A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.

learn more… | top users | synonyms

0
votes
0answers
11 views

Implementing ANOVA for a poisson distributed variable (count data)

I am currently working on a dataset that contains details on over 100k terrorist attacks. The variables of interest for each attack are attack type e.g. bombing (3 levels), country e.g. Iraq (5 ...
2
votes
1answer
41 views

Poisson and NB results

i did a regression with poisson model, and since the dependant variable is overdispersed (0.13) , i have also tried negative binomial. The problem is that my explanatory variable "repeated partner" is ...
0
votes
0answers
37 views

poisson process modeling

Consider a birth process, where at each unit time step t, on the average, there is a fraction of 0.012 among all the populations who will give a birth. Suppose the doubling time is t, then, from ...
0
votes
0answers
72 views

Inferring the lambda of a Poisson distribution

Lets consider the following scenario: We have 4 roads each with equal distance of 800 m. In traffic engineering, the ...
-1
votes
1answer
36 views

Solving: Poisson Distribution query [closed]

The distribution of a number of printing mistakes per page per book is Poisson with mean 3. Given that $e^{-3} = 0.047987$, the probability that there is some mistake is a) 0.049787 b) 0.950212 c) ...
1
vote
1answer
32 views

How to categorize count data

I have count data (basically histone modification data). The counts represents number of reads falling into each genomic region. I need to divide my data into $\text{low|medium|high}$ based on the ...
0
votes
0answers
13 views

scatter plot for underdispersion in Poisson

I did an equidispersion test and got a vary small negative value (Cameron and Trivedi), my Prof. said the this test is not very powerfull and that maybe i should try other tests and also use residual ...
0
votes
0answers
30 views

Superposition of two renewal processes

Usually, superposition of two independent renewal processes may not lead to a renewal process. However, in my problem, the interval time between two events of the renewal process is more specific ...
2
votes
0answers
30 views

Poisson regression: loglinear vs linear

In Poisson regression, there are two possible ways we can relate the dependent variable $y$ with the independent variables $x$: $E[y|x] = w^Tx$ $E[y|x] = e^{w^Tx}$ The likelihood functions are: ...
1
vote
0answers
14 views

Interpreting Poisson regression: Deriving results from the CDF

I am trying to interpret a Poisson regression without being very interested in the mean. As a complication, I also have an exposure variable. Let $y_i$ be a count variable, and $p$ the offset, for ...
0
votes
0answers
15 views

bayes estimate possion distribution function

Let {X\, ...,Xn) be random sample from random variable which has Poisson distribution with parameter A. Assume that the prior distribution A for is Gamma(1, 1) and that you have observed sample of ...
1
vote
1answer
23 views

GLM Model checking Plots - Quasi Poisson - Poisson

I wonder whether accounting for overdispersion in a GLM (Quasi - Poisson instead of Poisson family) has an effect on the model checking plots (plot of residuals against fitted values, a scale–location ...
0
votes
1answer
24 views

What methods exist to compare data sets from two different types of distributions

I want to compare two different types of data sets how well they correlate with each other. Lets say I have two datasets one follows a continuous distribution and another follows a poisson ...
0
votes
1answer
23 views

Poisson distribution with glmer - pairwise comparisons

I am analyzing counting data from a field experiment using the glmer procedure according to a Poisson distribution. The model works and I can visualize the results ...
1
vote
0answers
29 views

Panel poisson regressions on rates and values far from 0

I am estimating the effect of some treatment on yearly district-level stillbirths and stillbirth rates and births and birthrates in a panel with district and year fixed effects. Stillbirths are ...
2
votes
1answer
37 views

Using Poisson process model for prediction?

