All Questions
Tagged with pr.probability st.statistics
1,135 questions
2
votes
1
answer
419
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Approximation of the law of a stochastic process
Hello Dear fellows,
I thank you in advance for your help and ideas.
I have just read an article and want you to help me understand the rational behind a part of it.
We have two processes $v_t$ and $...
- 375
0
votes
1
answer
207
views
Copulas and marginals thereof
Hello everyone,
I recently became aware of the existence of the copula concept.
So, I have been reading a few things about copulas lately, but
I cannot seem to find information on the following ...
- 103
1
vote
1
answer
294
views
Stability of discrete queue (new twist)
Hi, I am new to queueing theory. I am interested in a question that I feel should be fairly basic, yet I haven’t really found a clear solution to it. Hopefully somebody here can help me.
We have a ...
- 501
1
vote
0
answers
177
views
Conditioning over Conditional probability? (also: $\phi$-mixing sequences)
For two sub $\sigma-$fields $\mathscr{F}$ and $\mathscr{G}$ of a probability space $(\Omega , \mathscr{A} , P)$ we define $\phi$ mixing as follows:
$$
\phi(\mathscr{F},\mathscr{G}) = \sup \{ |P(G|F) - ...
- 11
0
votes
1
answer
275
views
Conditional distribution of the modulus of the output of AWGN channel given the modulus of the input
Hi everyone,
I will be too happy if anybody help me find a solution for the following problem.
In fact, I have a big problem that I could not solve it for weeks.
Assume that we have we have two ...
- 197
1
vote
2
answers
175
views
is there an interpretation to the inverse of $I-M$ in multitype branching process, where $M$ is the mean matrix?
Assume we have a multitype branching process, i.e., we have a mean matrix $M_{ij}$ and $M_{ij}$ is the expected count of generating $j$ from $i$ in one time step, i.e.:
$M_{ij} = \sum_{r} n(r,j)P(r | ...
1
vote
3
answers
291
views
Is any bias introduced from initial clustering
I hope this is an appropriate forum for this question, and I asked on math.stackexchange as well. If it doesn't belong, I don't mind closing this. If my questions is not clear, please just let me ...
- 115
1
vote
1
answer
221
views
Estimating the Distribution of a Very Large Population of Known Size and Unknown Variance
I would like to estimate the distribution of a very large population of known size but unknown mean and variance. I cannot assume anything about the underlying distribution. The values of observations ...
- 11
0
votes
0
answers
112
views
Markov renewal process with failure?
I hope this question is not too elementary for this site, and that it contains a sufficient degree of detail.
I have a problem where I want to model sequences of variable length $\boldsymbol{e}_i = (...
- 101
3
votes
0
answers
108
views
"Soft" Voronoi cells or statistical criterias
It is probably some basic statistics question, but...
Informally 1: How to choose "criteria", such that it will guarantee that error decision probability is less than "epsilon", and maximize ...
- 24.9k
5
votes
0
answers
154
views
Positive estimator
Suppose that one knows how to generate (independent) random samples $X_1, X_2, \ldots$ distributed as the random varable $X$ with $\mathbb{E}[X]=\mu \in \mathbb{R}$. It is then easy to construct an ...
- 2,133
3
votes
3
answers
316
views
Finding a distribution family that is preserved under mixture.
Consider the following
$f_{t+1}(z)=p_{12} f_{t}(z/A)+ p_{21} f_{t}(z/B)+p_{22} f_{t}(z/(A+B))$, where $A$, $B$, and the $p$'s are constants and $f_t$ is a probability distribution. Are there any nice ...
- 457
3
votes
0
answers
206
views
representing vine copulas
Vine copulas is a way to represent multidimensional distributions (n-densitys)
as a product of the n 1-marginal densities and a product of (n choose 2) bivariate copulas, where som of them are ...
- 2,600
1
vote
0
answers
236
views
density for Gaussian gram matrices
Let $Z \sim \mathcal{N}(0,\Sigma \otimes I)$ (so the columns of $Z$ are distributed $\mathcal{N}(0, \Sigma)$) and $A = Z'Z.$ Is there a name for the distribution on $A$? Is the density known?
- 922
1
vote
0
answers
101
views
calculating how much to oversell given an acceptable risk (statistics)
I have a shared resource with a finite capacity (let's say 100), and I have usage data (2 hours average of samples taken each 20 seconds). I accept a risk of 10% per year to reach the capacity.
...
0
votes
2
answers
339
views
Efficient Method for Calculating the Probability of a Set of Outcomes?
Let's say I'm playing N different independent "games". For each game, I know the probability of winning, the probability of tying, and the probability of losing.
From these values, I've also ...
- 41
1
vote
1
answer
340
views
for a natural exponential family, A is the cumulant function of h?
Reading "Monte Carlo Statistical Methods" by Robert and Casella, they mention that if
$f(x) = h(x) \exp(\langle \theta, x \rangle - A(\theta))$
defines a family of distributions for $X$, parametrized ...
- 922
2
votes
1
answer
380
views
Parity, Balls and Boxes
Start with a distribution $\mu$ on [n], and drop m balls into these n+1 slots independently and according to the distribution &mu. That is, we have iid random variables x 1 through x m ...
