Questions tagged [skellam-distribution]
The Skellam distribution is a discrete distribution that describes the difference between two independent Poisson distributions with possibly different parameters.
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The convolution of a Poisson Distribution and Scaled Poisson Distribution
I am trying to do a likelihood analysis on a variable, $Z$, which is defined as
$(1)$ $Z = X - cY$
where $X$ and $Y$ are both independent Poisson distributions with rate parameters $\lambda_{x}, \...
4
votes
1answer
80 views
Is it always possible to find $X\sim\text{Pois}(\lambda)$ and $Y\sim\text{Pois}(\mu)$ with given $P(X<Y)$, $P(X=Y)$ and $P(X>Y)$?
Consider $P(X<Y)$, $P(X=Y)$ and $P(X>Y)$ in $(0,1)$ that sum to $1$.
Is it always possible to find Poisson parameters $\lambda$ and $\mu$ such that independent $X\sim\text{Pois}(\lambda)$ and $...
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vote
1answer
50 views
Deriving the mean values of summed poisson distributions
z is a poisson distribution, in which λ = 2.887. It has been formed by summing two other independent poisson distributions, x and y.
Three further pieces of information are given about the ...
3
votes
1answer
161 views
Simplifying modified Bessel function of the first kind
The modified Bessel function of the first kind shows up in the normalizing constant of a lot of random variables (e.g. the normal product distribution, the noncentral chi-square distribution, the ...
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1answer
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What probability distribution would be suitable for modelling scores in a basketball match?
In football (not American football but what Americans call soccer), it is pretty clear: we may consider the difference of two independent Poisson variables. In basketball, in theory, we could increase ...
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1answer
905 views
What is the expectation of the absolute value of the Skellam distribution?
In particular, for a Skellam distribution obtained by substracting two iid Poisson Processes. Thank you!
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votes
1answer
584 views
Is there a reason why the regression in the R Skellam package uses three optimisation steps?
I am not entirely sure whether this would be better posted in Stack Overflow, or maths.se, however as it is about model fitting I thought I would try here first.
The Skellam distribution $\...
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1answer
135 views
Distribution of one Poisson variable relative to another
Assume A and B are two independent Poisson random numbers with means a and b.
What is the conditional distribution of A given that A>B, A=B and A...
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1answer
223 views
What is the correct way to test if there are any statistically significant differences between values on some variable between any two years?
Let's say I have the murder rate for a large number of years. What would the correct way to test to see if there are any statistically significant differences between these rates for any two years?
...
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1answer
3k 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 ...
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votes
1answer
107 views
Computing $P(Z>0)$ with $Z\sim\mathrm{Skellam}(k;\lambda_1;\lambda_2)$
Given the variable $Z$, distributed as follows:
$Z\sim\mathrm{Skellam}(k;\lambda_1;\lambda_2)$
I would like to understand how to compute the probability $P$$(Z>0)$.
I know to compute the value $...
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votes
1answer
471 views
From the bivariate poisson to the Skellam (or Poisson Difference) distribution
I am looking at how to calculate the Skellam distribution (https://en.wikipedia.org/wiki/Skellam_distribution) from the bivariate poisson distribution.
I understand that the Skellam comes from ...
4
votes
1answer
2k views
Testing if the difference between two count variables is different from zero
I have two count variables for several hundred thousand comparisons, one expected and one observed, and I would like to test if the counts are significantly different.
One possible approach I have ...
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0answers
163 views
Skellam distribution with dummies - consistent ML estimates?
The difference of two Poisson distributed random variables follows a Skellam distribution.
We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
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1answer
442 views
Does the noise term in a SDE need to be Gaussian?
Most of the examples I've seen for stochastic differential equations are of the form:
$$
dX_t = \mu(X_t, t)dt + \sigma(X_t, t) dW_t
$$
where $dW_t$ is a Wiener process, i.e., the independent ...
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votes
0answers
227 views
Estimator of Bessel function?
I am trying to estimate the parameters of the modified Bessel function of the first kind for integer order case.
$I_n(wt) = \sum\limits_{m=0}^\infty \frac{1}{m!(m+n)!}(\frac{wt}{2})^{2m+n}$
In ...
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2answers
1k views
Is the absolute value of the difference between two Poisson distributions a Poisson distribution?
What is the distribution of the absolute value of the Skellam distribution?
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1answer
243 views
How to compare rates of occurence in consecutive time series count data?
My data consists of occurrences of words in time windows. E.g.:
Day; Word; Frequency
1; "dog"; 45
1; "cat"; 2
...
2; "dog"; 90
2; "cat"; 4
...
I would like to ...
4
votes
1answer
5k views
The difference between discrete and continuous variables
Is the number of hydrogen bonds or the number of rings in a molecule a discrete or a continuous variable ?
Can I say that the number of rings: 1, 3, 4, $\dots$ is a continuous variable because in ...
4
votes
1answer
438 views
Poisson processes
I have two realizations of a poisson stochastic process, they are over the same space with rate $\lambda_{1}$ and $\lambda_{2}$. What is the probability that N elements in both sequences are the same, ...
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votes
1answer
7k views
How to calculate cumulative Poisson probabilities without adding each one if no. of outcomes is large and hence, adding (without excel) is difficult?
One can calculate the probability of a correct score of a football match by Poisson(Number of Team1 goals, Mean average Team1 goals) x Poisson(Number of Team2 goals, Mean average Team2 goals)
So for ...
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votes
2answers
841 views
What is the distribution of the sample variance of the Skellam distribution?
I want to estimate the parameter $\mu$ using the difference between two Poisson distributions with the same parameter, i.e. a Skellam distribution with $\mu_1=\mu_2 = \mu$.
I can calculate the ...
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votes
2answers
4k views
Distribution that describes the difference between negative binomial distributed variables?
A Skellam Distribution describes the difference between two variables that have Poisson distributions. Is there a similar distribution that describes the difference between variables that follow ...
