0
votes
1answer
20 views

Test for Validity of Artificial Samples

I have a model that actually is learned from some observed samples. Then I use the model to generate several artificial data. My question is: Which test should I use to test if the data is of the ...
0
votes
1answer
28 views

the random heights of north american women

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. A random sample of four women is selected. What is the probability that the ...
0
votes
1answer
13 views

Generate samples from other samples

Given a family of continuous random samples $(x_i)_{i \in I}$ that approximate some unknown probability distribution. How can I generate more samples that fit to the same unknown distibution? ...
0
votes
0answers
20 views

Derivation of F distribution

Prove that the PDF of Snecdor's F distribution, given by: $$F=\frac{U/n_1}{V/n_2}$$ Where $U=\chi^2(n_1)$ and $V=\chi^2(n_2)$, is given by: ...
0
votes
0answers
46 views

Asymptotic/sampling distribution

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
1
vote
1answer
35 views

The radial part of a normal distribution

I am reading a paper that asks me to sample $s_i$ from a distribution like this: $s_i \sim (2\pi)^{-\frac{d}{2}}A^{-1}_{d-1}r^{d-1}e^{-\frac{r^2}{2}}$ "Here the normalization constant $A_{d−1}$ ...
1
vote
1answer
49 views

Uniformly distributed points over the surface of the standard simplex

I would like to generate points that are uniformly distributed over the SURFACE of a standard $k$-simplex ($k$ dimensions, $k+1$ vertices). One way to efficiently generate points that are uniformly ...
0
votes
0answers
49 views

Sampling uniformly from n-sphere using spherical coordinates

It has been explained here why sampling from n-sphere is not achievable with naive parametrization. And it explains how to correct it for 3 dimensions. Can somebody please guide me what is the correct ...
1
vote
0answers
25 views

Relation with $F$ distribution and $t$ distribution

If $X\sim F_{n,n}$ , then show that $$\frac{\sqrt n(\sqrt X-\frac{1}{\sqrt X})}{2}\sim t_n$$
0
votes
1answer
137 views

Gibbs sampling to produce posterior pdf

Suppose we have the following classical normal linear regression model: $$y_i = \beta_1 x_{1i} + \beta_2x_{2i} + \beta_3x_{3i} + e_i$$ where $e_{i} \sim iid.N(0, \sigma^2)$ for all $i = 1, 2, ...
3
votes
1answer
75 views

Is it possible to sample the Dirac delta function?

The Dirac delta function can be a probability measure with the unit/Heaviside step function as its cumulative distribution function. Is it possible to sample such a distribution? If a random variable ...
1
vote
1answer
58 views

An Exercise of noncentral $\chi^2$ distribution.

Let $Y_1,\ldots,Y_n$ be independent random variables with $Y_k$ distributed as $N\sim(a_k,\sigma^2)$, and $\bar Y=\sum_{k=1}^{n}\frac{Y_k}{n}$ denote the sample mean, $S^2$ denotes the sample ...
1
vote
1answer
64 views

cumulants of non-central $\chi^2$ distribution

Cumulant generating function is defined by logarithm of moment generating function. $$K_X(t)=\log M_X(t)$$ Let $X$ be a non-central $\chi^2$ variate with parameters degrees of freedom, $n$ and ...
0
votes
0answers
63 views

Twist on classic Weighted hypergeometric distribution problem

I am looking to model a situation, which I believe can be approximated as follows...it seems on the surface an extension / twist on the classic biased urn problem...any help much appreciated. We have ...
0
votes
0answers
54 views

Convex Hulls in Complex Vector Spaces?

I am trying to generate uniform samples over the convex hull of a set of points that are defined by a set of corresponding vectors with complex entries. In other words, I am trying to generate samples ...
3
votes
0answers
110 views

Problems sampling from a $pdf$ over $SO\left(3\right)$

I have a probability density function over $SO\left(3\right)$, which I am trying to sample from. The $pdf$ is given as a generalized fourier series: $$ f\left(\omega,\theta,\phi\right)=\sum ...
0
votes
2answers
53 views

Sample $x$ from $g(x)$

I got confused with all this randomness and probability functions. I was trying to implement the rejection sampling method which (apparently) is really simple. I was reading from Rejection Sampling in ...
0
votes
1answer
204 views

please prove the following proof related to F distribution.

Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively. Then show that ...
2
votes
3answers
378 views

estimate population percentage within an interval, given a small sample

Given a small sample from a normally-distributed population, how do I calculate the confidence that a specified percentage of the population is within some bounds [A,B]? To make it concrete, if I ...
1
vote
1answer
259 views

How to sample from a Gamma distribution with shape not integer

I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer. However, I found everywhere the method to sample from a Gamma with an integer shape ...
1
vote
0answers
112 views

generating a binomial distribution

I'm trying to sample from a data set using a binomial distribution with parameters p and n. Implementation-wise, I follow these steps I generate an array containing the values of the cumulative ...
2
votes
0answers
99 views

How to sample from a product-of-sums distribution?

$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution ...
0
votes
1answer
56 views

Independence of Random samples

I have a some questions that have been bothering for a while now. First, how does one obtain the joint probability distribution function of $X_{1},\cdots ,X_{n}$? Would it be $\prod\limits_{i=1}^n ...
5
votes
2answers
302 views

Collisions in a sample of uniform distribution

Asked at a Microsoft interview: Assume you have a uniform distribution (can be discrete or continuous) of size X and you randomly select a sample of size Y. 1) What is the probability in terms of X ...