Suppose some event $X$ occurs on average $10$ times per minute. The events are independent of each other. Now, if I have understood correctly, this can be modeled as a Poisson process, and I can ask ...
1
vote
1answer
31 views

Horrible fit of Poisson model versus good fit of negative binomial model

I am analysing the amount of detail views of a webpage. The data have the typical aspects of count data, being Always positive Positively skewed So I want to fit a Poisson model and a Negative ...
0
votes
0answers
22 views

Poisson/Negative Binomial/Gamma log-link for continuous dependent variable (scale DV)

In my research about sport injuries in football, I am trying to obtain Incidence Rate Ratios (IRR) comparing my categories with the reference category. I have number of days a player was absent due to ...
3
votes
1answer
66 views

Can you show that $\bar{X}$ is a consistent estimator for $\lambda$ using Tchebysheff's inequality?

This question was taken from a practice exam in my statistics course. Given a random sample $X_1, X_2, ... X_n$ from a Poisson distribution with mean $\lambda$, can you show that $\bar{X}$ is ...
2
votes
0answers
21 views

Identify deviations from trend

I have a panel with individuals $i$ measured at time $t$ (the date). The outcome is a count, which we can call $C$. There's some general time trend $g$ affecting all individuals. $E[C_{it}] = ...
0
votes
0answers
33 views

Relationship between Poisson and Exponential distribution problem

I'm struggling to understand why I can't use an exponential distribution to solve this question: Astronomers treat the number of stars in a given volume of space as a Poisson random variable. On ...
1
vote
0answers
19 views

How to model the following dependent variable? [closed]

If I got a dataset which the (count data) dependent variable has the following distribution, how should I model it? I am aware of the zero inflated model and the negative binomial model, but are ...
0
votes
1answer
52 views

How can we find $Cov(X(s), X(t))$ for a compound poisson process?

If I assume that $X(t)$ is a compound poisson process, how can it be found what $Cov(X(s), X(t))$ is? I have seen this over and over in books, but they only state it as fact. It is stated to be ...
0
votes
0answers
28 views

Cameron and Trivedi overdispersion test-Eviews 7

I would be glad for explanation about the Overdispersion test (Cameron and Trivedi,1990). I am working with Eviews 7, and i needed to obtain the fitted and the forecast values of the dependent ...
0
votes
0answers
16 views

implementation of Poisson regression [duplicate]

I am trying to work with Poisson regression. I came across this video which is very helpful - https://www.youtube.com/watch?v=HntUY8SsYZg. In the video one of parameters (Race) is categorical and ...
8
votes
5answers
143 views

Poisson Hypothesis Testing for Two Parameters

So, for fun, I am taking some of the data of calls from the call center I work at and trying to do some hypothesis testing on them, specifically the number of calls received in a week, and using a ...
0
votes
0answers
9 views

retrospective kpi study

I have data about a business that looks like: actions: <timestamp, # responses, cat1, cat2> where each action can generate 0 up to perhaps 20 responses. ...
0
votes
0answers
20 views

How to transform counts for correlation?

I have averaged counts (>= 0, so poisson-like distributed) and need to correlate them (for the purpose of cross-validation, but this is not important I believe). Should I transform them before ...
0
votes
0answers
21 views

Skellam Distribution with Dummies (Difference of two Poisson RV)

The difference of two Poisson distributed random variables follows a Skellam distribution. We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
2
votes
1answer
29 views

Probability of obtaining a greater-than or equal set of observations from a Poisson RV

I have a suspicion this might be fairly trivial, but for some reason I cannot obtain a satisfiable answer today. Assume a Poisson random variable $X$ with known parameter $\lambda$ (though I suspect ...
4
votes
1answer
20 views

Two rate chi squared tests infection rate

We would just like to display a crude statistic to compare infection rate pre/post intervention. Based on a paper I read the statistical test I need to apply is a 2 rate chi squared test. I've been ...
0
votes
0answers
33 views

Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
0
votes
1answer
31 views

Tree model with poisson distributed response variable

If I understand correctly the R tree model - library(tree) - can only be used if the response variable is normally distributed. Is there a way to create a tree model with poisson distributed response ...
0
votes
0answers
45 views

Auto insurance claim modelling

I am really struggling with finding the best model for predicting claims with my third party motor insurance data. First of all, I am not sure whether I have done correctly with the grouping of ...
0
votes
1answer
29 views

Does this variable follow a poisson distribution or a binomial distribution?

