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Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

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Inequality of Probability

This problem is from Matrix Analysis for Statistics by James R. Schott. Problem. Show that if $x$ and $y$ are two independently distributed random vectors with $x\sim{\rm Normal}(0,\Omega_1)$ and $y\sim{\rm Normal}(0,\Omega_2)$, such that…
Bernard Pan
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The PDF of Euclidean distance between a point uniformly distributed and several points from Poisson Point Process(PPP)

I've met a problem to solve. In Spherical coordinate system, a point A follows uniform distribution in the space, which is a part that the spherical cone with radius U1 minus the one with radius U2(from the centre of sphere O). Under the O, there is…
peng
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what will be the procedure to prove the following relationship?

Let $U$ follows standard uniform distribution , that is, $U\sim U(0,1)$ and $X$ follows Pareto distribution, that is, $X\sim Pa{(\alpha,a,h)}$ where , $a=$location parameter ; $-∞0$ $\alpha=$shape parameter ;…
time
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PDF of a squared L2-norm of a vector that is the difference between two uniformly chosen vectors on unit circle

Let $Z = ||X-Y||_2^2$ where $X$ and $Y$ are two points selected uniformly-randomly and independently on the unit circle. I'm trying to find the PDF of $Z$. It is very similar to this question but answers over there are too clever for me. So here is…
Mustafa Aydın
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Can an x value in a Bernoulli distribution take on any other value than 0 or 1?

I am puzzling over the parametric statement for the Bernoulli Distribution $p(x \vert \theta) = \theta^x(1-\theta)^(1-x)$ Can X take on other values than 1 and zero?
Kirsten
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Average number of tries to get an X number of unique elements

Assuming that we have the following loot table Type Chance Number of unique elements common 30.00% 21 Uncommon 30.00% 27 Rare 20.00% 32 Ultra 15.00% 14 Epic 5.00% 10 How can I calculate the average number of tries to get X…
Kahel
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Summation of independent discrete random variables?

We have a summation of independent discrete random variables (rvs) $Y = X_1 + X_2 + \ldots + X_n$. Assume the rvs can take non-negative real values. How can we find the probability mass function of $Y$? Is there any efficient method like the…
Mas
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Question on Poisson Processes

Good evening, I am sort of stuck in one problem of Poisson Processes and I hope I could get some help (no it is not a homework). Suppose that the customers arrive at the ticket booth independently. Let $T_{j}$ be the arrival time at the j-th…
Heber
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Distribution of $N$ balls numbered from $1$ to $N$ without replacement

Same question as "Distribution of $N$ balls numbered $1$ to $N$ with replacement", but without replacement: An urn contains $N$ balls numbered $1,2,3,...,N$. I draw at random $n$ balls, one by one WITHOUT replacement. Let $X$ the smallest number,…
Jean-Pierre
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Distribution of N balls numbered 1 to N with replacement

An urn contains N balls numbered 1.2.3...N. I draw at random n balls, one by one with replacement. Let X the smallest number, the largest Y and S the sum of all the n numbers How to compute: -the probability P(X=x,Y=y) that X=x AND Y=y -the…
Jean-Pierre
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Prove $E\left[^k\right]$= $\frac{r}{p}E\left[(Y-1)^k\right]$ for negative binomial distribution

Given $X\sim\text{NB}(r,p)$ and $Y\sim\text{NB}(r+1,p)$, how do I prove the above identity?
user761921
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Distribution of the entries of a matrix, which is the product of two normally distributed matrices

This is not a homework question, but a small part in understanding a research paper. Let $A$ and $B$ be two matrices, where $A_{ij} \sim \mathcal{N}(\mu_1, \Sigma_1)$ and $B_{ij} \sim \mathcal{N}(\mu_2, \Sigma_2)$, respectively. What can we say…
Jalaj
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Class of Probability Distribution with slowly increasing hazard rate?

I am looking for probability distributions with CDF $F$ which satisfy the following property: for all $\varepsilon > 0$, \begin{equation} \frac{F(h+\varepsilon) - F(h)}{\varepsilon}\frac{1}{F(h+\varepsilon)} \to g(h)~, \end{equation} where $g(h)…
is it normal
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Are the following distributions special forms of known distributions?

In my research I have derived the following distributions. I am curious if they could be perhaps forms of well-known distributions. I have looked at the list of distributions here but have not gotten any hits. I'd be glad for any insights the…
dsmalenb
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What distribution does the number of inversions of an array of n distinct numbers follow

An array of n distinct numbers. I want to know what distribution its number of inversions follows. I used Mathematica to simulate and initially felt that it obeyed normal distribution: << Combinatorica` data =…
Please correct GrammarMistakes
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