Questions tagged [discrete-distributions]
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128 questions
1 vote
0 answers
72 views
Capping a discerete probability distribution [closed]
I have a discrete probability distribution for the selection probability of $N$ "direction vectors" where the selected directions will be used in a Monte Carlo simulation. But sometimes the ...
- 33
0 votes
0 answers
82 views
Which test is better for evaluating goodness-of-fit for a dataset of millions of discrete values following Zipf distribution? KS test or Chi-square?
I have a dataset of 40 million discrete values, whose histogram follows a Zipf distribution with the following statistical parameters: Minimum = 1, Maximum = 1738, Mean = 2.16, STD = 16.50, P95 = 4, ...
- 1
6 votes
2 answers
126 views
Draw a negative covariance of $Y_1$ and $Y_2$
I have the following joint distribution for $y_1$ and $y_2$: $Cov(Y_1, Y_2) = -\frac{2}{9} \lt 0$, i.e. it has a negative slope, but I'm struggling how to draw those values in Cartesian coordinates. ...
- 235
3 votes
1 answer
95 views
Probabilities related to distributing $n$ items into $m$ containers
An ice-cream truck stops at a park and randomly distributes 10 ice-cream cones among 20 children. What is the probability that a randomly selected child receiving no ice-cream cone? Exactly one ice-...
- 133
4 votes
1 answer
154 views
Jeffreys' prior for a discrete parameter space
The following question speaks about binomial distribution with known probability $p$, but unknown number of trials $n$. Binomial confidence interval over the number of trials Trying to think of how a ...
- 93.9k
0 votes
1 answer
59 views
Bernoulli Factory for mean of discrete variable
Suppose $Z$ is a discrete random variable on $\mathbb{N}$ with $P(Z=z)=p_z$ unknown, and $\mathbb{E}[Z]=p$ where $0\leq p \leq 1$ a.s. We can simulate observations of $Z$. Is it possible to construct ...
0 votes
0 answers
63 views
Quantification of KL divergence error for approximating a distribution over discrete random variables
I would like to know the following which has been stated in some literature, but never explicitly proved Consider a setup consisting of a binary vector of random variables of length n say $\vec{v}=(...
- 1
8 votes
3 answers
458 views
CDF of a discrete random variable piecewise-constant?
In my script, it says: Given $X$ is a discrete random variable, $\Bbb P(X\in D)=1,D=\{a_1,a_2,\ldots\},p_i:=\Bbb P_X(\{a_i\})>0,\forall i\ge1,$ we have $F_X(x)=\sum\limits_{a_i\le x}p_i,$ which ...
- 183
3 votes
2 answers
256 views
Estimating Smooth Density Field from Limited Sampled Data
I want to estimate a “density field”, specifically $P(y|x, m)$, for binary labels $y$ associated with 2D points characterized by spatial coordinates $m$ and additional spatio-temporal features $x$. ...
- 81
0 votes
0 answers
144 views
What is this hybrid(mixed) random variable’s variance?
X ∼ Uniform(a,b), a<b (Discrete) where f(x)=1/n where n=b-a+1 and Y ∼ Uniform(c,d), c<d (Continuous) where g(y)=1/d-c. X and Y are independent. Let z = x - y. I was able to find the E(Z), ...
- 103
1 vote
1 answer
179 views
Calculation of multivariate probability mass function
How to calculate the following multivariate probability mass function: $P(X_1-X = n, X_2-X = n, ..., X_{N-1}-X = n)$ Where $n$ and $N$ are positive integers, and $X_i$ and $X$ are iid random variables ...
- 75
0 votes
0 answers
77 views
Probability of 2 discrete samples coming from same distribution
I would like to know how to calculate the probability that 2 discrete samples come from the same distribution, and if so, which one is the distribution they are coming from. Let's say we have 3 ...
- 314
2 votes
1 answer
124 views
Existence of Distribution with Given Multivariate Marginals
Consider discrete random variables $X_1,\cdots, X_n$, and let $D$ be their joint distribution. For each subset $S\subseteq[n]$ let $D_S$ be the marginal distribution $(X_i)_{i\in S}$. Fix $k<n$. ...
- 121
1 vote
0 answers
103 views
Exact Likelihood ratio statistic for discrete distribution
Suppose that the random variables in a sample $Y_1, Y_2, \ldots, Y_n$ are iid with values in $[0,1]$, and that an investigator knows that the underlying probability density $f_Y(y)$ has the form $f_Y(...
- 143
0 votes
0 answers
54 views
Understanding the Difference between Bernoulli Distribution and Binomial Distribution
In my recent study, I conducted 67 measurements and recorded 11 successful outcomes. Now, I am seeking clarification on the appropriate formulas to calculate the measurement error. Should I use the ...
- 101