- 263
0
votes
1
answer
284
views
The density of x_1^n+x_2^n where x_i are Gaussian
We define a process $\chi_k^n=\sum _{i=1}^k x_i^n$ where x_i are iid gaussian processes.
I try to find the distribution of $\chi_k^n$. If k=1 then we get $f(x^n=y)=\frac1n y^{\frac{1-n}{n}}\exp(-y^{2/...
- 1
3
votes
0
answers
143
views
finding rank-3 tensors compatible with a rank-2 tensor projection
I am interested in the following problem: Consider a rank-3 symmetric tensor $\boldsymbol{\sigma}$ with $\sigma_{ijk}$ where $\sigma_{ijk}$ can be 0 or 1, and the symmetry is with respect to any ...
- 41
0
votes
0
answers
319
views
Estimating a multinomial sum
I have the following sum
\begin{equation}
\sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\tau-r_1-\dots -r_\lambda} (\Lambda-\lambda)^{\tau-r_1-\dots-r_\lambda}
\...
0
votes
1
answer
107
views
Can one combine (join) probabilities from 2 aspects of a related process?
Consider 2 related aspects of a process for prices in a financial market:
time &
return.
Time
Say I've identified a distribution that reasonably models the occurrence of the lengths of price ...
- 111
3
votes
0
answers
171
views
Iterated Kumaraswamy distributions
The Kumaraswamy distribution has cdf $F(x;a,b) = 1-(1-x^a)^b$.
Does anyone know any formulas or properties relating to iterations of this on itself, meaning
$$ F_i(x;a,b) = 1-(1-F_{i-1}^a)^b$$
If ...
- 233
4
votes
0
answers
497
views
A Local CLT with large variance
For n an even integer, $0 \leq i \leq$ ${n} \choose{j}$, $1 \leq j \leq n$ let $X_{i,j}$ be a
random variable taking values $\frac{n}{2}-j,0,j - \frac{n}{2}$ with equal probability. Let $S_{n}$ be ...
- 263
3
votes
0
answers
125
views
Is a parametric family which is universally consistent for multiple quantiles impossible?
Suppose I am dead-set on using Bayesian inference on independent and identically distributed data, but I'm lazy and insist on using a parametric likelihood function come what may. I'd be reassured to ...
- 2,791
1
vote
0
answers
61
views
Distribution for probability of an incorrect inference based on a comparison of only two samples?
I'm trying to demonstrate the problems of how taking a sample and assuming it reflects the population accurately can be problematic.
Imagine say an urn with some large number of balls, black and ...
- 11
3
votes
1
answer
320
views
Joint Law with 2 marginals and marginal of the spread
I have a question for you and thank you in advance for your answers and ideas.
Let us suppose that we have the marginal distributions of two r.v X and Y, and also the law of X-Y (or any linear ...
- 375
3
votes
1
answer
367
views
Random generation of subsets using conditional probabilities
Edit: Rewritten with motivation, and hopefully more clarity.
I'm building a site for a card game called dominion. In it, people build 'decks' of 10 distinct cards from a set of (currently) ...
- 203
2
votes
1
answer
250
views
Expectation of RVs with Poisson-type decay
I need to bound the expectation of a nonnegative random variable that satisfies a Poisson-type tail bound:
$\mathbb{P}( X \geq t ) \leq \min( d \cdot (\frac{a}{t} )^{t}, \ 1)$ for $t > 0$
where $...
- 23
2
votes
1
answer
254
views
Brownian Bridge under observational error
Suppose that $Z_t$ follows a simple discrete random walk $Z_t=Z_{t-1}+e_t$ , where $e_t$ are a bunch of uncorrelated normal variables with arbitrary variance sigma^2, and that there are observations ...
- 457
2
votes
0
answers
90
views
Limiting distribution of the cardinal of a Markovian set
Let $S_1=\lbrace u_1 \rbrace$ where $u_1$ is a random uniform drawing on $[0,1]$. To build $S_{n+1}$ draw $u_{n+1}$ uniformly on $[0,1]$ (independently from previous draws) and draw $v_{n+1}$ ...
2
votes
1
answer
178
views
Maximal inequality over two indices
In Freedman's series of 3 books on Markov processes, I find that I keep on running into terms like:
P[$\max_{0 \leq s \leq 1, s \leq t \leq rs}$ | B(t) - B(s) | > $\epsilon$]
in the background of ...
0
votes
1
answer
207
views
Correlation of Statistical Tests
Suppose I have a sequence $\{x_i\}_{i=1}^\infty$ of zeros and ones. I want to test if they are randomly generated according to a conjectured scheme (the example to keep in mind is that they are ...
- 1,588
0
votes
0
answers
138
views
Why do I not use post hoc tests with a 2 x 2 factorial?
I know this is an obvious answer. I am probably over thinking what I'm doing, but I cannot recall. Does it have to do with not having enough variables to compare the various means?
0
votes
0
answers
37
views
Compatibility of 2-copulas
An $n$-copula is the joint distribution function of a distribution on $[0,1]^n$ with uniform marginals. A family of 2-copulas $(C_{i,j})_{i<j\leq n}$ is compatible if there exists an $n$-copula $\...
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