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

2
votes
1answer
36 views

Why two 'modes' for a Poisson Distribution with $\lambda$ an integer?

Let $X\sim \operatorname{Poi}[\lambda]$ such that $\lambda\in\mathbb{N}$. ...
0
votes
0answers
11 views

Confidence interval for fitted lambda from Possion distrubtion

So my question is: you are given a set of data and you know the distribution is Possion with parameter lamda > 0. I figure out xbar is 4.06, and the z value we are using is 1.96 and n=50? But how can ...
0
votes
1answer
27 views

offset in glm for poisson regression

The offset argument in the glm() quite troubles me. As below, m3 is the usage of offset that I have seen. m4 is a manually calculated analog. But the result obtained is completely different, with m3 ...
0
votes
1answer
44 views

Log-linear model, Poisson regression, categorical variable with 100 levels

I want to compare the incidence rate(asum) of 100 different cities(cityID) to see if there are significant differences among them. Given that the incidence rate is following Poisson, so it is a ...
0
votes
0answers
16 views

Zero-inflated Poisson (ZIP) [closed]

I am really struggling with this question. Could anyone please shed some light?
0
votes
0answers
44 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
0
votes
0answers
2 views

What component of the result should I look at when doing a LLM model fit?

I am running mixed effects models with poisson and negative binomial fits. To asses which of the models are better, what components of the models should I look at? Some popular methods I follow: a) ...
0
votes
0answers
9 views

Wald, LR and LM tests for Poisson distribution

Assume that $y$ is random variable which distributes: $$f(y)=\frac{e^{-\lambda}\lambda^{y}}{y!} $$ Where $\lambda=e^{\alpha+X\beta}$ and $\alpha$ and $\beta$ are unknown parameters and we assume that ...
1
vote
1answer
17 views

Generalized poisson model with time parameter

I tried finding this on the internet, but with little success. How do I get a generalized expression involving rate parameter and time parameter for the Poisson process? The expression, $P(n) = ...
0
votes
0answers
8 views

Estimated values for Chi-square

To test if my point pattern is random, I am going to conduct a Chi square test. The data has 40 points divided to 3 by 3 tiles. Should I use Binomial or Poisson probability to calculate expected ...
0
votes
0answers
11 views

Can I use an offset for the maximum number of consecutive trades in an experimental market?

I have run a study where we let students interact as buyers and sellers in an experimental markt. Every period buyers can buy from one single seller and sellers can only sell to one single buyer. We ...
0
votes
0answers
9 views

Systematic component variation

The appendix of the paper of McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the ...
0
votes
1answer
119 views

Question on Poisson Distribution (Assignment Help)

I've been given the following question which was part of a past exam paper. Q3) Trains arrive at a station at the rate of 25 per hour. a) What is the probability that the time between trains ...
2
votes
1answer
53 views

Poisson Regression in R based on categorical time variables

I am trying to make a prediction on the number of visitors of a website and am wondering if it can be done based only on categorical time variables. I received some guidance on how to structure my ...
1
vote
0answers
20 views

Standardized residuals vs fitted values for Poisson regression

McCullagh and Nelder's book on glm suggest to plot standardized deviance residuals against either the linear predictor ($\hat{\eta}$) or the fitted values ($\hat{\mu}$) transformed to the constant ...
0
votes
0answers
22 views

Count data that can take only 4 values

What is a good model for estimating a regression whose count dependent variable that only has 4 values: 0, 1, 2, 3? The variable is not truncated, it is just something that can only be from 0-3. I've ...
0
votes
1answer
50 views

Standard Error differences Binomial Regression vs Poisson Regression

I'm running three different models on a dataset found in table 9.1 of Dobson's Introduction to Generalized Linear Models textbook. Model 1 is a poisson regression, Model 2 is a binomial regression ...
0
votes
0answers
14 views

Offset instead of percent data?

