Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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68 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 ...
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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 ...
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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 \...
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1answer
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convolution and deconvolution of random variables of different dimensions

Preliminary: Let's say we have $Y=X+Z$ ($Y$ is data, $X$ is latent variable and $Z$ is noise), where the random variables are all in $\mathbb{R}$. Then an inverse Fourier transform leads to \begin{...
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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 such that samples from each dataset ...
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29 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.
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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 ...
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1answer
68 views

Integral involving Student's t distribution

Is there a reference that has the value of the following integral: $$F(a) =\int_{-\infty}^{a}xt_{\nu}(x)dx = \int_{-\infty}^{a}\frac{x}{s\sqrt{\nu\pi}}\frac{\Gamma\left(\frac{\nu+1}{2}\right)}{\Gamma\...
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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{...
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Why is there a kurtosis condition for joint distributions to be elliptical?

I read that if x1, x2 are 2 random variables with different excess kurtosis, their joint distribution cant be elliptical. Is there an intuition or proof of that? It is not very clear to me. Edit- in ...
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Generate data that matches a frequency distribution while preserving the original spatial structure [closed]

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 ...
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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 ...
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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 ...
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In a statistics paper, how to know which parameterization of a given distribution is being used?

Let's say I'm reading a paper, and the authors write $\alpha \sim \text{gamma}(a, b)$. How do I know which parameterization of the gamma distribution they are using? Is there a convention or must one ...
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How to relate a covariance matrix to the generated length and angle of a elliptical distribution?

I am trying to generate a plot of points randomly sampled from a 2D elliptical distribution. I want to control the length and orientation of the ellipse this random sample creates. It seems like ...
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1answer
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How to calculate number of cycles in twenty year from a daily distribution

I am asked to determine a distribution of the number of cycles a component is expected to do during its entire lifetime. What is do have now is a distribution of cycles the component makes per day. I ...
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What distribution has the p.d.f. of form $\frac{e^{-b \cdot x} \cdot x^c}{1 + e^{-k \cdot (x+a)}}$ for $x >0$ and parameters $b > 0, k > 0, c > 0$?

In my work I met the p.d.f. of form $$p(x) \propto \frac{e^{-b \cdot x} \cdot x^c}{1 + e^{-k \cdot (x+a)}}$$ with support $x \in [0, +\infty)$ and positive parameters $b > 0, k > 0, c > 0$. ...
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What distribution has exactly three parameters for mean, variance, and skewness?

Common distributions usually fix their skewness. Beta distribution has two parameters to determine all of the mean, variance, and skewness. Student-T's skewness can change by some definitions but it ...
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What is the distribution of time's to ruin in the gambler's ruin problem (random walk)?

In a gambler's ruin problem, where the gambler starts with a fixed amount of wealth. What is the distribution of times to ruin. That is, if each bet has a fixed payout. As I understand it, this is a ...
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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, ...
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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?
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what can I infer if my data follows power law?

I am working on data set of "Number of days taken to get a reply to mail". I have studied POWER-LAW DISTRIBUTIONS IN EMPIRICAL DATA - AARON CLAUSET. I have used powerLaw package in R to find if my ...
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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 ...
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1answer
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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 ...
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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....
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Why do we estimate population parameters using statistic?

I had been studying statistics, I have a doubt that I couldn't find the answer of. Its related to estimating population parameters using statistic. Suppose we have a population size of 10000, we want ...
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1answer
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Problem with Clamping mask in Biomod2

I'm trying to project an alien species distribution with Biomod2, algorithm GBM, random pseudo-absences in equal number to presences, background restricted to the zoogeographic realms in which the ...
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1answer
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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 ...
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Can someone Help me out to understand the lecturer says we're talking about Population quantiles, Population median wrt Probability density functions? [closed]

The definition of quantile given here is, Ath Quantile is at a point where the probability ( or area under distribution ) up till that point is A.
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understanding p value and distribution [duplicate]

