Tagged Questions

2
votes
1answer
21 views

Fast generation of Pareto-distributed randoms.

I'm developing a library of routines for generating random numbers for simulations (it's on GitHub). I've included fast routines for normally distributed and exponentially distributed randoms, using ...
1
vote
0answers
24 views

Probability distribution of the product of two independent complex gaussian random variables

I have to calculate the pdf of $Z = X*Y$, where $X \in \mathcal{C}(\mu_x,\Sigma_x)$ and $Y \in \mathcal{C}(\mu_y,\Sigma_y)$, where $\mathcal{C}$ is a complex distribution. It can be assumed that ...
-1
votes
0answers
20 views

Random process x(t) =C and C is uniform over [-2,3]

I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with x(t) constant equal to 1/5. I see ...
0
votes
0answers
9 views

How can the distribution characteristics in different random sample sizes be known?

Here is my logic: A sample from a random pool (algorithm or natural) is known to have a certain distribution (normal, uniform, etc.) assuming both the sample and the pool (population?) are big ...
0
votes
1answer
36 views

Probability density function for the normalised sum of N random variables

I was wondering what the PDF looks like for Z= (1/N)*SUM(z_1+...+ z_n), where each z_i is computationally represented by RAND(). What is the behaviour of the PDF as N -> infinity?
2
votes
2answers
48 views

Generating a random number from a given distribution

I have a problem (a part of a Monte Carlo simulation) where I'm given the energy of an incoming particle, $\varepsilon$ and want to split this energy in two parts, randomly generating the fraction ...
1
vote
1answer
77 views

What is the distribution of $\min(r_1, r_2)$?

If I have 2 uniform random numbers $r_1$ and $r_2$ in $[0,1)$, what is the distribution of $\min(r_1, r_2)$? I have a problem I'm trying to get my arms around, and getting some context on this ...
1
vote
1answer
91 views

Generating random numbers with skewed distribution

I want to generate random numbers with skewed distribution. But I have only following information about distribution from the paper : skewed distribution where the value is 1 with probability 0.9 ...
0
votes
0answers
40 views

Random rectangles placement with minimal overlap and good dispersion.

I have a Big Rectangle (axis-oriented) containing a lot of Small Rectangles (with the same orientation of the parent and with a fixed size of 82x176 pixels). Now I have a Small Rectangle which is ...
0
votes
1answer
46 views

Random sampling from a conditional bivariate normal distribution

How does one draw a random sample $\begin{bmatrix} X_i \\ Y_i\end{bmatrix}$, $i=1,\ldots,n$ from the conditional distribution of a bivariate normal distribution, given specified values of the the ...
1
vote
0answers
65 views

What discrete distribution is completely determined by its mode and variance, is easy to sample, and has nice border properties?

I need to generate random ordered unranked trees that will be used to test some computer program. I'd like to incorporate some kind of control into the generation process, so that the generated trees ...
7
votes
1answer
150 views

Repeatedly Toss Balls into Bins

$n$ balls are randomly tossed into $m$ bins, each bin can hold $k$ balls. If a ball is tossed into a full bin (already has $k$ balls in it), it can be tossed repeatedly and randomly into the $m$ bins ...
1
vote
1answer
39 views

Finding a distribution for random number generation

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
0
votes
1answer
66 views

How to deal with non random data in statistical analysis?

I have a set of monthly water quality data, and I want to use them in a few statistical analysis (such as finding distribution or using in copula models) which require random variables as input. I ...
0
votes
1answer
189 views

Cumulative distribution function determine the random variable

I don't know that determine is the right word, but I try to explain. What I need to understand. :) So.. We know's that if a function fit this conditions: Monotonically non-decreasing for each of its ...
1
vote
1answer
31 views

Off-lattice Brownian bridges in R^3

Start at a point $(0,0,z_0)$ and take $n$ steps of unit length in a random direction (for each step) in $\mathbb{R}^3$. Let such a walk be valid if the position of the last step, and only the last ...
4
votes
3answers
366 views

Repeating something with (1/n)th chance of success n times

Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every ...
1
vote
1answer
158 views

CDF of standard normal random variable never actually is 0 or 1, right?

