The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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.

1,356 questions
Filter by
Sorted by
Tagged with
32 views

How can I describe a heavy skewed population?

I have a set of data on the size of a group a person is apart of for 100 persons. member group_size bob 16 sally 30 jim 5 The size of the group a person ...
17 views

Poisson distribution question

An airline has found that the number of people booked on flights who do not arrive at the airport follows a Poisson distribution at the rate of 2% per flight.For a flight with 146 seats ,150 are sold ...
24 views

Poisson distribution - adapting for different intervals

Over a long period of time ,a plumber finds that on average he receives 2 emergency calls per week .Work out the probability of one emergency call on one day assuming the plumber is available for ...
24 views

Are these two distributions independent?

In a probability cheatsheet, there's the following claim: That $Z_1$ and $Z_2$ should be independent seems very unintuitive to me. It seems to me that if $Z_1$ is high, then $Z_2$ is low, and vice-...
34 views

Poisson distribution with large mean

The hits in a website can be modeled as a Poisson process with a rate of 5000 hits per day. Let X be the number of hits in 6 days. Give the distribution of X. So, is the percentile x = 6 and the ...
53 views

Confidence interval over multiple Poisson distributions

There are five different periods (one following each other) of unequal lengths where one specific event is happening such that it follows Poisson distributions (e.g. meteorite falls). It is always the ...
19 views

Adding probabilities of different Poisson distributions

There are three different periods of unequal lengths where one specific event is happening such that it follows Poisson distributions (e.g. meteorite falls): in the 1st period (100 hours) the average ...
28 views

Conditional independence problem for poisson random variables

I have this problem: Let $X = V + W$ and $Y = V + Z$ where $V, W, Z$ are independent Pois($\lambda$) random variables. I found that $Cov(X, Y) = Var(V) = \lambda$ It now asks to find whether $X$ ...
34 views

How can I apply the Poisson ($\mu$) distribution to two series of random draws?

I have the following question: A box contains 1000 balls, of which 2 are black and the rest are white. If two series of 1000 draws are made at random from this box, what approximately, is the chance ...
22 views

Finding joint distribution of sum of independent Poisson random variables and calculating probabilities [duplicate]

My textbook, Introduction to Probability, by Blitzstein and Hwang, provides the following problem: Let $X = V + W$ and $Y = V + Z$ where $V$, $W$, and $Z$ are independent $\text{Pois}(\lambda)$ ...
360 views

Probability of a 500 year flood occuring in the next 100 years - comparison of approaches

I'm looking at this problem A $500$-year flood is one that occurs once in every $500$ years. a) What is the probability of having at least $3$ such floods in $500$ years? b) What is the ...
14 views

DIspersion Parameter of Generalized Poisson Distribution

Could someone please explain how the dispersion parameter in a generalized Poisson distribution is calculated? I'm currently trying to write an EM algorithm for a zero-inflated generalized mixed ...
15 views

Estimate quasi AIC for GAM models in R

I am new to R with little statistical backround. I want to built a GAM model which consists of categorical and continuous variables and cross basis matrices(cb). I use dlnm and mgcv packages. So, I ...
35 views

Poisson regression with offset vs poisson regression with weight [duplicate]

I would like to know the linear expression of weight and offset in terms of poisson regression in glm. for instance for offset ...
79 views

Standard deviation of a scaled Poisson process

Assume we have some Poisson process that produces events. In a given year we have counted $N$ of these events. Further assume that for some reason we need to report a monthly rate instead of this ...
15 views

Using the Neyman-Pearson lemma to construct UMP test for Poisson rates

We have two Poisson processes with rates $\lambda_1$ and $\lambda_2$. We observe $n_1$ events in $t_1$ time from the first process and $n_2$ events in $t_2$ time from the second. The UMP test for ...
51 views

15 views

Test design Poisson Rates

I would like to design a test for the following problem, where the Poisson distribution applies: Samples from a population can be either defective or not (e.g. some technical component from a ...
26 views

Poisson regression for count data that is not Poisson distributed?

Is it true that Poisson regression is used to model count data? But not all count data follow a Poisson distribution? Then you can still use Poisson regression in that case?
37 views

Comparison of Poisson cumulative probabilities between models with different rates

I'm building an anomaly detection model using the Poisson distribution. I'm calculating the Cumulative Probability: P(X >= x) for thousands of count data, all of them with different rates. I need to ...
27 views

How to generate under-dispersed Poisson variables in R?

In this article "generate quasi-poisson distribution random variables", it is shown how to use the function rnbinom to simulate overdispersed Poisson data: ...
22 views

Creating a classification model for a target value with Poisson distribution

I have a dataset with a target variable following Poisson distribution. It starts at 0 and goes until 30. But there are 8300 0's and only 2 30's. From this data, I need to create a classification ...
109 views

Possible methods for parameter estimation of a compound Poisson

Let $X_i$ be iid and each $X_i$ takes one value among $(0,1,-1)$ with probs $(p_1,p_2,1-p_1-p_2)$ respectively. Let $N$ be a Poisson RV with mean $\lambda$, and $$Z=\sum_{i=0}^N X_i$$ be a compound ...
19 views

Is there a difference between a “binary Poisson variable” and a “Bernoulli random variable”?

I am currently reading this paper which includes some stochastic modeling, and the authors describe a term in their model as being a "binary Poisson variable" which takes the value 1 with (time-...
14 views

Modeling variable recensus/exposure count data using gam, quasipoisson with cloglog link

I am modeling tree recruitment in a forest. Foresters visit a forest monitoring plot twice. Recruitment is defined as the number of trees above a certain size threshold that are in the second census, ...
52 views

How to use poisson to estimate arrival time (generate random integers)?

In my assignment, I'm supposed to use a distribution curve to describe how many minutes will the employee come to work in advanced or later than the planed start time. I decided to use Poisson ...