Questions tagged [poisson-distribution]

Question 1

I am trying to figure out how to calculate the probability of no overlap over a given observation window between events from two independent Poisson distributions. I found a bunch of helpful stuff ...

Question 2

I'm trying to prove the following bound on the centered Poisson$(\mu)$ moments: $$E|X-\mu|^k \le \sqrt{2} \left(\frac{k\mu}{e}\right)^{k/2} \cosh\left(\frac{k^{3/2}}{6 \sqrt{\mu}}\right)$$ I have ...

Question 3

As part of a course in branching processes, the teacher gave the following definition of a branching process: A stochastic process $X_t$ is called continuous-time branching process if there exists a ...

Question 4

I am trying to understand the proof given for the expectation of a Poisson random variable (see also here) $X \sim P(\lambda)$, when $X$ is transformed to represent a deductible: $$Z = \max \ (X-d,0)$$...

Question 5

Prove that if the sum of two independent infinitely divisible random variables is distributed according to the Poisson law, then each of the terms is also distributed according to the Poisson law. I ...

Question 6

Background: Working on Exercise 9.23 (a) in "Statistical Inference, 2nd Edition" by Casella and Berger. Simply speaking, the problem asks for a $1 - \alpha$ confidence interval for a Poisson ...

Question 7

An urn contains 2n balls, of which 2 are numbered 1, 2 are numbered 2, ... , and 2 are numbered n. Balls are successively withdrawn 2 at a time without replacement. Let T denote the first selection in ...

Question 8

i'm trying to complete this exercise in Cinlar's Probability and Stochastics (Cap VI 6.53b). Context. Suppose that $M$ is a Poisson random measure, with mean measure $\nu = Leb \times Leb$ i.e, the ...

Question 9

I am trying to work through Rasch's 1961 paper On General Laws and the Meaning of Measurement in Psychology, which is one of the seminal papers in the establishment of item response theory (IRT). I am ...

Question 10

On Wikipedia (https://en.wikipedia.org/wiki/Relationships_among_probability_distributions#Compound_(or_Bayesian)_relationships) I found the following statement, but no proof or reference to a proof: ...

Question 11

I'm actually interested in the derivation of the probability mass function of the Poisson distribution which just happens to have the term Eulor's number raised to the value of negative lambda. And ...

Question 12

In football, Expected Goals ($\texttt{xG}$) quantifies the likelihood of scoring from shots, where a team’s $\texttt{xG}= k$ is the sum of probabilities $\left\{ p_{1}, \ldots, p_{N} \right\}$ of $N$ ...

Question 13

I was solving the following problem from debore: At time t = 0, 20 identical components are tested. The lifetime distribution of each is exponential with parameter λ. The experimenter then leaves the ...

Question 14

I am reading the N. Ross's Fundamentals of Stein’s method. In the lecture note, section 4.3., he discussed the size-biased coupling. In the Corollary 4.14., when the size bias coupling is constructed ...

Question 15

The Poisson distribution of discrete random variable $X$ has the following useful property: $E[ XE[X] ] = E[ X(X-1) ]$ Does a similar property exist that is something like $E [XE[Y] ] = f$ (only X and ...

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Questions tagged [poisson-distribution]

Chance of Overlap Between Events from Two Independent Poisson Distributions

Prove $E|X-\mu|^k \le \sqrt{2} \left(\frac{k\mu}e\right)^{k/2} \cosh\left(\frac{k^{3/2}}{6 \sqrt{\mu}}\right)$, where $X\sim\text{Poisson}(\mu)$

Definition of a continuous branching process using Poisson random variable

Expectation of a Poisson with a deductible $Z = \max(X-d,0)$

Stability of the Poisson distribution in the class of infinitely divisible distributions

Connectedness of LRT Poisson Confidence Sets, i.e., Monotonicity of the LRT Poisson Acceptance Regions

Trying to solve an urn poblem

Equivalence between two expression for the queue variable.

Rasch's argument for the separability property of a Poisson distribution with expectation $\xi = \theta\sigma$

Show that if $X$ | $\mu$ $\sim$ Poisson($\mu$) with $\mu$ $\sim$ Gamma($m,\theta$), then $X$ $\sim$ NegativeBinomial($m, \theta /(1+\theta)$) [duplicate]

Can someone explain to me the concept/theory Taylor's Series to me simply? [closed]

Analytical methods to derive expected points from $\texttt{xG}$ differential using multidimensional integrals

Doubt in Possion and Exponential Distribution co-relation

Some basic questions about size bias coupling: Poisson approximation

Can I cheat to compute the product of two Poisson-distributed variables? [closed]

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