I am from a biology background. Using t, χ2, F tests day-to-day, following like a recipe. However, I feel I must understand the background of this. I took an online lecture on p-value and hypothesis ...
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What features can be extracted from a probability distribution? [closed]

I have been looking online regarding feature extraction and I am looking at extracting features from probability distribution by getting the characteristics of the distribution. I know that most ...
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Density function [closed]

Consider the density \begin{align} f(x)&=(2\pi)^{-n/2}e^{a}b\\ a &= \frac{-\sum_{i=1}^nx_i^{2}}{2}\\ b &=1 + \prod_{i=1}^n x_i e^{\frac{-x_i^{2}}{2}} \end{align} on $\mathbb{R^{n}}$ : Is ...
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1answer
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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 ...
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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 ...
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1answer
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What distribution is $P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x$?

What kind of distribution is the following: $$ P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x $$ and how can I find $P_X(x < x_0 \mid K, N)$?
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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 ...
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1answer
162 views

Can I estimate Variance of Gamma from Negative Binomial distribution distributed data, given NB is Gamma-Poisson compound

I believe the data I have follows Negative Binomial distribution (over-dispersed Poisson). We know Negative Binomial is a Gamma-Poisson compound distribution. The variance of this Gamma distribution ...
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Statistics student [closed]

Senior management at Forever Young has identified a source of uncertainty not present in their intul assesment They have come to the conclusion that price in addition to demand and exchange rate are ...
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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 ...
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57 views

Sum of correlated squared normals

Assume that $(X_1,X_2)' \sim \mathcal{N}((\mu_1,\mu_2)', \Sigma)$, $j =1,2$, and $Cov(X_1,X_2) = r > 0$. We know that $X_1 + X_2 \sim \mathcal{N}(\mu_1 + \mu_2, \sigma_1^2 + \sigma_2^2 + 2r)$. ...
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X follows a normal distribution with mean= 0 and variance =1. Y is defined as I {X>1} - I{X<-1} . find the distribution of Y [closed]

In this question I is the indicator function. Let X ∼ N(0, 1), Y := I{X>1} − I{X<−1} find distribution of Y and classify what type of random variable it is.
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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 ...
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1answer
142 views

Distribution of the stddev of movie ratings

I have a database of 10-star movie ratings (similar to IMDB). For each movie the raw data is a distribution of votes from 0-star all the way to 10-star, and I have also computed the mean and standard ...
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Intution about the memoryless property of geometric distribution

I was watching the video about the memoryless property of geometric distribution. Here is an excerpt from the video. $$\begin{aligned} P(X \geq x+y \mid X \geq x) &=\frac{P(X \geq x+y, X \geq x)}...
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What is the parameter of this Gamma posterior distribution with Poisson likelihood and constant prior?

I am trying to figure out the parameter for this driven posterior distribution. I have searched online and found that the constant prior distribution with the Poisson likelihood function should give a ...
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31 views

How to interpret Hill estimate of tail index

I'm seeking a non-technical explanation of how to interpret the Hill estimate of the tail index for fat-tailed data, and, if possible, some explanation of seemingly contradictory results that ...
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1answer
35 views

Seeking clarity regarding kernels

With regards to Bayesian statistics, I understand the kernel of a probability density function (pdf) or probability mass function (pmf) to be the form of the pdf or pmf in which any factors that are ...
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1answer
876 views

Variance of Normal Order Statistics

Suppose we have $X_1, \cdots, X_n \overset{\textrm{i.i.d.}}{\sim} \mathcal{N}(0, 1)$ with $n > 50$, and let $X_{(1)}, \cdots, X_{(n)}$ be the associated order statistics. Are there any references ...
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How to find distribution of Data for building a predictive model [closed]

I am working on a project "To predict scores" . The distribution of target variable is as below : I want to identify the type of distribution of this variable (CC$Score) .After I identify ...

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