Questions tagged [poisson]

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Poisson Process Conditional Probability computation

Given $N(t)$ a Poisson Process with generation rate $\lambda$ with $t_1<t_2$ and $N_2>N_1$ I'm looking for a way to express the following probability: $$ P[N(t_2)>N_2|N(t_1)<N_1]$$ In ...
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71 views

How to estimate the intensity rate $\lambda$ of a Cox Process

In a Cox Process, or doubly stochastic Poisson process, the intensity rate itself is a stochastic process that varies across space or time. Let us assume that the intensity rate has the following form ...
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2answers
38 views

Why would you want to fit/use a Poisson regression instead of Negative Binomial?

Given that Poisson is a special case of Negative Binomial which seems to just make error more likely in the case of overdispersion, without offering any real benefits, why would you fit a Poisson ...
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1answer
100 views

leverage() diagnostic test not supported for glmmTMB models in r

I am using a glmmTMB to look at the effect of numerous variables on how far individuals travel (distance). The example below is ...
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45 views

Poisson Counting Process over Variable Threshold

Let's consider a Poisson Counting Process $N(t)$ with generation rate $\lambda$ and a piece-wise constant threshold $M(t)$ that changes with time. $$ M(t)=m_i \ \ for \ \ t\in(t_{i-1},t_{i}],\ i\in \...
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1answer
40 views

Controlling for a variable with unequal sample size

I'm dealing with a Poisson regression model for count data. My DV is the number of Covid infections in a particular city. My explanatory variables are both categorical and continuous. One of them is ...
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22 views

How to include offsets of 2 variable in one linear model

I've been conducting some research on recruitment of fish and fish survival in estuaries. I'm analysing recruitment and mortality against environmental variables such as temperature and river flow. ...
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1answer
35 views

Interpret Negative-Binomial mixed-model output in R

I am modelling the number of jobs in a year, with a random intercept to account for regional variation. How do I interpret the model output when using the model to predict/ for inference? For example, ...
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2answers
33 views

How to know whether a zero-inflated model is the way to go? Both poisson and negative binomial do not fit my count data

I have a dataset with count data as response variable ranging from 0-5 (number of chicks fledged). I intend to carry out a GLMM and need to know which distribution my data follows. I used the descdist(...
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6 views

Interpret Poisson GLMM output plot

How do I interpret the predictor effects plots for month and year below using the predictorEffects function in the effects ...
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1answer
33 views

Including time data into a Poisson regression model

I'm working on a project based on Covid-19 infections, I want to regress the total number of infections for each geographical partition onto some predictors. My DV is the total amount of infections in ...
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3 views

How can I estimate a percentage in a two-stage sample design?

I'm trying to solve a exercise that I have to do. In this, there is a two-stage sampling design. The first stage is a Poisson design and in the second stage is an IS. The problem that proposes the ...
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12 views

Help with multivariate analysis

I'm looking for some guidance on a multivariate analysis that I am trying to run on my data. For context, my response variable is counts of abnormal behaviours displayed during [~60] observation ...
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1answer
13 views

Poisson regression model in R

I am working on a uni assessment with COVID-19 topic and trying to work out a poisson regression for COVID 19 pandemic. My predictor is the number of confimred cases as count, my predictors in the ...
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1answer
31 views

Multicollinearity for Offset Variable?

In a Poisson model, do we need to check for multicollinearity between the offset variable and other covariates? For example, if I offset by population size, would it be problematic to include ...
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35 views

Conditional expectation and variance of a poisson distribution, where $𝑋_𝑛$ is conditioned on $𝑋_{𝑛βˆ’1}$ [closed]

Suppose that $𝑋_0 \sim \text{Poi}(πœ‡)$ (where $πœ‡ > 0$ is fixed) and that for $𝑛 = 1, 2,…$ the distribution of $𝑋_𝑛$ conditional on $𝑋_{π‘›βˆ’1} = π‘₯$ is Poisson with parameter $π‘₯$. Determine ...
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Modelling count data with extreme underdispersion - what distribution?

Suppose we have some count data, and we want to use a model that allows for "overdispersion" or "underdispersion" in the data (i.e., higher or lower variance than the Poisson distribution). Let $X$ ...
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20 views

Interpreting GLM with poisson distribution outputs for assessing affect of two categorical variables on frequency

I'm currently trying to see if the frequency of a behaviour measured in a binary format (yes/no (where yes means the behaviour is present) is related to 1. the month in which behaviour took place and ...
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29 views

Types of Covariates Permitted in Negative Binomial Regression

To the best of my knowledge, the dependent variable (outcome) in a negative binomial regression should ideally represent count data. In R, if the interest is to model rates, I understand the use of <...
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14 views

the difference between poisson distribution and poisson process in terms of application

What is the difference between poisson distribution and poisson process? I don't know technically in terms of application. I know the value of lambda = 8 and k = 3, for 100 variates, how can I ...
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1answer
44 views

Poisson regression for modeling standardized mortality ratio (SMR)

I have a data set with individuals with a certain diagnosis who are observed from the time of their diagnosis until death or the end date of the study. I want to calculate SMR for the whole group, and ...
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32 views

Priors and nested random effects in MCMCglmm

I am trying to construct a zero inflation poisson GLMM using MCMCglmm(). I am new to Bayesian Statistics and this function and I am struggling to understand a couple of things. For my data I am ...
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1answer
362 views

Poisson regression appropriate?