In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ...
1
vote
1answer
32 views

Linear Mixed Effects Model [closed]

I have data with some of the following columns: Site (categorical, 1-4), Species (Categorical, 1-21), Damage (continuous), and Age (categorical, 0-6). Age represents the visits to each site where I ...
1
vote
0answers
3 views

Validation of prediction interval for count data

I have developed a random-effects (frailty) survival model for repeated events which enables calculating individual-specific mean and prediction interval for the cumulative incidence (rate) of future ...
0
votes
0answers
10 views

What is the best test to measure deviations from tiny proportions?

What is the best (most reliable and robust) test to measure deviations from tiny expected proportions (e.g., p0 < 10^-6) in a huge sample? Binomial? Poisson? Negative binomial? Something else? ...
1
vote
1answer
33 views

Why is the Negative Binomial typically preferred over the Poisson?

I know that the Poisson is a special type of negative binomial, but from some shallow readings I've noticed that people claim that the Negative Binomial is better than the Poisson as it accounts for ...
0
votes
1answer
36 views

Poisson Convergence Example

For any $n\ge1,$ let $X_{n1},...,X_{nn}$ be independent with $$P\{X_{nk}=5\}=1-P\{X_{nk}=0\}=p_{nk}, \ k=1,...,n$$. Assume that $$\lim_{n\rightarrow \infty} \max_{1\le k \le n} p_{nk}=0$$ and ...
0
votes
0answers
23 views

Need help interpreting lmer output (ie should glm and lmer p values differ significantly?) [duplicate]

I posted this in Stack Exchange, but figure it may be better suited here given that it isn't a programming question per se: I initially ran a mixed model to calculate p values from a mixed model: ...
4
votes
1answer
43 views

Need help interpreting lmer output

I'm not sure whether this belongs here (or Cross Validated), but until somebody tells me otherwise, I'll keep it here. I initially ran a mixed model to calculate p values from a mixed model: ...
2
votes
1answer
28 views

Unbiased estimators of a transformed Poisson

So the question I have is$:$ Let $X$ follow a Poisson distribution with mean $\mu$, except that $X=0$ cannot be observed; this gives a random variable $Y$ which has a truncated Poisson ...
0
votes
0answers
17 views

Which statistical test is most appropriate for my count data?

I did a study looking at how the number of times a specific behaviour is performed during a courtship ritual is affected by temperature treatment, while trying to control for the body size of the male ...
4
votes
1answer
63 views

Forecasting Poisson, accuracy and prediction intervals

I'm trying to forecast Poisson data, divided in groups, of 1-26 months of data, depending on the group. Of the pooled data ...
1
vote
0answers
25 views

Is Quasi-Poisson the same thing as fitting a Poisson GEE model?

The title says it all. I'm wondering if someone can help me understand the difference (if there even is one) between a Quasi-Poisson model and fitting a Poisson Regression Model using GEE? It is my ...
2
votes
1answer
15 views

What method for forecasting error measuring in a poisson process?

There's so much different measures for the forecast error that I kind of lose the sight on which one to use. Out of the following: MAPE, ...
0
votes
0answers
12 views

Is there a goodness of fit test for Poisson regression with complex survey data?

I am doing an analysis of complex survey data using a binary response variable and several covariates. I am using Poisson with robust standard errors to obtain relative risks. Is there an ...
0
votes
0answers
17 views

How to calculate MSPE in winbugs when I use Zero Inflated Poisson regression?

I have had question about Winbugs code. I used ZIP(Zero Inflated Poisson) regression code in winbugs, and I want to compare two models(Poisson Model and ZIP model) using MSPE(Mean Square Predict ...
0
votes
1answer
39 views

Estimate the number of points scored by a team in baseball

Let’s say I’d like to estimate the number of runs Team A will score against Team B Team A (away) vs Team B (home). Starting pitcher for Team B is a lefty named “Ben James” Team A scores 5.2 runs per ...
0
votes
0answers
41 views

UMVUE for $E(y^2)$ in Poisson distribution

If $Y \sim \text{Poisson}(\lambda)$. How do I find the UMVUE for $E(y^2)$? I know that $E(y^2)$ is $\lambda$+$\lambda^2$, since I want to use Rao-blackwell thereom, I need a complete sufficient ...
0
votes
1answer
43 views

