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 ...
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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 ...
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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 ...
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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 ...
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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'...
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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 ...
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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 ...
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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 ...
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KS test for Poisson distribution data
I have a dataset comprising 1000 integers. It represented as follows:
...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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$N \sim$ 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 ...
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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 ...
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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 ...
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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:...
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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 ...
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When is a conditional hazard rate increasing?
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 ...
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Variable selection - Decide for family, link, etc. after or before?
This may be a dumb question but I was wondering about the appropriate chronology to
adjust model parameters in a glm when performing variable selection.
Suppose, one has a set of predictors $x_1$, $...
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Generate sample from poisson distribution with fixed sum
I want to generate a random sample of size n from poisson distribution with parameter l but the sum of these samples should be equals to some number say y. Is there any way to achieve this? i dont ...
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Difficulties with the PGF of X+Y with Y~Poisson(1) and X~Poisson(Y)
The pair of random variables $(X, Y )$ is distributed as follows. $Y$ has probability mass function $\text{Poisson}(1).$ Given $Y , X$ has probability mass function $\text{Poisson}(Y ).$ Show that the ...
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Probability distribution of actual time spent if randomly sampled at a known mean rate
I was experimenting with tagtime, which randomly asks the user what they're doing at a known mean rate $\lambda$. Let's say that every time I am sampled, I give a yes/no answer. If I answer yes $k$ ...
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Bayesian reparametrization are they equivalent?
Suppose that we are in a Bayesian context, we we have the following matrix $n,$ $K\times K,$ as parameter, and we assume that
$$n_{ij}\sim Pois(w*w_{ij})$$
where $w\sim Gamma(N+1,1)$ and $w_{ij}$ is ...
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Testing correlation coefficients from two bivarate poisson
I have datasets from two bivariate poisson distributions, $BVP_x(\lambda_1, \lambda_2, \lambda_{12})$, and $BVP_y(\lambda_3, \lambda_4, \lambda_{34})$ respectively.
Now we know the correlation ...
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Choosing a suitable GLM family for zero-inflated data non-integer data
I am currently aiming to find any statistical difference between site fidelity for four shark species between sex and sample site. This uses a mark-recapture method and thus the data is heavily zero ...
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Why does dbeta not sum to 1?
Both dpois and dnorm in the code below sum to 1 (or thereabouts). This appears to confirm my understanding of the ...
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MLE of a weighted sum of Poisson variables
I have n Poisson random variables with the same parameter $\lambda$: $x_i\sim POI(\lambda)$.
I know that $\frac{\sum(x_i)}{n}$ is a MLE of $\lambda$.
My question is, observing the weighted sum of ...
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Zero-inflated poisson model producing NaN results [closed]
I have been trying to run a zero-inflated poisson model as follows:
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Statistics Interview Question
Imagine you are solving difficult Math problems and you expect to solve one every 1/2 hour. Compute the probability that you will have to wait between 2 to 4 hours before you solve four of them.
I ...
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(Ab)Use of offset() in Poisson GLM to weight the damaging effect of counted insect stages
According to A.F. Zuur et al. (2009) in 'Mixed Effects Models and Extensions in Ecology with R', p. 239ff and this post: When to use an offset in a Poisson regression?, ...
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Compare chi-squared goodness of fit results for Poisson and Negative binomial
Steps followed for testing :
Derive parameter estimates using fitdistr() function in MASS package for the dataset, dt ...
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Issue with Poisson regression
I am analyzing count data (number of negative mental health symptoms). I ran a 1 sample KS test in SPSS and the sig is <0.001 for both a Poisson distribution and a normal distrubtion - indicating ...
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Application of Poisson distribution
A group or a fleet of “m” independent components operates in a plant. These components are non-repairable and we just have “s” items in stock to replace with failed components (no emergency ...
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Find the $\alpha$-level uniformly most powerful test (UMPT) of Poisson distribution
Let $(X_1, X_2, X_3)$ be a sample from $Poisson(\lambda)$. Here we test $H_0: \lambda\le 1$ v.s. $H_1: \lambda>1$. Fix $\alpha=0.05$. Find the $\alpha$-level uniformly most powerful test (UMPT).
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How to demonstrate amount of virus required to lyse all cells using Poisson distribution?
In a seminal article in virology ('Sur l’unité lytique du bactériophage'
Comptes rendus des séances de la Societé de biologie et de ses filiales, 1939, 130, pp. 904-907) the Nobel prize winner ...
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Appropriateness of Tweedie GLM for modeling average daily driving distance with unknown numerator and denominator
I have a dataset of cars and want to model a variable called average daily driving distance. The variable was calculated before I received the dataset as:
average daily driving distance = total ...
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Offset using Poisson distribution
I get everything but the two sentences are confusing me.
Offset is a variable that serves to consider the different exposures of different observation. When properly included, the target variable is ...
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Distribution for a sequence of events which the first one follows a Poisson distribution
Imagine a simple website where a user can access and can click on a button that will refresh the page. On average, 50 000 requests are made to the webserver of this website in a month. We can assume ...
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What is the approximate distribution of the distance between gas stations along a highway?
Thinking it should be exponential, but I could be wrong.
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Distribution of Poisson Sample Variances
Understanding that the variance of a sample of normally distributed random variables is chi-squared distributed with mean = population variance, what distribution describes the variance of a sample of ...
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What exactly needs to be independent in GLMs?
I am reading up on Poisson Regression.
Say I have an input vector $X^{T} = (X_1, X_2, \ldots, X_p)$ and I want to predict an output $Y$ which is correlated to these inputs.
Then the mathematical form ...
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Why can weekends cause harmony?
The following plot shows power spectra (periodograms) of a sample from $X_t \sim \operatorname{Poisson}(1)$ along with that same sample where:
Weekends were set to zero
Sundays were set to zero
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