Geometric Poisson distribution Puns

Hi all! I've been stumped on this problem for about a week now, so I thought I would turn to reddit.

I am supposed to find a numerical solution to the integral of the Poisson pmf times the Gamma pdf (from 0 to +infinity). This supposedly results in the pmf for the Negative Binomial distribution. The

I'm supposed to use at least two numerical integration methods such as quadrature (gauss-hermite, newton-cotes, etc), the method of Laplace, etc. Whichever ones are most appropriate.

My problem is that the integral I'm supposed to solve has many parameters such as lambda, alpha, beta, and since this is a numerical solution I need to fill those parameters in with.. numbers. I don't know what to do about this. Do I choose random numbers for them? Do I create the Lambda using something like dgamma() in R?

I just cannot find anything online about numerical methods for integrals like this, so I feel super super lost. Any guidance at all would help. Thank you!

For example: Let say we want to know if Steph Curry is going to score over or under 29 points in a game. Is it better to count the number of times he does and use binomial or count the average and use Poisson? What are the factors that would determine which one is better?

Hi there.

So I have a data of how [for the sake of anonymity, let's say] users of a particular application have interacted with this application, particularly, the number of times they have used the application since they've installed it.

I think number of times someone uses an application (this particular application is used rarely, the mean is somewhere around 4) might follow a Poisson distribution and the plots also look very close to Poisson in the first inspection.

However, the mean and variance are not equal as should be in Poisson and not even nearly close. In fact variance is around 6 times bigger than the mean. So that puts Poisson out of options. So what are other options to test for this type of data?

I have considered negative binomial which doesn't require the mean and variance to be equal, but logically it seems that Poisson should be a better fit here. Are there any explanations to why the data wouldn't follow Poisson?

Bellow is a plot of the data:

https://preview.redd.it/5s65lfyfkew71.png?width=646&format=png&auto=webp&s=1b8bbc81f1beff5733ee8dd21cbe31bf14a5cf64

Learn about Poisson distribution and Poisson process in Python.
Complete walkthrough with formula explanations and examples:

https://pyshark.com/poisson-distribution-and-poisson-process-in-python/

Serious answers only please!!

Edit (and a long edit at that)

If this sub let you post "cells" of excel, like most other Subreddits do, it would be a whole lot easier.

Imagine first column is xGC (expected goals conceded), second column is how many games have been played where the xGC falls within that category (ie 20 games have been played with an xGC for any given team between 0 and 0.1), and the third column is how many clean sheets the teams that had that xGC kept. I.e if 20 teams had an xGC of 0-0.1, you'd expect 19-20 cleansheets.

By doing this, I can calculate the %age chance of a clean sheet, given what their xGC was. I'm using this for a form guide. It's unrealistic in my opinion that Tottenham have kept 3 clean sheets given their xGC of 4.21. So I wanted to look at the individual matches they played and calculate how many clean sheets they should have kept.

Hope that clears things up.

I’m looking for something along the following lines of:

xGC of 0-0.1, games played 20, clean sheets 19

xGC of 0.1-0.2, games played 30, clean sheets 26

All the way up. Any increments is fine, doesn’t have to be every 0.1 xGC.

Any way of working this out is also ok, if you don’t have the actual information!

Thanks

The prompt gives you a Poisson distribution for x occurrences of an event in 3 years. How do I find the probability that there is exactly 1 occurrence in 1 year? Am I supposed to use lambda/3 for the Poisson distribution for x occurrences in 1 year?

I'm a noob, so I'm trying to imagine this intuitively. Are they only the same in a standard normal distribution? I'm just picturing a bell curve. I am long out of school, but I am dealing with stats for bio

Hi. I have a dataset containing a variable that I think has a (roughly) zero-truncated Poisson distribution. I'm struggling to find libraries and commands that will derive the (Poisson) mean of my data, and help me assess (over)dispersion.

Also, I've checked out vglm to run zero-truncated Poisson regression on the data. Can anyone recommend any tools / guidance for conducting regression diagnostics in R please?

Given a variable X~Poisson(lambda), at time t, each variable X has a positive probability of survival, define the lifetime as some positive random variable L with pdf f and cdf F.

Let the number of failures of X (Non-survival) be X(t). Prove X(b)-X(a) is independent of X(d) - X(c) for 0 < a < b < c < d

The problem is this is intuitive to me, but I have no idea how to formally prove.

My main 'proof': X(t) = Pois(lambda) * Pr(f < t) X(t) = Pois(lambda) * F(t) X(b) - X(a) = E(Pois(lambda, b)) * F(b) - E(Pois(lambda a)) * F(a)

X(d) - X(c) = E(Pois(lambda, d)) * F(d) - E(Pois(lambda, c)) * F(c)

With poisson distributions being independent with the same scaling factor, and the lifetime cdf F(x) not dependent on F(y) for y not equal x, the two expressions are independent.

The last assertion seems very wishy-washy and doesn't seem to work as a proof to me.

Thanks for the help!

Hello friends! I am bit confused between poisson distribution and poisson process what's the difference between them.kindly answer in simple words so that I can understand it easily and if possible pleas elaborate the difference with the help of examples.It will be so nice of you

Until now, I was familiar with the poisson probability distribution (https://en.m.wikipedia.org/wiki/Poisson_distribution).

