All Questions
Tagged with gamma-distribution poisson-distribution
73 questions
4
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2
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What is the interleaved probability like when two Gamma distribution processes fired together?
As opposed to the similar question here:
Is there a probabilistic (not analytical) argument for why the sum of independent Poissons is Poisson?
The difference is to consider the interval between two ...
- 43
5
votes
1
answer
73
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Questions around modelling arrival process of randomly sized groups
I have the following situation:
I'm trying to model groups arriving to some location by some process. I assume the distribution on some interval $T$ is a Gamma-Poisson mixture where $\Lambda \sim ...
1
vote
0
answers
29
views
Difference in Gamma Distributions have Poisson? [duplicate]
Today I learned about a Double Stochastic Process for the first time.
Apparently a Cox Process is a Double Stochastic Process. Here is my attempt to summarise this:
Cox Process: A point process (I ...
0
votes
0
answers
95
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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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1
vote
1
answer
28
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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 $k$ ...
0
votes
0
answers
99
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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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1
vote
0
answers
61
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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 ...
- 11
3
votes
0
answers
262
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Deriving a gamma distribution from a Poisson distribution
At the instant $t = 0$ a certain radioactive focus starts emitting particles. The infinitesimal probability that the focus emits a particle in the differential interval is $\lambda dt$. Let $N_t$ also ...
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0
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1
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91
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Should the updated posterior for a Poisson distribution be discretized if based on the Gamma distribution as the prior?
I know that the Gamma distribution is the conjugate prior of the Poisson distribution, such that given $\alpha$ and $\beta$ that describe the prior distribution, the posterior distribution is $Gamma(\...
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1
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237
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Proportional to Gamma means the posterior is gamma
I'm reading through these lecture notes on posteriors and conjugate priors.
https://web.stanford.edu/class/stats200/Lecture20.pdf
In particular, it asserts that: "This is proportional to the PDF ...
0
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0
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56
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Calculating the Gamma Posterior distribution Scikit Stats
Say I have lots of data that I am using to model the weekly rate of some event, with 0 being the minimum frequency and 7 being the maximum frequency. I am looking to perform bayesian analysis on this ...
0
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0
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89
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Identifying the value of parameters of the prior distribution. Arbitrarily?
Referring to this Question, let's not use Jeffrey's prior for $\theta$ but use $Gamma(\alpha,\beta)$ as the conjugate prior for $\theta$. Under quadratic loss function, the bayes estimator for $\theta$...
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0
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0
answers
44
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Intersection of multiple gamma distributions
Let's say I own a few hundred McDonalds locations. In a subset of those (say 100) I observe vegans eating there and I estimate the arrival time of vegans at these 100 restaurants using a Poisson ...
6
votes
1
answer
435
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Law of Total Variance
I trying to experiment with law of total variance in order to empirically recreate theoretical results.
In particular I am interested in verifying that:
$$
Var(Y) = E[Var(Y|X)] + Var(E[Y|X])
$$
Let's ...
4
votes
2
answers
2k
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Using GLM: Gaussian, Poisson vs Gamma
I am trying to perform a GLM analaysis using R for an outcome that is:
Bounded by 0 - 10
In steps of 1
(Numerical Rating Scale for Pain: 0 - 10)
I have a set of demographic factors, age, sex etc, ...
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6
votes
3
answers
4k
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Predicting with a GLM
I wanted to check my understanding of predicting with a GLM:
A binomial/logistic regression model predicts the binomial parameter = p = P(success). To convert the probability into classes, we have to ...
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1
vote
1
answer
4k
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Relationship between Poisson and Gamma Distribution
There are several solutions to this problem but I am interested in the solution in Casella & Burger Pg. 100. The problem shows that if $X$ follows gamma($\alpha$, $\beta$), a random variable and $...
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1
vote
1
answer
280
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gamma prior and Poisson for data $X_i$, why we only $\sum_i X_i$ for posterior
I'm looking at problem 7.24 in Casella and Berger (see below)
to calculate the posterior of $\lambda$, I think we need to calculate $\pi(\lambda|X_1=x_1,...,X_n=x_n)$. However, the solution (see ...