How to prove $\bar{x}$ is UMVUE estimator for lambda without using CRLB? [closed]

How to prove $\bar{x}$ is UMVUE for lambda for poission distribution without using CRLB(cramer-rao lower bound)?
1
vote
0answers
35 views

Should I use such adjustment

In this question I would like to ask you to choose between two simple scenarios of testing differences of rates between two random variable of Poisson distribution over different time periods. We ...
4
votes
1answer
43 views

equivalent of t-test for Binomilal/Poisson variables

I have to try to estimate and explain conversion rates that can be extremely low, on limited dataset. Because I have very few observations, a normal framework would give me a poor estimate, because ...
0
votes
2answers
69 views

Negative-Binomial vs Poisson for Count Data

Say that I was modelling the number of upvotes for a Facebook post under two treatments. What would be a more ideal distribution for modelling these counts: negative-binomial or a Poisson? What would ...
0
votes
0answers
13 views

Statistical test between two Poisson processes [duplicate]

I've observed two Poisson processes and my goal is to determine whether they came from the same process or not. Is there a test to determine this?
0
votes
1answer
20 views

Multinomial vs Poisson for Modelling Count Data

Say that I was modelling the counts for two different treatments. Afterwards, I would fit a particular type of distribution to each treatment population respectively. The data is count-based. What ...
0
votes
1answer
17 views

Decomposing multiple poisson process

Assume a time series composed by many recurring events coming from many different poisson process each with a different rate. Lets assume for simplicity no overlap between events. Is there any ...
0
votes
0answers
13 views

How can I test for seasonality with autocorrelation on a 100+ Poisson distributions (without graphs)?

I want to test Poisson distributions on seasonality by autocorrelation (without graphs, I want to calculate the LCL and UCL and program to test which autocorrelation lags exceed this). Now I know ...
3
votes
1answer
37 views

The number of defects in a piece of wire that is x yards long is $X\sim\operatorname{Poisson}(ux)$ for any $x>0$

The number of defects in a piece of wire that is x yards long is $X\sim\operatorname{Poisson}(ux)$ for any $x>0$. If five defects are found in a 100-yard roll of wire, find a conservative ...
0
votes
0answers
25 views

What's the best strategy for testing 100+ Poisson distributions on seasonality and trend in Excel?

I have pooled data which can be divided into 4 categories, and those can be divided in 6-50 groups each. I tested the pooled data and the categories with time series plots. Now I'd like to test all of ...
1
vote
0answers
32 views

Poisson or Binomial

A company has 6 customers, each one having 0.25 probability of calling on a given day. What is the probability that at least two customers call daily? I want to use the Poisson distribution to do ...
3
votes
1answer
62 views

Approximating Binomial Distribution with Normal vs Poisson

I have a doubt regarding when to approximate binomial distribution with Poisson distribution and when to do the same with Normal distribution. It is my understanding that, when p is close to 0.5, that ...
1
vote
0answers
8 views

Distribution to model availability of exposure to past events over time

Sorry for the weird title. I'm not sure how to best summarise the question, so I'll provide an example. Here is a histogram of movies I have rated on MovieLens, binned by release year: I propose ...
0
votes
0answers
35 views

What if no Model fits and no non-parametric alternative exists?

I'm doing analysis on data from an ecological field study. I have fields (n=12) of different age. I treat age as a factor (age class) having 4 levels (1,3,5,and 7/8 years old). Hence the number of ...
3
votes
2answers
89 views

Which model to use for longitudinal count data?

I have data for four years on the number of foreign subsidiaries of 120 firms, along with some variables that explain this phenomenon. I was able to obtain decent results using only one year of my ...
2
votes
0answers
44 views

How to construct a predictive model for poisson distributed univariate panel data? [closed]

I have a problem to understand univariate panel data. I would like to construct a predictive model and forecast future values. The data structure of my panel is as follows: ...