Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [skellam-distribution]

The Skellam distribution is a discrete distribution that describes the difference between two independent Poisson distributions with possibly different parameters.

The Skellam distribution was first investigated by Skellam (1946), after Irwin (1937) investigated the special case of the underlying Poisson distributions having the same parameter. It is discussed by Abramowitz & Stegun (1965, pp. 374-378).

References:

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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 negative binomial distributions? My data is produced…
chrisamiller
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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?
Ricardo
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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 estimate the ratios of all day-to-day differences (i.e., for dog day 1->2: 90-45/45 =…
dimitris fekas
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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 0:0 scoreline, Poisson(0, 1.05) x Poisson(0,…
O P
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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!
Marius Andrei Zoican
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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 variance of the Skellam distribution as the average…
Jonas
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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 theory this number could rise up to infinity? On…
beginner
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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, e.g., $X(t) \in [0,1000]$? Note: The two…
raygozag
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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 increments are normally distributed. I played around a…
RJ Nowling
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Is it always possible to find $X\sim\text{Pois}(\lambda)$ and $Y\sim\text{Pois}(\mu)$ with given $P(XY)$?

Consider $P(XY)$ 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 $Y\sim\text{Pois}(\mu)$ satisfy these conditions?…
Stephan Kolassa
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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 the intensity of the Poisson process, however in…
user32141
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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 $\operatorname{Skel}(\mu_1, \mu_2)$ is the distribution of the…
Alex
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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 the population times the convertion rate is too…
WNG
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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 looked into is simply subtracting the expected from…
cifrus dumbledore
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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 $\lambda_{x}, \lambda_{y}$ and $c$ is a constant scaling factor such…
Jack
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