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Results tagged with poisson-process
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user 11887
For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.
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Test for a Poisson process with a statistic related to clustering
For a one-dimensional Poisson process (assuming constant intensity), the interarrival times have an exponential distributio9n. So just test for an exponential distribution (make a qq-plot against the …
- 82.8k
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Is there a family of processes centred on the Poisson process?
In a pure Poisson process, the interarrival times (times between each bus) has an exponential distribution. So you want some family of distributions which includes the exponential as a special case. …
- 82.8k
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vote
How can you model the arrival times of 2 different events?
I can imagine cases where the above is independent and also where it's not - ie if the person has been waiting for 1hr it's more likely they have gotten bored.
There must certainly be some dependenc …
- 82.8k
4
votes
Accepted
Motivation for gamma distribution with a non-integer parameter
It seems you are asking for "real-life" examples where gamma distributions are used to model some real-world observables represented by random variables. There are many such examples. Take the Erlang …
- 82.8k
2
votes
PMF of compound Poisson process?
First, I will simplify your notation and let $Y = \sum_{i=1}^N D_i$ (with the understanding that the sum is zero if $N=0$.) The $D_i$ are iid geometric random variables and $N \sim \mathcal{Pois}(\lam …
- 82.8k
3
votes
Is there any gold standard for modeling irregularly spaced time series?
In spatial data analysis data is most of the time sampled irregularly in space. So one idea would be to see what is done there, and implement variogram estimation, kriging, and so on for one-dimension …
- 82.8k
2
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Predict background counts given past observations and assumption of linear variation of the ...
You have a Poisson point process with intensity (rate) function $\lambda(t)$, say. Assume the observation window is contained in the interval $[0, T]$ and the observed points $t_1, t_2, \dotsc, t_n$. …
- 82.8k
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Accepted
Understanding the assumptions of a Poisson regression model? Modeling plant diversity
First, you should visualize your data:
made in R by:
library(tidyverse)
ggplot(plants, aes(x=Fertilizer:Light, y=Diversity)) +
geom_boxplot(notch=TRUE, notchwidth=0.9) +
geom_jitter(position=p …
- 82.8k