- 3,050
1
vote
1
answer
143
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Modelling catch rates: difference between Gamma and poisson distribution
I am confused about the difference between modelling counts (i.e. catch) using a poisson distribution with an offset (i.e. effort) and modelling catch per unit effort using a gamma(link=log) ...
2
votes
0
answers
61
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When and why to use specific probability distributions?
I'm a graduate mathematics student and I've taken several courses on statistics, probability theory, stochastic processes and machine learning.
In all the textbooks I consulted and all the classes I'...
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7
answers
2k
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What distributions have an undefined mean but are not symmetric?
What distributions have an undefined mean but are not symmetric?
I'm looking for a probability distribution function (and CDF) for which the mean is undefined, but not symmetric like Cauchy, but a ...
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4
votes
1
answer
494
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Showing $X\sim \operatorname{Poi}(\lambda)$ is minimax
Assume that $X$ has $\operatorname{Poisson} (\lambda)$ distribution and the loss function is $\ell(\lambda,a)=\frac{(\lambda-a)^2}{\lambda}$. Now, I want to show that $X$ is minimax. A hint that is ...
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3
votes
1
answer
109
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How to calculate the posterior distribution from the density
I'm stuck on a answer from an old exam.
The task is to use a Poisson distribution and a Gamma distribution as prior to calculate the posterior density:
$$
p(\lambda|x) \propto L(\lambda)p(\lambda)\...
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4
votes
2
answers
1k
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MLE of Poisson-Gamma distribution?
I am trying to create an example that applies fully parametric estimation. I am using a Gamma-Poisson distribution where the random variable is a Poisson random variable with mean $\lambda$ which has ...
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vote
2
answers
3k
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Why are Poisson distribution and Exponential distribution special case of Gamma distribution?
I am aware that Gamma distribution is used as a conjugate prior distribution for various types of rate parameters such as in Poisson distribution and Exponential distribution.
People say that ...
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-1
votes
1
answer
109
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Is the question requiring the use of a gamma or exponential distribution? [closed]
Incoming telephone calls to an operator are assumed to be a Poisson process with
parameter $\lambda$. Find the density function of the length of time for $n$ calls to be received, and find the mean ...
1
vote
1
answer
933
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Gamma-Poisson conjugate prior, posterior exploding?
I've been looking for simple code that can model ad clicks per day. Notionally, gamma-poisson would be a good conjugate prior. However, I'm finding that for slightly large daily click rate values, the ...
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1
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0
answers
1k
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How to use scipy stats gamma pdf to update the posterior distribution?
I'm trying to "get my bearings" performing bayesian analysis, specifically I'm exploring the Gamma-Poisson conjugate prior. The definition of the PDF is below
If the prior takes the form of ...
- 3,520
0
votes
0
answers
930
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Box-Cox vs GLM for skewed non homoskedastic data
I need to do a regression on a variable Y that is skewed right (non normal) and heteroskedastic and therefore violates two assumptions of the normal linear model.
The data is non negative (some 0 ...
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0
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0
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220
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Density Function for Time until Second Arrival with Poisson Process [Solved]
Problem Statement: The number of arrivals $N$ at a supermarket checkout counter in the time interval from $0$ to $t$ follows a Poisson distribution with mean $\lambda t.$ Let $U$ denote the time until ...
- 6,039
1
vote
1
answer
2k
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Should I use Binomial, Poisson or Gamma distributions? With or without a log link?
I want to run a GLM to answer a few questions about differences in diet between sex and calendar year.
Questions:
Does frequency of occurrence (FO) of pieces eaten differ between sex or year?
Does ...
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1
vote
1
answer
500
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Deriving Marginal Distribution of Poisson [duplicate]
How do you find the marginal distribution of a Poisson distribution given a gamma(a,b) prior?
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1
vote
1
answer
2k
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Poisson-Gamma conjunction - calculating posterior [duplicate]
How to calculate posterior distribution step-by-step while given:
some observed numbers of customers from the last days
that number of clients is distributed by Poisson($\lambda$) ($\lambda$ is not ...
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1
vote
1
answer
1k
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getting negative binomial from poisson and gamma
This equation is from a statistical genetics research paper. I'm struggling to understand how they get negative binomial from the integral. x_cn is poisson and q is gamma. Is there such a rule? Or is ...
