Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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2
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1answer
226 views

ANOVA (assuming different distributions) vs Kruskall-Wallis and post-hoc tests

During stats courses on Uni I learnt (if I remember correctly and hopefully don't put my teachers to shame) that if you want to compare multiple groups with eachother you look at the residuals of an ...
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Looking for the name of a distribution and/or a way to calculate its cumulative distribution function

For parameters $\nu_1$, $\nu_2$, $\lambda$, define random variables using a chi-squared distribution and a non-central chi-squared distribution: $$ S \sim \chi^2_{\nu_2} / \nu_2 $$ $$ F \sim \frac{\...
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expectation of the third moment of Wishart matrix

Let $W$ follow the Wishart distribution $\mathcal{W}_p(n,\Sigma)$ and let $A,B,C$ be $p \times p$ constant matrices. Then, I want to know $E[tr(AWBWCW)]$. I found a result for $E[tr(AWBW)]$, but could ...
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Rejecting samples/events in one distribution/dataset based on known rejection ratios of another using a common variable

Problem: I have two observational datasets (A & B) containing events and an independent variable related to each event (lets call it this variable 'elevation'). At lower/smaller elevations, an ...
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Arrival time of the first among N released particles in a first arrival time process

I need to find the random arrival time of the first particle out of the $N$ particles that were released at time $t$ into a fluidic medium with no directional flow. Based on the first arrival time ...
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Given two samples that have the same mean, standard deviation, and N: are the values in each sample identical?

If not, are there any restrictions that would need to be imposed to ensure that the values of the two samples would be identical? I apologize in advance if this is such a basic question.
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Significant support of non-central chi-quared distribution

I want to find the support of a non-central chi-squared distribution ($99.9 \%$ of the energy). For example, If I have a Gaussian distribution with parameters $\mu$ and $\sigma$, I know $99.9 \%$ of ...
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Minimizing variance vs. expected shortfall: distributions where the difference is salient

In portfolio theory in finance, given a set of $n$ assets to choose from, one often selects portfolio weights so as to maximize expected return and minimize some measure of risk, e.g. variance or ...
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1answer
954 views

Estimating parameters in a truncated negative binomial distribution?

I would like to find the estimates of the parameters in a truncated (at zero) negative binomial distribution. Suppose $Z$ has this distribution with parameters ($\alpha,\beta$). (The parametrization ...
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Adjusting OverAll Time Performance using sectional Times

Assume I have two runners, Runner_1 is the average runner and Runner_2 is Usain Bolt. We let the two runners compete in 3 different races on a 100m distance. We assume that the benchmark time for 50m ...
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Noncentral t-distribution — relationship to shifted/scaled normal distribution

Let $x$ be 100 random samples from a $N(10,4)$ distribution. Suppose that I want to calculate the likelihood of these data, given my knowledge that $\mu=10,\sigma=4$. For the normal distribution, this ...
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Recovering Distribution from Percentiles

I have data on the 10th, 25th, 50th, 75th, and 90th percentiles of a probability distribution, together with the mean, and standard deviation. I am interested in recovering a continuous distribution ...
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Significant change over NxM distributions

I have 100 sets of data, each of which consists of ~ 15 distributions along time, I've attached a figure of 1 of these sets to hopefully clear up what I mean. The plot shows the 95% confidence ...
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How is the kurtosis on the Cullen and Frey graph in the R package fitsidtrplus calculated?

I am using the package fitdistrplus in R to fit distributions to my data. My first step was to check my data against the Cullen and Frey graph that is produced using the descdist function. This is ...
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How to determine the distribution of a parameter fit by nonlinear regression

The following (rectangular hyperbola) equation is used often in biology, often with additional terms (this is simplified). K is the Km of enzyme kinetics, the EC50 of pharmacology, etc. X is ...
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1answer
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How do I normalize a bimodal distribution?

