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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Relationship between Poisson arrival rate and Exponential inter-arrival rate

A poisson distribution has a lambda 1.5 per minute. I would like to know as to how would i use this for the lambda in exponential distribution? Would both the lambda values be the same?
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26 views

Comparing two Poisson counts

I am running some simulations and need a hand with the stats. Suppose I have $N$ systems. I simulate all of these systems and an event occurs in $x$ of the $N$ systems. I then make a small change to ...
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88 views

Log vs square root link for Poisson data in R

I am currently working to model deaths from AIDS over time using a GLM in R. I know that there are two possible options for the link function for Poisson data, log and square root. I know that square ...
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16 views

Estimating Poisson-distributed rate using sampling

You have been hired by the border patrol agency of a nation to estimate the number of people who enter into the country by circumventing the fence during their busiest season. You have reason to ...
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25 views

Fit truncated Poisson distribution in R

I am trying to fit a Poisson distribution with zero-truncated, imperfectly observed data. I have a set of samples for which I can observe 1 counts and >1 counts, although I don't know what the >1 ...
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117 views

OLS vs. Poisson GLM with identity link

My question reveals my poor understanding of Poisson regression and GLMs in general. Here's some fake data to illustrate my question: ...
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42 views

Convergence of moments of binomial to Poisson

As is well known, the $\mathsf{Binomial}(n,p)$ distribution converges to the $\mathsf{Poisson}(a)$ distribution as $n\rightarrow \infty$, $p\rightarrow 0$ with $np=a$. I'm pretty sure that the ...
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49 views

Model approach for count data with a large range of y values

I am modeling ridership data for specific routes by month over a number of years. Some routes have as little as about 1000 riders per month while other routs may have over 20,000 riders per month. I ...
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18 views

How do I use the poisson binomial distribution mass function?

Here is the wikipedia page describing the function. I'm trying to use this to calculate the probability of a sports team's record on the season. So, say the team is 8-2 in 10 games, I want to find ...
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23 views

Prediction Error for a Poisson Process

So I have a fleet of cars. I've sampled their breakdown rates (per hour driven) for the last 10 years. Their breakdown rate follows the gamma distribution. I am trying to do two things. Predict ...
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21 views

Poisson process to determine request arrival times in LTE network

I need some help with this problem. A Poisson process is generally used to describe the arrival of calls in a mobile network. Since I am developing a simulator for LTE, i need to implement such a ...
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14 views

Multiple poisson statistics and, “and”

I have a data set $X$ which can be broken up into, say, $n$ bins and an expected value for each bin, $a_i$. I am modeling the probability within each bin with a Poisson distribution. I would like to ...
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9 views

Two-way ANCOVA with count data— Poisson model in SPSS

I am attempting to compare the number of eating episodes by gender and diagnosis (4 levels), adjusting for BMI and age. I am assuming that a Poisson model would be preferred over a factorial ANCOVA ...
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22 views

Optimization of a non homogenous Poisson process with unknown intensity distribution

Customers arrive at a bank counter according to a non-homogenous Poisson process with rate parameter $\lambda_k$. The service time at the counter is exponentially distributed where $\lambda_k$ and ...
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54 views

Conditions to be in a class of Poisson distribution

Ambulance cars are arriving at a traffic signal in accordance to a Poisson process. The arrival rate of ambulance cars is measured at every 1 hour. $\lambda_k$ is defined as $k_{th}$ hour arrival ...
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44 views

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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9 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
56 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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36 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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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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15 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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41 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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161 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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81 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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48 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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21 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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21 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 ...
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48 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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26 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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127 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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68 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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118 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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48 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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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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37 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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25 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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22 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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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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48 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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16 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
45 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
83 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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19 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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30 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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24 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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82 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 ...
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106 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 ...