Questions tagged [distributions]
A distribution is a mathematical description of probabilities or frequencies.
7,938
questions
0
votes
0answers
11 views
Difference of independent random variables that is not unimodal
This paywalled article shows that the difference of two i.i.d. random variables is unimodal and symmetric if the distribution of the random variables is unimodal. Is there a non-unimodal distribution ...
0
votes
0answers
8 views
Approximation for Multivariate Gaussian
I am reading a paper, where they say they approximate a 2D multivariate Gaussian distribution by its second moment. The corresponding formula is the following:
$\displaystyle d(u) = \frac{1}{1 + (u - \...
1
vote
0answers
14 views
Marginal distribution of uniform distribution over sphere
Let $(x_1,…,x_n)$ be a random vector uniformly distributed on the $n$-dimensional unit sphere.
Is there a closed form solution for the joint distribution of $P(x_1, x_2)$?
1
vote
1answer
33 views
What is the probability distribution of the sum of random variables
I assume that the $Y_1$ and $Y_2$ are independent and can only take two values: $b$ or $c$. Further, I know that:
$$P(Y_1=b)=a \;\; \text{and} \;\; P(Y_1=c)=1-a$$
And similarly for $Y_2$:
$$P(Y_2=b)=a ...
0
votes
1answer
14 views
Cumulative Distribution Function of $S_{N_{t}}$ where $S_{N_{t}}$ is the time of the last arrival in $[0, t]$
I am confused on this problem. My professor gave this as the solution:
$S_{N_{T}}$ is the time of the last arrival in $[0, t]$. For $0 < x \leq t, P(S_{N_{T}} \leq x) \sum_{k=0}^{\infty} P(S_{N_{T}}...
0
votes
0answers
32 views
Example where $Cov(x_i, \epsilon_i) = 0$ and $E[\epsilon] =0$ yet $E[\epsilon | X] \neq 0$? [duplicate]
I'm told that it's possible that $Cov(x_i, \epsilon_i) = 0$ and $E[\epsilon] =0$ yet $E[\epsilon | X] \neq 0$ but I haven't been able to find an example. My professor proposed $\epsilon_i = x_i^2$ ...
0
votes
0answers
26 views
How to determine normal variability and understand whether other values may be clinically relevant?
I have been examining asymmetry in a new measure of brain pathology in a large sample of 300 clinically normal individuals. Many of these variables are normally distributed, some have a bit of a skew ...
0
votes
0answers
8 views
What features can be extracted from a probability distribution and how does the features change from baseline to different category/cases?
I have been looking online regarding feature extraction and I am looking at extracting features from probability distribution in order to understand the characteristics of the distribution. I know the ...
0
votes
0answers
17 views
Uniform distribution or Poissonian distribution?
Suppose I take a 6-sided dice and roll it N=1000 times; then I organise the measures in a histogram whose bins are the 6 faces and each of them contain the number ...
0
votes
0answers
7 views
How to calculate how frequently a number will fall inside a range in a flat distribution?
Basically assume I have a random number generator with a flat distribution from 1-100.
If I get repeated sample sets from this of variable size (sample_size), and I group the output into arbitrary ...
0
votes
0answers
22 views
What kind of distribution is this..? [closed]
I'm trying to plot the clustering coefficients distribution of some graph, and I got this histogram, it's the first time I see this kind of graph, may someone explain?
0
votes
0answers
27 views
Cental limit theorem, Chebyshev's inequality, and convergence of distributions through rescaling
I've been thinking about this issue for a few days and although read some of relevant questions on this site, still couldn't get it off my mind.
Suppose we have $n$ i.i.d random variables $X_i$ with ...
2
votes
1answer
54 views
Residuals in Generalized Pareto Distribution
I'm learning generalized Pareto distribution for fitting extreme value data. I came across an R package evir that is able to plot residuals. Residuals from a GPD ...
0
votes
0answers
30 views
+50
Projecting a distribution onto an arbitrary norm
So we represent the Dirichlet distribution as the projection of the $d$ independent gammas (on $R_+^d$ onto the unit simplex, and we arrive at that through the $L_1$ norm. That is, divide ${\bf x} \...
0
votes
0answers
22 views
How is this given distribution specified? What is the PDF?
If you say that
$$
Y \sim \sigma^2 \chi^2(n-1) / (n-1)
$$
what does that mean then? Is it just a scaled version of the expression of the pdf?
0
votes
2answers
25 views
Trying to find a proper regression model for non-negative dependent variable
I'm trying to build a regression model predicting passenger numbers on trains using a number of different variables. Originally my plan was just to do a linear regression, but the issue is the model ...