The CDF of a standard normal random variable is never actually 0 or 1, they only approach 0 and 1, correct?
3
votes
2answers
308 views

Trends in the distribution of reordered digits of Pi (OEIS A096566)

First let me try to describe in more details below the approach of "reordering" digits of Pi, which is used in OEIS A096566 https://oeis.org/A096566 and what I have done analyzing it so far. I am ...
1
vote
0answers
62 views

Are my steps to generate random values based on a given dataset correct?

I have a dataset of 100 cases. Each case has a class {I,II,III,IV,V} and a value A and V, each class appears exactly 20 times in the dataset: ...
1
vote
1answer
232 views

A problem on random variable in probability

I am a starter in maths. I am doing pretty good in all other topics except for probability. I don't know why I am always confused in it. My exams are nearby and I still cant solve simple problems. Can ...
0
votes
0answers
204 views

jointly stationary random process

If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is $R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$, which will be a constant, ...
0
votes
1answer
84 views

Inner product of two vectors with Rademacher random entries

I am lost with the signs cancellation. Please help me to calculate this inner pruduct. Let $a$ and $b$ be two $2m$ dimentional vectors such that their entries are Rademacher random variables and ...
0
votes
0answers
270 views

Prove that $aX + bY$ is a random variable for all $a, b$ in $\mathbb{R}$

Given $X$ and $Y$ as random variable, how to prove that $aX + bY$ as random variable for all $a, b$ in $\mathbb{R}$? (from Karr) $$ \{X + Y <t\} = \bigcup\limits_{r\in\mathbb Q}\{X < ...
0
votes
0answers
26 views

generating random density operators

A quantum (mixed or pure) state is a Hermitian, positive semi-definite operator with unit trace. I need to construct states by using available pseudo-random number generators (I personally use ...
0
votes
0answers
121 views

minimum of two non-central chi squared distributed random variables

[ Continuation to the question at maximum of two non central chi squared random variable ] Let $$s_i \sim \chi^2(k_i, \lambda_i), i\in \{ 1, 2\}$$ be two non-central chi-squared independent random ...
0
votes
1answer
153 views

maximum of two non central chi squared random variable

Let $$s_i \sim \chi(k_i, \lambda_i), i\in \{ 1, 2\}$$ be two non-central chi-squared random variables with $k_i$ degrees of freedom and $\lambda_i$ parameter of non-centrality I am wondering if ...
0
votes
2answers
130 views

Selecting numbers on a number line where distribution tends to cluster at one end.

Lets say I've got a number line from $1$ to $100$. I want to randomly select $20$ integer numbers from the number line. But I want the numbers to tend to come from say $1$-$50$, with only a few coming ...
0
votes
1answer
31 views

what should be the frequency distribution of the eigenvalues of a randomly generated hermitian matrix?

I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a ...
2
votes
0answers
42 views

Generate random numbers that are sums of hidden variables

I have $Y = A X$ where: $Y$ is an $m$ vector of random variables $X$ is an $n$ vector of random variables, uniformly distributed in $[0, 1]$ $m \ll n$, ($n$ ~ $m!$) $A$ is an $m \times n$ $0/1$ ...
0
votes
1answer
64 views

How to generate random samples from a ratio distribution?

