A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.
1
vote
0answers
51 views
Fit poisson regression
I have a data set $Y$, $Y$ is assumed to follow a poisson distribution with mean = $\lambda$ .
However, each element $y_i$ in $Y$ is accompanied with a covariate $x_i$. So here I want to use poisson ...
0
votes
0answers
42 views
How to calculate the predicted probability of poisson regression model
I have a data set $Y$, each element $y_i$ in $Y$ has the covariate $\lambda_i$. Here, I want to use Poisson regression to fit a model: ...
0
votes
0answers
50 views
Distribution of independent binomial variables conditional upon the sum
Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
1
vote
0answers
32 views
GLM with unequal sample size
I am trying to figure out how to run a GLM with a poisson distribution in R. The data has 4 treatments: A(n=16), B(n=17), C(n=16), D(n=20), and 2 time periods. This data is count/area so there are ...
0
votes
0answers
27 views
Optimizing a Poisson Process
So, I was standing in line for a Paramore concert for a very long time this past weekend because the boyfriend wanted to be up front during the show. I got to thinking, what would be the optimal time ...
3
votes
1answer
53 views
Poisson Repeated Measures ANOVA
The following is a general background into my data analysis problem:
I am working with count data that is non-normal.
Data was collected at 2 time periods.
I am interested in comparisons of species ...
1
vote
1answer
50 views
Fitting a Poisson distribution from missing observations
I am interested in fitting a Poisson/negative binomial distribution to estimate the number of times a phenomenon happens within a period, let's just say 10 years. I can count the events from monthly ...
0
votes
0answers
10 views
Unable to load gamlss.mx package [migrated]
I am working on building a generalized linear mixed-effects model with Poisson distributed errors. I worked through it using glmer() in the lme4 package, but realized that my model is very ...
0
votes
1answer
43 views
how to test for overdispersion in Poisson lmer()
I have the following model:
> model1<-lmer(aph.remain~sMFS1+sAG1+sSHDI1+sbare+season+crop
+(1|landscape),family=poisson)
...and this is the summary ...
-2
votes
0answers
32 views
Is there a R function that can give me parameter estimation of data following a zero inflated poisson distribution? [closed]
I have a series of numbers, I know it's from zero-inflated poisson distribution. Is there an R function that can give me the parameter values? For example, I used rzipois function in VGAM package to ...
1
vote
2answers
60 views
Should the predictor variables be normally distributed for Poisson glm?
This is probably a really basic question, but it's the first time I've created a model that defines Poisson as its error family.
In setting up my variables to make the model, should I be concerned ...
1
vote
1answer
78 views
How do I interpret the 'correlations of fixed effects' in my glmer output?
I have the following output:
...
3
votes
0answers
36 views
Poisson regression for change in count following an event
I have a count of sickness absences before and after an accident,
and I want to find out whether an accident increases the sickness
absences differently in different groups.
I'm trying to formulate a ...
1
vote
0answers
40 views
Fisher information for Poisson Model
Assuming the data structure given below,
$$
\left[\begin{array}{l|l}
y & x \\ \hline \hline
y_{1} & x_{1} \\
y_{2} & x_{2} \\
\vdots & \vdots \\
y_{n} & x_{n} \\
...
3
votes
1answer
55 views
Questions on likelihood analysis
Whilst studying likelihood methodologies, I've come across some results that I haven't been able to work out.
If $X$ and $Y$ are Poisson with means $\mu_{X}$ and $\mu_{Y}$, then the conditional ...
1
vote
1answer
25 views
Appropriate distributions for infrequent events with copycats
I know that infrequent events, especially disasters like earthquakes, can often be modeled by the Poisson distribution. I was thinking of recent events like the Boston bombing and the ricin envelope; ...
1
vote
1answer
61 views
Confidence interval for a small number of iid Poisson
I want to calculate the confidence interval for $\lambda$ from a small ($n=10$) set of repeated observations from a Poisson distribution. That is, I have $X_1, \dots, X_{10}$ which I believe are ...
0
votes
3answers
76 views
Regression for a Rate variable in R
was tasked with developing a regression model looking at student enrollment in different programs. This is a very nice, clean data set where the enrollment counts follow a Poisson distribution well. I ...