2
votes
2answers
115 views
Probability distribution of a random variable
The table below shows the number of ice creams brought and the number of customers brought that number of ice creams.
...
0
votes
0answers
23 views
Chi Square test of normalised data and fit
I have done lots of data fits in the past, but this is the first time I approach with this kind of problem and I don't know what is the way to proceed.
This is my problem: I have measured the time ...
0
votes
1answer
60 views
Mapping a wrapped Cauchy distribution to a uniform distribution?
I'm investigating model mismatch and have a wrapped Cauchy distribution of
f(x,p) = (1-p^2)/ (2*pi*(1+p^2-2p*cos(x)))
Is there a way to map this to a random ...
0
votes
0answers
9 views
How to model distributions of correlated variables and pick from it for montecarlo simulation
I have time data. Different variables with some degree of correlation among them. What I would like is to pick a sample from the distribution of those who have no or low correlation with the others ...
-2
votes
0answers
15 views
Determine regression confidence interval from advertising and sales [closed]
Attempt:
xi=20
Syx=110.9
y^=-44.5+15.14x
=-44.5+15.14(20)
=258.3
b1=-51
c=98%
ybar i +- t(alpha/2) Syx sqrt(1/n + (xi - xbar)^2 / (sum of (xi-xbar)^2))
=330....
-2
votes
0answers
21 views
Find confidence interval for the average y value using t table distribution [closed]
Attempt:
df=16-1=15
a=0.05
t=2.131
0.05/2=0.025
ybar i=97334.467
t=2.131
Syx=1605.3325
n=16
xi=214k
xbar=194994.4
ybar i +- t(alpha/2) Syx sqrt(1/n + (xi -...
3
votes
1answer
46 views
Change of metric for probability density vs for probability
When one changes the variable in a probability density function, one must account for the jacobian to ensure the elementary probability is constant (eg Derivation of change of variables of a ...
0
votes
0answers
18 views
Applications of Markov, Chebyshev, Chernoff and Hoeffding inequalities [closed]
Can someone help me. I want some examples of applications of the Markov, Chebyshev, Chernoff and Hoeffding inequalities in known distributions such as Uniform, Exponential and Normal distributions.
1
vote
0answers
34 views
A question about fisher's z transformation detail of his paper published in 1921
Typically, people will use Fisher's z-transformation (arctan) to turn the r into a variable that is approximately normally distributed. When I look though his paper published in 1915(https://www.jstor....
1
vote
1answer
31 views
Comparisons of distributions: How to deal with discrepancies between visual impression and statistical tests (K-S, ranksum)?
I'm having some doubts how to properly compare my data (because of visual discrepancies), represented as histograms.
Here's an minimal and representative example, illustrating the data:
I measure BMI ...
1
vote
2answers
43 views
How to match the distribution of one dataset when subsampling from another?
I have two datasets that measure the same variable under different conditions. The first dataset (d1) is much larger (9,000 observations) than the second dataset (d2; 900 observations).
A histogram of ...
2
votes
2answers
73 views
Fitting a distribution like exponential but with always negative $\frac{d^2}{dx^2} \log \text{pdf}(x)$
I have some continuous data in the domain $[0,\infty]$ which I have physical reason to believe is almost, but not quite exponentially distributed. The difference between my idea of a distribution and ...
0
votes
1answer
31 views
Convergence Distribution and Probability [closed]
Suppose that $|X_n - Y_n|$ converges in probability to 0, and that $X_n$ converges in distribution to X. Show that $Y_n$ converges in distribution to X.
Thanks in advance.
0
votes
1answer
21 views
Deriving distribution for multiplayer game results from pairwise probabilities
Suppose there is a game with three participants: Player A, Player B, and Player C. One player will finish in first place, another in second place, and another in third place (no ties allowed). I know ...
2
votes
0answers
19 views
Do Particle Filters actually approximate the posterior distribution?
Im reading a tutorial paper about particle filters (Link) in which it is stated that as the number of samples tends to infinity the approximated posterior density given by
$p(x_k|z_{1:k}) \approx \...
1
vote
1answer
82 views
+50
How to sample from different datasets such that they have similar distributions?
I have data from multiple datasets with the boxplot given below
In the above figure, I have data from 7 different datasets. I am looking for a sampling strategy without replacement such that samples ...
1
vote
1answer
35 views
What is the MLE of the Continuous Bernoulli distribution?
The continuous Bernoulli is a distribution I recently discovered. What the maximum likelihood estimate of the distribution's parameter? I'm struggling with the normalizing constant.
