# 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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### What is the quantile function of a Skellam distribution?

Reading Is there a formula for the 95% confidence interval for the Skellam distribution or difference of two Poisson r.v.'s?, I realized that I would rather have the quantile function. Unfortunately ...
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### What is the PMF of the Zero-Truncated Skellam distribution?

Vaguely related to the notion of a Lindley equation, I am considering a recurrence $$L_{t+1} := L_t + \max \left( 0, A_t - S_t \right)$$ where $$L_t$$ is the number of customers in a queue system at ...
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### Should $3\!-\!$pointers be worth $2.5{\it ?}$

I was seeking an alternative scoring rule sets instead of three points for a win (gained more engaging and balanced) to cancel the theory "Banking a draw meaning a new kind of loss". It's ...
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### Proof of $\left|c_{i}-c_{j}\right|\left\{\begin{matrix}\ge 2,{\rm of}\,3/4\,{\rm probability}\\<2,{\rm of}\,1/4\,{\rm probability}\end{matrix}\right.$

FA Premier League 2019/20. The season was affected by the COVID-19 Pandemic while each team had a so-called quarter of their schedule left. ("quarter" ? Since each team has 4/9 or 5/9 number ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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