I dance an average of 2/7 nights during a week. D = Number of nights dancing in one month/4 weeks. My first thought was Poisson, but am now unsure. Is it none of the above?
3
votes
1answer
50 views

Zero-inflated Poisson and Gibbs sampling, proofs and sampling

I am trying to figure out zip-inflated Poisson (ZIP) model. In this model, random data $X_1, .., X_n$ are of the form $X_i=R_iY_i$, where the $Y_i$'s have Poisson distribution ($\lambda$) and the ...
0
votes
0answers
44 views

UMP test for poisson vs geometric

I have two hypotheses: $H_0\!: X\sim\rm{Pos}(1)$ $H_1\!: \rm{Geometric}(0.5)$ for any $\alpha$ in $(0,1)$ How can I construct a uniformly most powerful (UMP) test? I used the ratio under the $H_0$ ...
0
votes
1answer
143 views

Finding a UMVUE for a specific function

Let $X_1....X_n$ be a random sample from the Poisson distribution with parameter $\lambda$. Find the uniformly minimum-variance unbiased estimator of a) $\lambda^3$ b) $E(e^X)=e^{\lambda (e-1)}$ ...
0
votes
0answers
5 views

Poisson parameter lambda confidence interval [duplicate]

Based on x arrivals in time t, what is the alpha level Confidence interval for lambda?
0
votes
1answer
35 views

On deriving the Poisson distribution from the binomial distribution

My own personal understanding of modeling the number of independent uniformly distributed events occurring in a fixed time interval, is that we can first approximate this with a binomial distribution ...
2
votes
0answers
33 views

Compound Poisson Distributions: When, Why, and How To Split the Problem

I've just stumbled upon the Compound Poisson Distribution (CPD) and it seems to be precisely what I need. For the purposes of this post, let's suppose I have a store that sells many items of ...
5
votes
3answers
204 views

Is there a way to define a statistic similar to the z-score for the Poisson distribution?

Let's say I want to compare samples taken from Poisson distributions that have different values of lambda (rate). If the samples were from a normal distribution, I could convert each observation into ...
3
votes
1answer
95 views

Conditional Poisson Distribution

The number of claims, $N$, in a year on a portfolio of policies follows a Poisson distribution with parameter $λ$. Large claims have a probability $p$ and small claims $(1-p)$, independently of ...
0
votes
0answers
28 views

Difficult Counting problem

Just started a probability course and this problem is giving me a hard time A bookie offers two bets I and II on a soccer game I You win this bet if the total number of goals scored in the first half ...
1
vote
0answers
51 views

Predicted number of events from xtnbreg, fe make no sense

I am trying to compute the number of predicted events from a fixed effects negative binomial regression model in Stata. I run the model first using random effects, then using fixed effects, and ...
0
votes
1answer
42 views

What transformation should be carried out if the count is non-integer in poisson glm in r?

My data is like this: person final sex 1 34.20 1 2 2.00 0 3 15.58 0 4 18.00 1 5 50.06 1 I am fitting ...
2
votes
1answer
72 views

How to choose between poisson regression and zero inflated models

I have data on children visiting the A&E department. I want to see which variables are associated with the numbers of visits. For instance, if genetic factors are associated with more visits to ...
0
votes
0answers
17 views

Uncertainty on ratio of integrals (correlated)?

I have a histogram, and a quantity defined as the integral of a subrange of that histogram (int_sub) divided by the integral of the full range (...
0
votes
0answers
8 views

Approach to plotting a shock model with a Poisson parameter?

I know the shock model is defined as: $$ A(t) = \sum_{i=1}^{N(t)} A0\exp[-a(t-sn)] $$ where: $a = 0.5$ N(t) is Poisson ~ lambda, and lambda = 4 $t = 5$ $A0$ is given its own uniform ...
0
votes
1answer
32 views

Bypassing exponential waiting times for Poisson simulations?

Hello StackExchange users, I am trying to figure out how do I simulate a time dependent Poisson process through N(t). However, my main problem is having trouble understanding what N is and how to go ...