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Results tagged with poisson-process
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user 164061
For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.
2
votes
What kind of physical processes are well modeled as poisson processes?
TL;DR Processes with a probability density of events in time or space that is constant (and independent from what happened before) have an exponential waiting time distribution, and from this you can …
- 86.5k
1
vote
From Poisson to Erlang
You can use the following approaches:
The waiting time for a single event is exponential. The waiting time untill $k$ events is the sum of $k$ independent exponential distributed variables and is Erl …
- 86.5k
6
votes
Accepted
Does exponential waiting time for an event imply that the event is Poisson-process?
Not necessarily a Poisson process
The answer is already sort of given by WHuber in the comments. You need more (restricting) assumptions before the exponential waiting time is to be considered a Poiss …
- 86.5k
3
votes
Intuitive explanation of paradoxical interval times distribution
Here is some intuitive viewpoint different from simply adding the two exponential distributions:
The point 0.5 was fixed, but we can also consider it as a randomly chosen point.
In that case we may wo …
- 86.5k
2
votes
Probability of drawing two differently colored balls in a partition of equally sized partitions
Interpretation 1: No red and blue balls within any possible square of 1m x 1m
#### plotting situation
### drawing boxes around the blue points
box <- function(x, y , col = "blue") {
polygon(c(x,x …
- 86.5k
2
votes
Probability of drawing two differently colored balls in a partition of equally sized partitions
Interpretation 2: No red and blue balls within the same 1m x 1m square of a grid
In this case, the problem is similar to an urn model: you have $100^2$ urns in which you place red and blue balls, an …
- 86.5k
1
vote
Accepted
Probability of compound Poisson process
$X$ will be distributed as a Skellam distribution.
Intuition
You can view it intuitively as following. For a Poisson process on some piece of length $L$, you randomly designate each event as $Y_i = +1 …
- 86.5k
3
votes
Can Negative Binomial parameters be treated like Poisson?
The negative binomial can be treated like Poisson, but it is ambiguous how to treat it. It will depend on the underlying process that causes the overdispersion. This can occur in different ways.
Below …
- 86.5k
0
votes
Is it valid to simulate a Poisson process with a sequence of Bernoulli trials?
You used the Poisson approximation of the Bernoulli distribution. For large values of $n$ probability close to zero, you get that the Bernoulli distribution is approximately equal to a Poisson distrib …
- 86.5k
2
votes
Accepted
Densities of Arrival Times of Poisson Process
Computational
Question 5 is similarly based on different reason
It may often help to play a bit with some simple computations to get an idea how these arrivals look like.
Below I am using the method …
- 86.5k