I'm working with the Iris dataset. One of the variables, PetalWidth, has a clear bimodal distribution. My understanding is that multivariate regression sssumes ...
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1answer
19 views

Normal Distribution Probability Question [closed]

A recent study by the EPA has determined that the amount of contaminants in Minnesota Lakes in parts per million averages 64 ppm with a variance of 17.6. Suppose 35 lakes are randomly selected and ...
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1answer
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Comparing groups of vectors / clustering based on how similar each persons 'group of vectors' is

Say I have N people and K weeks. For each person-week, I have a vector of a fixed length filled some number between 0 and 1, summing to 1 across the whole vector (so for each person, I'll have K ...
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Obtaining Standard Error of an estimate knowing its likelihood function (in R)

Suppose I know that the likelihood function for an estimate of effect size (called dppc) measuring the change in a control group from pre-test to post-test in ...
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1answer
154 views

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 can I check whether two time series has same distribution? [closed]

In what approaches, I can compare two-time series data for their distributions.
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1answer
49 views

Is this an Appropriate Application of a Permutation Test?

Suppose I have count data between three groups, each with a different number of observations: $n_1 = 11, n_2 = 6$ and $n_3 = 5$. My data is listed below: \begin{array} {|r|r|}\hline group 1 & ...
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1answer
25 views

KL-divergence: P||Q vs. Q||P

Assume, that we have several data generating measures $P_{1}, \dots, P_{k}$ and $Q$, all defined on the same probability space. Next, assume, we have the same amount of independently sampled data from ...
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Determining probability from past distribution

Consider there to be 200 courses being taught in the current semester in a university. Post completion of the end-semester examinations (For the sake of simplicity, assume the examinations for all ...
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How to randomly shuffle tiny spheres inside a big sphere? [duplicate]

I have a list of spheres with some known characteristics (ids, radii, masses, and positions) with ids, radii, and masses being 1D arrays with shape (511, ) and positions being 3D array with shape (511,...
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1answer
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Probability distribution of the product of two dependent random variables

It is well known that being $X$ and $Y$ two independent random variables with distributions $f_X(x)$ and $f_Y(y)$, respectively, then the probability distribution of the multiplicative function $z = ...
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2answers
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Is there a discrete distribution I can use for sampling in R?

Firstly, I don't have a stats background, so please accept my apologies for any errors or misunderstandings in the question below. I'm trying to use R to draw values from a discrete probability ...
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These questions regarding probability distribution are confusing to solve. Need your help [closed]

Consider a race with 140 participants. How many possible outcomes are there for the top three positions of gold, silver, and bronze? (4 ...
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14answers
189k views

What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
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1answer
29 views

Distribution Selection based on Kolmogorov Smirnov Test

I am trying to model the distribution of some non normal data, to do so i am fitting many different distributions(Student, Pareto...) to the data. When computing the Kolmogorov Smirnov Statistic for ...
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2answers
174 views

Find $P\{ (A \, \text{or} \, B) \, \text{and} \, (A_1 \, \text{or} \, B_1) \}$ or a lower bound in this specific case

Define $X$, $Y$, $X_1$, $Y_1$, and $Z$ to be some positive random variables, for each of which we know the distribution. Note that these variables are independent of each other. Let $t, a$ two ...
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1answer
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(Non-limit) distribution of maxima from different univariate, discrete and stationary time series

Motivation: I'm currently studying the convergence of maxima from simulated time series to max-stable distributions, and in order to do so, I want to better understand the penultimate distribution of ...
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1answer
33 views

What length are some segments of a broken rod?

If a rod (of unit length) is broken into $n$ segments (assuming the $n-1$ breaks occur with uniform probability across the entire length) and $k$ of those segments are chosen at random and laid end to ...
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Laplace-Stieltjes Transforms and distribution

I was going through a paper, I came across below relation, \begin{equation} T=\begin{cases} C, & \text{with probability $P(H<C)$}\\ 0, & \text{with probability $P(H>C)$} \...
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1answer
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Proving Identifiability Using Law of Large Numbers? [closed]

Well normally proving identifiability follows by showing that $p_{\theta}(x)=p_{\theta'}(x)$ implies $\theta=\theta'$. Usually this proceeds by showing that a function dependent on $\theta$, such as ...
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12answers
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Why can you not find the probability of a specific value for the normal distribution? [duplicate]

I am learning about the normal distribution and was watching this video. At 6:28, the question imposed is what is the probability of an ice-cream weighing exactly 120 grams (using the normal ...
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Minimize the limit of K-L (Kullback Leibler) divergence for a given conditional probability $p(y|x)$ distribution?