2
votes
1answer
66 views
What is the difference between a zero-inflated and a zero-truncated poisson?
I'm trying to make sense of a question which uses a zero-inflated poisson model given by:
$$
f(x; \lambda,\omega) = \begin{cases} \omega + (1-\omega)e^{-\lambda} &\mbox{if } x = 0 \ \ \ \ \ \ ...
2
votes
1answer
68 views
Computing probability one program is faster than another
So I often have the situation where I want to compare the runtime of two computer processes. Even when measuring only user+system time (as opposed to wall clock time) there is a random element in the ...
2
votes
0answers
22 views
Searching for a model like ZIP, but to model three data-generating processes, not just two
What type of test would fit my data in this situation?
I'm measuring a count variable. Like in a zero-inflated poisson, I have numerous observations that are zeros because of a separate process. But ...
0
votes
2answers
73 views
Application of Poisson distribution to image processing
I'm trying to write a program to detect water bubbles in heated oil. I've applied a canny edge detection filter to the image and the results look like the following:
No bubbles: ...
7
votes
2answers
167 views
What's a good visualization for Poisson regressions?
I want to associate code defects with code complexity metrics like closeness. One common model is to view this as a Poisson process, where the duration is how much time is spent coding and the density ...
2
votes
1answer
93 views
Relationship between poisson and gamma
Supposing that I have an interval n units long with m arrivals, and I model arrival using a poisson distribution with lambda = m/n, it's pretty easy to show that the distance between successive ...
1
vote
1answer
37 views
Poisson distribution conditional on Poisson-distributed mean
I am looking for some details on the following distribution: assume the probability of a random variable $n \sim \text{Pois}(k)$ is conditional on $k \sim \text{Pois}(\mu)$. After some trying I ...
1
vote
0answers
26 views
Markov chain from Poisson: null or positive recurrent?
Let $K_t$ be a Poisson process with rate $1$ and $X_n=K_n-n$ $, \ \ \ n\in \mathbb{N}$
Now I want to determine whether it is null or positive recurrent, we already know it is recurrent.
I ...
0
votes
1answer
56 views
Conditional fixed effects Poisson *with population exposure*
Reading a paper, the authors use a "Conditional fixed effects Poisson with population exposure." I wasn't sure what "population exposure" meant, so I looked it up. It seems like the term comes from ...
0
votes
1answer
66 views
Poisson regression - dealing with widely different population sized
I have a dataset of counts (responses to a marketing campaign), collected at the zipcode level. I am trying to use a poisson regression to determine underlying response rate of each zipcode.
How do ...
1
vote
0answers
29 views
For count data from a survey, do variance corrections for survey design imply that the Poisson distribution will not accurately model the counts?
I have categorical count data that comes from a complex survey. Each unit of analysis in the survey (household, individual, etc.) is put into one and only category per dimension, ranging from 2 to 20 ...
1
vote
1answer
85 views
Can I use 3-way ANOVA for testing the difference between small proportions?
I'm looking at daily purchasing data over a period of several weeks. Specifically, we're interested in the % of users who make purchases in our app (it doesn't matter the type of purchase or amount ...
0
votes
0answers
280 views
Uniformly Most Powerful Test and Rejection Region of Poisson Distribution
Let $X_1, \dots,X_n$ be a random sample from a Poisson$(\lambda)$ distribution where $\lambda > 0$.
(1) Find the Uniformly Most Powerful (UMP) level $\alpha$ test for the following set of ...
0
votes
0answers
49 views
Estimating log-linear models of survey data from the published marginal distributions
Suppose you have a complex survey that identifies each subject on N dimensions, N > 10, each of which places the subject in one and only one of k sub i categories, where the probability of the k sub ...
2
votes
1answer
97 views
How can I test the likelihood that two Poisson data sets are drawn from the same distribution in R?
Suppose I want to test whether or not code patches created on weekends have a greater bug rate than those created on weekdays. (We might guess that this is so because people who are at work on ...
