am trying use a Poisson model to make some predictions. The original data is discrete count data. I would ...
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2answers
59 views

How do you calculate a Poisson distribution for matched data?

I am trying to find the rate of infections with 2 different treatments and to see if there is any difference between them. I want to work out whether the rate of 'no infections' is different between ...
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0answers
16 views

Implementing ANOVA for a poisson distributed variable (count data)

I am currently working on a dataset that contains details on over 100k terrorist attacks. The variables of interest for each attack are attack type e.g. bombing (3 levels), country e.g. Iraq (5 ...
2
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1answer
54 views

Poisson and NB results

i did a regression with poisson model, and since the dependant variable is overdispersed (0.13) , i have also tried negative binomial. The problem is that my explanatory variable "repeated partner" is ...
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85 views

Inferring the lambda of a Poisson distribution

Lets consider the following scenario: We have 4 roads each with equal distance of 800 m. In traffic engineering, the ...
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1answer
42 views

Solving: Poisson Distribution query [closed]

The distribution of a number of printing mistakes per page per book is Poisson with mean 3. Given that $e^{-3} = 0.047987$, the probability that there is some mistake is a) 0.049787 b) 0.950212 c) ...
2
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1answer
48 views

How to categorize count data

I have count data (basically histone modification data). The counts represents number of reads falling into each genomic region. I need to divide my data into $\text{low|medium|high}$ based on the ...
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23 views

scatter plot for underdispersion in Poisson

I did an equidispersion test and got a vary small negative value (Cameron and Trivedi), my Prof. said the this test is not very powerfull and that maybe i should try other tests and also use residual ...
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41 views

Superposition of two renewal processes

Usually, superposition of two independent renewal processes may not lead to a renewal process. However, in my problem, the interval time between two events of the renewal process is more specific ...
2
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0answers
39 views

Poisson regression: loglinear vs linear

In Poisson regression, there are two possible ways we can relate the dependent variable $y$ with the independent variables $x$: $E[y|x] = w^Tx$ $E[y|x] = e^{w^Tx}$ The likelihood functions are: ...
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19 views

Interpreting Poisson regression: Deriving results from the CDF

I am trying to interpret a Poisson regression without being very interested in the mean. As a complication, I also have an exposure variable. Let $y_i$ be a count variable, and $p$ the offset, for ...
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26 views

bayes estimate possion distribution function

Let {X\, ...,Xn) be random sample from random variable which has Poisson distribution with parameter A. Assume that the prior distribution A for is Gamma(1, 1) and that you have observed sample of ...
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1answer
44 views

GLM Model checking Plots - Quasi Poisson - Poisson

I wonder whether accounting for overdispersion in a GLM (Quasi - Poisson instead of Poisson family) has an effect on the model checking plots (plot of residuals against fitted values, a scale–location ...
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1answer
70 views

What methods exist to compare data sets from two different types of distributions

I want to compare two different types of data sets how well they correlate with each other. Lets say I have two datasets one follows a continuous distribution and another follows a poisson ...
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1answer
48 views

Poisson distribution with glmer - pairwise comparisons

I am analyzing counting data from a field experiment using the glmer procedure according to a Poisson distribution. The model works and I can visualize the results ...
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42 views

Panel poisson regressions on rates and values far from 0

I am estimating the effect of some treatment on yearly district-level stillbirths and stillbirth rates and births and birthrates in a panel with district and year fixed effects. Stillbirths are ...