I have decided to use Poisson regression for my analysis of weight gain and would like to get a second opinion about whether it's appropriate. Weight is measured at baseline and and a second value ...
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1answer
34 views

Variances of photon numbers and electrons

In optical sensors (e.g., photodiodes), the number of electrons $N$ generated by photons follows Poisson distribution. e.g., $Var[N] = N$.The number of photons $P$ also follows Poisson distribution. e....
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28 views

Poisson and Binomial distribution: coinciding on parameter transformation

I'm working on this exercise: A student sits on a street corner for an hour and records the number of bicycles $b$ and the number of other vehicles $v$ that go by. Two models are considered: The ...
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2answers
126 views

Posterior entropy behaviour for Poisson model

Suppose $Y \sim Poisson(k \theta)$ is observed (number of events), where $k>0$ is a constant (length of observation time) and $\theta$ is an unknown parameter (event rate) with some prior ...
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1answer
49 views

log-offset in rpart regression tree

I have understood that one commonly adds log(exposure) as an offset in the formula for GLMs, when dealing with poisson distributed rate data. I am dealing with insurance claim data where I want to ...
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20 views

Poisson process, combined waiting time

Passengers arrive at a railway station according to a homogeneous Poisson process with rate Ξ». At the beginning (time 0), there are no passengers at the station. The train departs at time T. Denote by ...
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1answer
25 views

Large Set of Random Variables with Exponential Distribution

I'm struggling to understand how to solve the following problem. I have a random variable $X$ that represents the life time of a cellphone (in years) and I know that such variable follows an ...
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18 views

How to interpret coefficients off a quasi-poisson regression with weights and a fixed effect?

My Quartile variable is a binary variable, 0 = lowest quartile, 1 = highest quartile. My variable being explained cases_100k is ...
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0answers
30 views

Is there a way to check the independence of observations within a Poisson distribution?

I have the understanding that one of the key assumptions of a Poisson distribution is that the observations are independent. Is there a way of testing the independence of the observations within a ...
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23 views

Why does using the pnorm function on the intercept estimate of a binomial regression recover the mean of the dependent variable?

I've fit a series of mixed effect models with the lme4 package in r on a set of binomial outcome variables (1: the event happened, 2: it did not). The fixed effect specification is intercept only, and ...
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3answers
597 views

Count Poisson Regression dataset [closed]

I'm looking for a dataset which I can use in R modelled by the glm function with family=poisson. I need there to be at least four predictor variables and the count has to be the explanatory variable.
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1answer
22 views

Mean of Nth Poisson Arrival Time Given T<X

I have a poisson process with 0.1 observations per minute. What is the expected time of the 2nd arrival, given that the 2nd arrival occurs in the first 2.5 minutes?
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31 views

Offsets variable subjects and behaviors

I have a set of behavioural data. It consists of about 600+ 50 mins long observations within 35 different bee nests, with many different numbers of observations per nest, and variable numbers of bees ...
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1answer
329 views

Convergence of Poisson Random Variable

For $n \in N $, if $X_n \sim Poisson(\frac{1}{n})$ then PT: 1. $X_n \xrightarrow[n\rightarrow \infty]{P} 0 $ $nX_n \xrightarrow[n\rightarrow \infty]{P} 0 $ It says $X_n$ converges to 0 in ...
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1answer
86 views

Zero-inflated Poisson Regression for Continuous data

I have a continuous variable that I'm trying to model but have a number of issues. The variable is continuous, positive, right skewed and has a large zero-inflation. Whilst the formulation of the ...
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1answer
25 views

Big outlier in dependent variable

I have my data from the official statistics office of my country and I rechecked multiple times already. I have a big outlier skewing all my glm (poisson) modells to the extreme (like 5 times the ...
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16 views

How do you estimate the age at which a maximum rate occurs in a population?

Can you directly estimate the age at which a maximum rate occurs in a population? I have a dataset including counts of events and person-years, stratified by year and age. There is a strong cohort ...
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2answers
42 views

Negative Count Variables in Data — modeling migration

I'm trying to explain migration rates in Europe with my regression using pca/pcr in glm. Of course some of the count data has to be negative in regions people move out of. This presents a problem for ...
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6 views

How do I get RMARK to identify the correct number of occurrences in a PoissonMR model?

I have the latest version of RMARK and MARK installed on my computer and the example code from https://rdrr.io/cran/RMark/man/PoissonMR.html runs perfectly. However, when I try to run the code using ...
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39 views

negative binomial inter-arrival

I am trying to find out what is the distribution governing the inter-arrival of events for a counting process that follows a negative binomial? I know for a Poisson counting process the inter-arrival ...
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40 views

Is it possible to show that this estimator has minimum variance?

Doing some exercises I stumbled upon this tricky one: Suppose we have an independent random sample $(X_1, ... , X_n)$ with $X_i \sim Poisson(\lambda)$. Define $\theta = e^{-\lambda}$. Let $$ \...
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43 views

The difference of Standard Error from vcov() and sigma() of poisson regression by glm in R

I got the SE of glm(y=x) by the following program. But I couldn't get the same SE as vcov() and sigma() by the following program glm(y ~ x, family=poisson(log)). I can't understand the difference of ...
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1answer
61 views

Poisson confidence interval in poisson.test similar

Here is my data. I observed 3 intervals (for example each 1 month long). In each interval my random variable assumed the following values 10, 15, 12. I would like to estimate confidence interval for ...
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38 views

Expected value and Maximum Likelihood Estimation

I'm doing this exercise about Poisson distribution and maximum likelihood estimation: I have had no problem with points a and b, but I'm struggling with the correct answers of the C part. From my ...
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6 views

How to estimate number of views when supplied with lower and upper limit only, for Poisson-like data?

I'm looking at some Facebook advertising data. It has a row for each ad and the upper and lower bounds of the impressions for that ad (i.e. number of times it was displayed). For example: ...