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1
vote
0
answers
74
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Poisson and Gamma distribution for testing randomness
In genetics I want to test whether InDel (insertion and deletion in DNA) sizes occurs with the same probability.
I heard that I should gamma distribution to model it. I found
...
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5
votes
1
answer
602
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Truncated Gamma Distribution
The Gamma distribution is the conjugate prior of Poisson distribution. What about the Truncated Gamma distribution? Is it still the conjugate prior of Poisson distribution?
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4
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0
answers
195
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two independent Poisson Arrivals
I have two types of customers (type 1 and type 2) enter a shop. Their arrival processes are independent and follow Poisson process with the arrival rates of $\lambda_1$ and $\lambda_2.$
Consider two ...
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4
votes
2
answers
1k
views
sum of $N$ gamma distributions with $N$ being a poisson distribution
I have an event having poisson distribution with time intervals of one minute. Every event has accomplishment time with gamma distribution.
I $N$ number of events start in $t$ minutes, the what will ...
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1
vote
1
answer
1k
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Exact Confidence Interval for Poisson using Gamma-Poisson Relationship
I'm reading Casella-Berger's Statistical Inference and trying to follow along in example 9.2.15, which constructs an exact confidence interval for a Poisson rate. In this example, the authors solve ...
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2
votes
0
answers
2k
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Why do Chi-Square distribution and Poisson look similar
I am new to statistics and I am looking at Chi-Squared distribution, and I found that it looks similar to Poisson distribution.
Is there any theoretical relation between them, or its just coincidental?...
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0
votes
1
answer
625
views
Gamma/Poisson Posterior Distrib Given Prior:
I need to find the model over a period of length t. This is what I've done:
Based on the Bayes' theorem, the relationship between the prior, the posterior, and the likelihood function is
$p(\theta|x) ...
- 121
2
votes
0
answers
86
views
Analyzing standardized / fractional count data
In my experiment I want to figure out how the size of different planting containers, i.e. their volume, affects the number of regenerated plant shoots from root fragments (terminology here is root ...
- 6,551
0
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1
answer
231
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Mean of nearest neighbour distance in a clustered distribution
What would be the expected value of distances to the nearest neighbor in a set of points in 2-dim space that have a clustered (not random) spatial distribution? If the distribution is random the ...
1
vote
1
answer
490
views
Story Proof relating Poisson and Gamma
I'm having issues proving the following identity:
$P(X ≥ j)$ = $P(Y ≤ t)$, where $X$~ Pois($\lambda$$t$) and $Y$ ~ Gamma($j$, $\lambda$)
More specifically, I can prove it algebraically but not ...
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2
votes
1
answer
2k
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Null & Residual Deviance in GLM in R
For a GLM in R, is it correct to interpret that Higher the difference between NULL & RESIDUAL deviance, better is your model? If not, then how do i know if my model is good or bad (for GLM - ...
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4
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1
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Can I still update my prior if I have been waiting a long time without observing any successes of a Poisson process?
This is related to my previous question: How to update Poisson conjugate prior with observations of arrival time instead of counts?
Using the same notation, suppose $N \sim \operatorname{Pois}(\mu)$ ...
- 4,552
3
votes
1
answer
1k
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How to update Poisson conjugate prior with observations of arrival time instead of counts?
Suppose a random variable $N \sim \operatorname{Pois}(\mu)$, with Gamma conjugate prior such that $\mu \sim \operatorname{Gamma}(\alpha, \beta)$. Then given a sequence of $n$ observations of counts $\...
- 4,552
3
votes
3
answers
5k
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Use of Gamma Distribution for count data
I am working on my data including the insect abundance in dependence of landscape variables with a nested random effect.
Since i collected the individuals in the field i have count data and thought a ...
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3
votes
1
answer
82
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Poisson distribution and minimum parameters
I am trying to work out a research problem I recently faced.
I have a group of Poisson random variables and I want to find the distribution of the first sample that is equal to a specific number. In ...
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7
votes
1
answer
467
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Using empirical Bayesian estimation (Gamma-Poisson) to analyze high arrival counts (n ~= 5000)
Here's a problem I'm currently working on, as well as the empirical Bayesian approach I'm using. I'd like to make sure my approach is grounded in solid statistical theory.
I have a set of entities $e=...
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