# Questions tagged [poisson-distribution]

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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### Identify the distribution of data [closed]

I did one experiment two times with the same subject. I want to find the repeatability of my result. repeatability in a sense is the fraction of behavioural variation that is due to differences ...
1 vote
28 views

### Expected number of elements in random bucket, where the probability of a bucket is proportional to its size

I distribute n balls into m buckets randomly and uniformly. Let's assume that n/m is greater than 1, and m is a large number. Next, I choose a bucket at random, but the probability of selecting a ...
1 vote
56 views

### Observation Method for Poisson Process

I have about a year's worth of timestamps at which boxes exit a manufacturing production line. ti are the timestamps, where the first timestamp is t1, second timestamp is t2, etc. These can be ...
28 views

### How do you sample from a Poisson distribution when the observed count is zero?

I have some data showing the count of deaths in a population. The data are stratified by age. For example, the data might show that at age 40 there were 30,000 years of observation and 300 deaths. In ...
1 vote
100 views

### Poisson Regression and Linear Regression give the same error

I'll use the data azdrg112 from COUNT package. The los will be the response variable while ...
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### How can you model the arrival times of 2 different events?

I was looking at a poisson process and using an exponential distribution to model arrival times of the event. For example the chances that a person is arriving at a bus stop. Then in the simple case I'...
28 views

### Distribution model for Multiple-choice Data?

I am running an experiment where I am testing the effects of three interventions (A,B,C) and measuring participants' performance via a multiple choice test with 5 questions. To perform hypothesis ...
1 vote
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### Can I fit a Poisson distribution to a continuous variable to apply event detection algorithm?

Preprocessing: I have a time series of number of tweets per 10 minutes time interval that are all taken from a given discussion on a specific topic in a specific region. I preprocessed the data by ...
125 views

### Probability approximation and computation given Compound Poisson random variable

Consider a compound Poisson random variable $S = \Sigma_{i=1}^N X_i$ where N is Poisson with mean 2 and $X_i$ is equally likely to be any of 1,2,3,4 . Find P{S = 6}. Solution: Let me solve this ...
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### Estimating the mean of a Poisson process from data

My data shows the daily number of logins per person over the last three months. I am modelling the number of events per person per day as a Poisson process. I am interested in estimating the ...
44 views

### KS test for Poisson distribution data

I have a dataset comprising 1000 integers. It represented as follows: ...
27 views

### How to calculate lambdas from Bivariate Poisson distribution?

I have three random variables X1, X2, X3 which follow independent Poisson distributions with parameters λ1, λ2, λ3 >0 and then the random variables X = X1 + X3 and Y = X2 + X3 jointly follow a ...
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### Testing the effect of a customer loyalty initiative

I work for a company with a chain of auto workshops. We are interested in testing the effect of a data gathering initiative on customer loyalty (visits per year) and spend per visit, hoping that the ...
1 vote
51 views

### Why do Poisson regression and Linear regression give the same error? [closed]

I use the badhealth data as an example, I'm modelling the number of visit (doctor) based on the health condition and the age as two features. Mean absolute error is ...
50 views

### Count distribution in which the mean is equal to the standard deviation?

I have a data set with counts that exhibit the sample property that $$\hat \sigma_x \approx \bar x$$ which is to say that the sample standard deviation (with Bessel's correction) appears to ...
1 vote
33 views

### If I have a Bernoulli(x) random variable that counts poisson(y) if it returns successful and counts poisson(z) if it fails, what is the variance?

I'm attempting to calculate the variance of this problem in a way that I can apply to future, similar problems.
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### Estimating survival curve with changepoint from Poisson regression

Suppose I fit data according to the following piecewise exponential model. So that the intensity is 1/50 for event times in the first 50 days and then 1/200 subsequently. ...
34 views

### Tweedie distribution with zeros being the second most common value

I want to perform a multilevel glm model. I have a continuous non-negative outcome variable (not count data), with many 1 values, second most common value at zero, and then a right tail of positive ...
1 vote
35 views

### Poisson process for small sample size

Suppose I have a data set that contains insurance claims $X$. Each claim also is assigned the calendar year during which the insured event happened. Now, I want to build a frequency/severity model but ...
113 views

### $N \sim$ Poisson iff number of heads & tails independent?

Consider $N$ to be the total number of fair coin tosses such that $N \sim \mathrm{Pois}(\lambda)$. Then for the events (sorry) random variables defined as, $A:$ No. of heads observed and $B:$ No. of ...
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### Distribution of time intervals in Poisson process

I am studying computational neuroscience, particularly the modeling of neuronal spikes. Abstractly, we may think of a spike plainly as some event that either occurs or fails to occur in time. It has ...
74 views

### Understanding emmeans outputs for poisson and negative binomial GLM fitted on count data with or without offset

I fitted a poisson and negative binomial GLM on count data (=larva) and try to explain it as a function of a factor (=modality). However, as the traps used to trap larvae from inflorescences were ...
1 vote
67 views

### Likelihood Ratio Test for Comparing Two Poisson Distributions

I am currently studying statistical hypothesis testing, specifically the Likelihood Ratio Test (LRT), and I've come across a problem that I'm struggling to solve. I would greatly appreciate any ...
23 views

### Binary and count variables as endogenous variables

I set up an APIM (actor-partner interdependence model) in R (lavaan). No I'm facing the following issues: Model: My endogenous variable is a count variable that follows a poisson-distribution. Model:...
59 views

### Relationship between Poisson count and Exponential inter-arrival times [duplicate]

This picture represents transactions. $T_1$ is the time of the first transaction, $T_2$ time of second, $T_x$ time of the $x$th transaction $t$ is the observation period, $X(t)$ denotes the number of ...
1 vote
Cross posted from Mathoverflow Let $X$ and $Y$ be two random variables such that $X\sim Exp(\lambda)$ and $Y$ have positive support and (strictly) increasing hazard rate $h_Y$. $X$ and $Y$ are ...