I have two i.i.d. random variables $X$ and $Y$ and I want to generate a set of $n$ random samples from the distribution of the ratio between the two variables $Z=X/Y$. The pdf of $Z$ is described by: ...
0
votes
1answer
202 views

Expected value for the number of goals in a game

I'm trying to use odds data from bookmakers to estimate the expected number of goals in a game. We have these known facts: P(o4.5) = 0.573 P(o5.5) = 0.458 P(o6.5) = 0.279 P(o4.5) is the ...
1
vote
1answer
145 views

Help with a short paper - cumulative binomial probability estimates

I was hoping someone could help me with a brief statement I can't understand in a book. The problem I have is with the final line of the following section of Lemma 2.2 (on the second page): Since ...
1
vote
2answers
262 views

Probability, Joint Distributions, Standard Normal

I'm working through a course in Probability (2nd/3rd year) and would like to clarify some idea on joint distributions. Suppose for example we have independent random variables $(Z_1,Z_2)$ from a ...
1
vote
0answers
62 views

Bayesian Network: Probability distribution of random variable itself a random variable

I'm doing a thing with a Bayesian Network. There is a tool to analyze such networks and there is a "doubt" setting in [0, 1]. If the certainity of a prediction is less than that value, then it is ...
4
votes
2answers
193 views

What type of distribution would rand()/rand() produce?

If rand() is a function which produces a linearly distributed random number over a range not containing zero, then what type of distribution would rand() / rand() produce? I know it would center at ...
1
vote
0answers
573 views

Generate random number from Gaussian, Cauchy and Levy distribution [closed]

I am working on Genetic Algorithm. I have to generate random number from above three distributions. How can I do this?
2
votes
2answers
60 views

Expectation of random callers distribution

In a country with $N$ people, if everyone calls one random person in the country, what is the expected number of people who dont receive a call? If $f(m,n,a,b)=$Expected fraction of people who ...
0
votes
1answer
232 views

doubt on iid distribution vs uniform distribution

I am a bit confused when I read "iid distribution". It looks to me like what is called "uniform distribution" i.e. a distribution of probability that is constant in a range. Am I correct in thinking ...
1
vote
1answer
122 views

Signal extraction from multivariate normal

Define: $y= \theta + \varepsilon + a,$ where $a$ is a choice variable in a behavioral economic model, with equilibrium solution $a^e$, and $\theta$ and $\varepsilon$ are independently distributed ...
0
votes
2answers
115 views

Drawing random values from a distribution

If I have a set of $n$ elements, and I want to assign to each-one some value $\phi$, drawn at random from a distribution $f(\phi)$ such that $\int_0^1f(\phi)\;d\phi\:=\:1$ Does this mean that the ...
4
votes
2answers
413 views

Random number generation inside an interval based on cdf (Zipf and Exponential)

Consider for example the Exponential distribution with c.d.f. $F(x) = 1-e^{-\lambda x}$. $F^{-1}(x)$ would be inverse cdf (quantile function). If I generate y=F−1(x) with x uniformily distributed on ...
3
votes
3answers
211 views

Definition of random

Suppose that you has to guess given a set of numbers If they are random. The mathematical expectation Is there a definition of randomness that allow this prove/test? Is even possible? if so: How ...
1
vote
0answers
120 views

Normal distribution times a log-normal distribution

First of all, am I correct in assuming that given a normally distributed random variable A, and an independent log-normally distributed random variable B, the random variable A·B is normally ...
2
votes
2answers
132 views

Expected value of the product of the sum of a specific distribution

How can we find the value of the following term, $$ E[\prod_{i = 1}^{L}{\sum_{j = 1}^{K}{a_{ij}}}] $$ i.e., the expected value of the product of the sum of $a_{ij}$'s where $a_{ij}$ is a random ...
1
vote
1answer
129 views

bound of Erlang distribution

Is there any known polynomial bound of the Erlang distribution? I'd like to say that, given $k$ and $\lambda$ with probability p the r.v. is going to be less than some value x.
4
votes
1answer
150 views

Power Mean Random Distribution

I'm trying to find a the distribution for the power mean of $n$ random variables on $[0,1]$. I've got the arithmetic mean: $\frac{n}{(n-1)!}\sum_{k=0}^{\lfloor ...
1
vote
3answers
3k views

Sum of independent Binomial random variables with different probabilities?

suppose I have independent random variables $X_i$ which are distributed binomially via $$X_i \sim \mathrm{Bin}(n_i, p_i)$$. Are there relatively simple formulae or at least bounds for the ...