I also learned how to determine if a given variable (e.g. 1000 recorded measurements) follows a poisson distribution. This can be done by simulating different poisson distributions and seeing how closely they match your data. (https://stats.stackexchange.com/questions/78139/how-to-know-if-a-data-follows-a-poisson-distribution-in-r).

Now, I am trying to learn about something called the "poisson process" (https://en.m.wikipedia.org/wiki/Poisson_point_process). My question : is there a way to check whether your data follows a poisson process?

I am learning about queueing models. In these problems, you try to represent a queue (people arriving in line, waiting in line and getting served) using statistical models (e.g. the m/m/1 model) that require "arrival times" (a common and important variable used in queuing problems) to follow a poisson process.

Suppose i have a list of arrival times : e.g. the first customer arrives 10 minutes after the shop opens, the second customer arrives 7 minutes after the first customer, the third customer arrives 3 minutes after the second customer, etc. This can be expressed as either (10, 7, 3 ...) or (10, 17, 20...).

Is there a way to find out if this variable follows a poisson process? I saw that there are ways to simulate a poisson process (e.g. https://stats.stackexchange.com/questions/148997/poisson-process-in-r-from-exponential-distribution or https://stackoverflow.com/questions/55854071/manually-simulating-poisson-process-in-r). But how can you check if individual measurements follow a poisson process?

Thanks

I am really stuck with a statistic approach. I have data of outgoing calls from a month with the hour of the day and day it was made.

What I first did is groupby hour of the day and count the number of calls for the entire month, and I noticed it has the shape of a Possion distribution (left skewed). What I want to do is to get the pdf so I can now the probability of finding anyone doing a call at a given hour of the day.

Yet I am really confused because of...

1. Time unit, I am graphing the entire month and I would just like to calculate the probability of one day of the month, so should I take the mean of calls at each day and hour, and then fit the distribution?

2. Besides count an event like how many cars with pass in 1 hour. I would like to count the hour passed in one day. For example, X=1, means an hour has passed from 12pm and this is the probability of finding someone doing a call. Is that possible?

I would really appreciate your help or any reference. I feel like I am overthinking it

discuss

Here's the question:

Let N ~ Poisson(μ). Given N = n, toss a fair coin n times and denote the number of heads obtained by X. What is the distribution of X?

I am doing my IA on Poisson Distribution and can't kind any similar IA's on the topics online. Does anyone happen to have or have links to resources relevant to the Poisson Distribution IAs (Preferably marked).

In a town, crimes occur at a Poisson rate of 4 per month. (1) What is the probability of having at least 3 months with exactly 4 crimes each during the next year? (2) What is the probability that there will be an odd number of crimes for a particular month?

If a call center is functioning from 8:00 AM to 8:00 PM every day, and incoming calls occurs according to a Poisson process with rate 0.1 per minute, then for any given day, the probability that 8th call occurs between 8:40 AM to 8:50 AM given that the first call occurred at 8:10 AM, is  -

I’m a student who hasn’t had any experience with Poisson distribution. How would you recommend I go about this project? (any feedback/tips welcome)

I have a statistics course and we have been learning about linear models and generalised linear models. I understand that if my random variable is continuous, if I repeatedly take large enough samples then the sample means will follow a normal distribution (the central limit theorem). I understand that we can use this idea for statistical inference, using a hypothesised population mean and our sample mean and the normal distribution they both lie on (central limit theorem).

But... where does the poisson distribution come in for count data?

Do repeated samples from count data approximate to the shape of a poisson distribution? In my mind it makes sense why sampling means from continuous data might lead to a symmetrical bell shape around the true mean, but I don't have this intuition for the Poisson distribution (e.g. for a mean of 1: https://en.wikipedia.org/wiki/Poisson_distribution)

Why do we assume the shape of the Poisson distribution as the one sample means will follow for count data? Where does this shape come from, and why can we use it for inference in statistics (our lectures are on GLMs where we are told to use those of the Poisson family for count data e.g. number of moths in a light trap).

Many thanks!! Apologies if I am simply confused.

I'm interested to model the number of Electric Vehicles (EVs) which arrive to a charging station during one day and their Time-of-Arrivals (ToA).

I read that the number of EVs arriving at a charging station during a time interval is considered to follow a Poisson distribution, which uses a parameter which is called "λ", which is determined by "arrival_rate * time_duration".

Example:

• arrival_rate: 1 EV / hour
• time_duration: 24 hours

I know that the probability with which n = 20 EVs arrive at the charging station during 24 hours is:

P(n=20) = (e^(1*24) * (1*24)^20) / (20 !) = 0.0623 = 6.23 %

but it's not what I'm looking for, because I'd like to obtain:

• number of Electric Vehicles (EVs) which arrive to a charging station during one day;
• and their Time-of-Arrivals (ToA);

or, alternatively (if what I request above is not possible), could also be sufficient to obtain:

• the number of EVs which arrives at each hour of the day.

Which could be a way to reach my goals?

Say I enter a lottery that had 1/15 chance of winning per ticket. If I want to be 95% certain of winning, how many lottery tickets would I need to buy? Is this the math:

(14/15)^k= 0.95 and solve for k?