1
vote
2answers
98 views
testing independent of data assumption, before doing Poisson Regression
I have got a set of data and decided to do a Poisson regression so $log(\lambda)=X\beta$.
I wonder if there is any test available for such purpose?
The first thought is to use the Durbin-Watson test ...
3
votes
1answer
59 views
Cumulative counts or counts for Poisson regression
I have a set of data with measurements X1 and X2 across multiple time points, T1, T2 and T3. I would like to conduct a Poisson regression using X1 and X2 on the counts of a phenomenon. An example of ...
2
votes
0answers
75 views
Why is Poisson regression different with glmer and gamlss?
I have a set of count data that seems to fit "Poisson" = not overdispersed, alpha = 0.
The problem is, I get different results using gamlss vs ...
2
votes
0answers
52 views
Dealing with zeros in a poisson regression
Our code goes through multiple stages of review. I wish to use the number of defects at an earlier stage of review as a "defect density" estimate for later stages.
It sometimes happens that code has ...
2
votes
2answers
385 views
The sum of two independent Poisson random variables
Using wikipedia I found a way to calculate the probability mass function resulting from the sum of two Poisson random variables. However, I think that the approach I have is wrong.
Let $X_1, X_2$ be ...
0
votes
0answers
67 views
Comparing ln(y) =bX vs. OLS and other count data models
My data is a balanced panel.
12 years X 600 ids/year X 12 months = 864,000 observations.
For about 150 of my 600 ids, at a certain point in this 12 year period a treatment is applied switching them ...
2
votes
0answers
155 views
The distribution of a linear combinations of poisson random variables
I would like to know what the distribution is of linear combinations of Poisson random variables.
I know that a linear combinations of Poisson random variables is not always a Poisson random ...
6
votes
4answers
341 views
What advantages does Poisson regression have over linear regression in this case?
I have been given a data set that contains the number of awards earned by students at one high school where predictors of the number of awards earned include the type of program in which the student ...
4
votes
0answers
61 views
Finding the limiting distribution
I was given an exercise to do that sounded something like this:
The Arizona football team scored $45$ goals in $19$ games in the 2007/08 season. If $y_i$ denotes the number of goals scored in the ...
0
votes
1answer
244 views
How to estimate Poisson process using R? (Or: how to use NHPoisson package?)
I have a database of events (i.e. a variable of dates) and associated covariates.
The events are generated by the non-stationary Poisson process with parameter being an unknown (but possibly linear) ...
5
votes
1answer
163 views
Non-intuitive answer from a Poisson regression
I am not very familiar with Poisson regression, so I think I must have made a mistake in the below analysis:
I am studying the effects of smoking on lung cancer rates. The dataset is provided here. ...
1
vote
0answers
41 views
Probability of collisions in queues of Poisson process
I have a process whereby objects of width W land on a gene at rate F (per second, poisson process, lets assume), and then start to move along at constant speed V. I'm trying to work out the rate at ...
7
votes
5answers
367 views
If not a Poisson, then what distribution is this?
I have a data set containing the number of actions performed by individuals over the course of 7 days. The specific action shouldn't be relevant for this question. Here are some descriptive statistics ...
1
vote
1answer
179 views
Using fitted GLM model to simulate y's from new x-values
I have a fitted GLM model: m1=glm(y~x,family=poisson,data=data). I would like to use this fitted model to simulate new data but ...
4
votes
1answer
155 views
Cost function for validating Poisson regression models
For count data that I have collected, I use Poisson regression to build models. I do this using the glm function in R, where I use ...
0
votes
0answers
118 views
Bivariate Poisson - Cant seem to understand it. Could someone pls tell me how to work it out in laymans terms?
Researching bivariate poisson over the web is no easy task unless you can make sense of the greek symbols.
I am familiar with poisson and have a deep understanding of it. So could someone explain ...
3
votes
1answer
505 views
How to calculate cumulative Poisson probabilities without adding each one if no. of outcomes is large and hence, adding (without excel) is difficult?
One can calculate the probability of a correct score of a football match by Poisson(Number of Team1 goals, Mean average Team1 goals) x Poisson(Number of Team2 goals, Mean average Team2 goals)
So for ...
