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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MGF of the absolute Value of a Skellam RV
I am trying to derive the moment generating function for the absolute value of a Skellam random variable $Skellam(\lambda_1, \lambda_2)$
Suppose $X_1 \sim Pois(\lambda_1)$ and $X_2 \sim Pois(\lambda_2)...
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Numerical evaluation of infinite sums
I am working with Skellam random variables and I would like to evaluate the CDF of the absolute value of a Skellam random variable in which both Poisson random variables have the same rate, $\lambda_1 ...
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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}, \...
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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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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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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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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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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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equivalent of t-test for Binomial/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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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$$(Z>0)$.
I know to compute the value $...
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From the bivariate poisson to the Skellam (or Poisson Difference) distribution
I am looking at how to calculate the Skellam distribution (https://en.wikipedia.org/wiki/Skellam_distribution) from the bivariate poisson distribution.
I understand that the Skellam comes from ...
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Testing if the difference between two count variables is different from zero
I have two count variables for several hundred thousand comparisons, one expected and one observed, and I would like to test if the counts are significantly different.
One possible approach I have ...
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Skellam distribution with dummies - consistent ML estimates?
The difference of two Poisson distributed random variables follows a Skellam distribution.
We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
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Does the noise term in a SDE need to be Gaussian?
Most of the examples I've seen for stochastic differential equations are of the form:
$$
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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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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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 ...
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