Let, $p(x);p(y)$ are the probability distribution function of random variable $X$, $Y$ and the Conditional probability $p(y|x)$ is given e.g. $p(y|x)=Q(x+2y)$. where, $Q(x) = \frac{1}{{\sqrt {2\pi } }}...
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2answers
915 views

Application of Pareto/NBD and Pareto/GGG models for customer lifetime value estimates in high churn setting

I have been attempting to estimate customer lifetime value in the context of online classifieds (high churn context) using probabilistic models, chiefly the Pareto/NBD and Pareto/GGG techniques ...
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1answer
34 views

Error for operations for Two Poisson distributions

Can error (std dev) in A +B or A-B be $\sqrt{A}$+$\sqrt{B}$ if A and B are Poissonian? If yes, what would be similar expressions for AB and A/B ?
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2answers
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Is Pr(A | B, C) = Pr (A | B) * Pr(B | C)? If not, what assumptions do I need to establish it?

I came across the following statement in a paper: $$Pr(A | B, C) = Pr (A | B) * Pr(B | C)$$ A, B, C are discrete variable. Right before this, they say that this comes from the assumption that the ...
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1answer
33 views

estimation of KL-divergence of continuous distributions

Assume we have two independently sampled datasets, $X = \{x_{1}, \dots, x_{n}\}$ and $Y = \{y_{1}, \dots, y_{m}\}$ from continuous distributions $f$ and $g$. I aim to estimate the KL-divergence ...
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1answer
55 views

sampling from $\frac{1}{1+x}$ times Gamma distribution density

I am simulating a process by drawing many random variates $X$ from a Gamma distribution with parameters $\alpha$, $\beta$, $$f_X(x) = \frac{\beta^\alpha \, x^{\alpha-1} \, e^{-\beta x}}{\Gamma(\alpha)}...
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0answers
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What is the correct procedure for adding random noise to observed predictor data in order to generate binary response data?

Suppose we have an observed data matrix $X$ of length $N$ with $2$ column predictors. If I wanted to generate continuous response data from this, we might do $$ Y^{cont} = X\beta + N(0,1) $$ or in <...
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1answer
521 views

What is the assumption on the distribution of data in gaussian mixture models?

I am reading about Gaussian mixture models from this slide https://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf However, I am super confused at the very first line. It says: We ...
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Impurity measurement of a group

I tried to use Gini Impurity to measure the impurity of a group of animals but is having trouble adding the distance between different animals to the equation. For example, the gini impurity of group (...
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0answers
10 views

Exponential vs Gaussian Distribution in time problems

I'm wondering what about exponential distribution makes them better suited for time problems than gaussian distribution. For example, if I know that on average it takes the pizza delivery 20 minutes ...
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3answers
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Can someone explain to me the sampling distribution of sample variance in comparison to that of the sample mean?

I have read tons of things already about the sampling distribution of the sample variance but I can't get quite a good grasp of exactly what it is like in terms of the formulas of the measurements. ...
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0answers
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Saddle point method used to calculate the inverse Fourier transform

Here I want to find the asymptotic behavior of the following integral $$f(x,t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\exp(-ikx)*\exp(t(1-\exp(-|k|^\beta)))dk,~~~~~~~Eq~1$$ where $x$ goes to infinity. ...
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2answers
83 views

Maximum likelihood estimator of $\theta$ for uniform distribution [closed]

For Uniformly Distributed random variables $X_1,X_2,\dots,X_n$ $\in \mathcal{R}$, the p.d.f is given by: $f(x_i) = 1/θ$ ; if $0≤x_i≤θ$ $f(x) = 0$ ; otherwise If the uniformly distributed random ...

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