0
votes
0answers
24 views
Gaussian distribution with Kronecker product in the Covariance matrix
Assume we have two correlated multivariate Gaussian random variables $\mathbf{d_1}$ and $\mathbf{d_2}$ both distributed as $\mathcal{N}(\mathbf{0},\mathbf{R})$. We also know that $\mathbf{d_1}-\mathbf{...
1
vote
0answers
27 views
Generate data that matches a frequency distribution while preserving the original spatial structure
I am dealing with a 3D array containing values representing the "importance" of each voxel. For my analysis, I would like to synthesize n new arrays from my original array to have a ...
2
votes
1answer
72 views
R Confidence Intervals for quantiles from Generalized Lambda Distribution
I'd like to compute confidence intervals in R for quantiles from generalized lambda distribution.
Steve Su (2009) introduces below 2 ways to calculate confidence intervals. I think I could understand ...
3
votes
1answer
85 views
Expected value of (continous) exponential distribution proof/derivation
I started with the following exponential distribution:
$$ f_{exp}(x;\lambda) = \lambda\, e^{-x\lambda} \quad \forall\, x \in \mathbb{R}^+ $$
I know from internal courseslides and wikipedia that the ...
0
votes
0answers
23 views
Hypothesis testing — time between two actions
I am a complete newbie to statistics, and have gotten stuck on a difficult real-world problem.
What I'd like to do is demonstrate confidence that, for a set of < 50 observations of two actions, the ...
1
vote
0answers
27 views
What is the distribution of the time-to-ruin for a gambler's ruin problem that allows “pauper bets”?
In another question on this site I have derived the distribution for the time-to-ruin in the gambler's ruin problem where the wealth of the gambler follows a discrete-time random walk. In this ...
0
votes
0answers
13 views
Finding the (approximate) beginning of a novel based on the distribution of newline characters
I am working on a NLP project in the domain of literature. My dataset consists of a collection of books but most of the books are prepended with meta-information such as the copyright, the outline, ...
0
votes
0answers
13 views
Prove that the conditional distribution of a normal random variable is also normal random [duplicate]
How to prove the claim that the conditional distribution of a normal random variable is also normal random? And how to think it intuitively?
2
votes
0answers
12 views
Are sample means ordered by strict second-order stochastic dominance throughout the support?
Consider random variables $X_1,X_2,\dots$.
Each $X_i$ is independent and identically distributed on $[0,1]$ with a cumulative distribution $F$ that has a positive density $f(x)>0$ throughout the ...
1
vote
1answer
25 views
Use of Change of Variables (in probability distributions) in Machine Learning
I am learning about machine learning from a probabilistic perspective via Kevin Murphy's so far fantastic Textbook (2021) Machine Learning - Probabilistic Machine Learning - An Introduction. I'm in ...
0
votes
0answers
13 views
scipy norm.pdf return probability of a particular outcome [duplicate]
The Probability of a particular outcome is always zero, but Scipy's norm.pdf() function returns the probability value of a particular event.
For example onlinestatbook.com/2/calculators/normal_dist....
3
votes
1answer
44 views
Gaussian Distribution: How to calculate the Cumulative Distribution Formula (CDF) from the Probability Density Function (PDF)? + Error Function? [duplicate]
I understand that we can calculate the probability density function (PDF) by computing the derivative of the cumulative distribution formula (CDF), since the CDF is the antiderivative of the PDF.
I ...
0
votes
0answers
20 views
The relationship between two probability mass function (poisson distribution)
There are two cylinder bottles with radius r1 and r2 was on the ground to collect rain drop.what is the relationship between the probability mass function of two bottle?
I guess that each of the ...
1
vote
1answer
29 views
Which assumptions should be checked for regression tree to validated model?
I am working with regression tree. I have four predictors. There is a exponential relationship between predictor and dependent variable. But after building predictive model I cannot understand whether ...
0
votes
1answer
28 views
Analyzing lie in a cardgame
We are playing a card game in which cards can be of three categories — good, bad, neutral.
A player draws a variable number of cards $n$ and then states the composition of his cards. The player does ...
1
vote
0answers
35 views
How to find outlier data points on a log-gamma distribution?
I’m dealing with a correlation network (only positive values) with M nodes where I’ve grouped features by N categories and ...
1
vote
0answers
36 views
Likelihood loss function for finite support probability distribution in Neural Networks
I have managed to reproduce solution from this article and made it work for my dataset.
Instead of making a Neural Network output a scalar (regression), we make it output two parameters of a ...
