Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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24 views

Why isn't information theory taught in traditional classes on probability theory? [closed]

Information theory consists of several tools that can measure the information content of entire probability distributions, each one calculated purely from probabilities unlike traditional frequentist ...
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Bounded probability distribution wanted [closed]

I am searching for a bounded continuous probability density function with the following two properties: (1) it should be a distribution of probabilities (i.e. it occupies the space [0; 1]) (2) as the ...
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Bayes' Theorem Application

Ontario Public Health conducted a study on their test results for detecting SARS-CoV-2 (the virus that causes COVID-19) from Jan-April 20201. These are all patients who had symptoms and went to get ...
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How to check for linearity assumption in GLM?

Let g be the link function, y be the target variable, and $\beta_1x_1$+... $\beta_nx_n$ for some $n \in \mathbb{N}$ be the linear predictor. One of the assumptions for a GLM states that there exists a ...
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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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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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Intuition behind unequal class interval histograms

In a histogram with unequal class interval, say for example, the data: ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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31 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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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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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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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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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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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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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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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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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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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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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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What test for verifying statistical significance for difference in 2 groups [closed]

How to verify the difference in estimated effects of 2 variables on a dependent variable using a statistical test. Q: Determine the estimated effect of X1 on retention, controlling for a,b,c, Include ...
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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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Generating random numbers that are log-normally distributed

Even though I don't quite understand why and how this works, I appreciate how simple it is to generate a set of numbers which are Poisson distributed: ...
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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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In these domains do they have different conditional probability distribution AND marginal probability distribution?

For simplicity, I'm going to focus on subject 1 and subject 4 and only observe class 3 (green) and class 2 (blue), here's my understanding: The have different conditional probability distribution, ...
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Estimate rolling distribution of sign-up durations from time series?

Conceptual question: Suppose I have a times series (500 entries or so) of daily number of individuals signed up on a list, from the start of this list (i.e. zero people on it in the beginning). At any ...
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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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When is mutual information difficult or easy to estimate compared to correlation?

I came across the following statement about covariance/correlation vs mutual information, Covariance can be calculated directly from a data sample without the need to actually know the probability ...
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Does every statistic have a sampling distribution, not just the sample mean?

I am curious because most basic undergraduate statistics reference just start out Inferential Statistics by mentioning sampling distributions and the sampling distribution of the mean. My question is ...
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Scaled sample variance as sum of squares of normal variables

I want to prove that $(n-1)S^2 = \sum_{i=1}^{n} (X_i - \bar{X})^2$ can be written as $\sum_{i=2}^{n} Y_i^2$, with $Y_i = N(0,\sigma^2)$, $X_i$ and $Y_i$ $i.i.d$. I managed to do it by taking a big ...
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Does entropy have less estimation error than mean and variance estimates?

Estimating the mean or expected value of a continuous random variable's (r.v.) empirical distribution is known to be difficult, moreso than estimating the variance. Estimates of the mean and variance ...
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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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Estimate Unique Number of Visitors

Is there a way to estimate the number of unique monthly visitors to a site based on a limited sample of one week of data? I have information about when a given user visited the site. This isn't as ...
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Softmax vs the Dirichlet distribution

As far as I understand one can in principle model the distribution over a set of $k$ categories using e.g.: the Dirichlet distribution A softmax model. As far as I can tell, both use $k$ parameters ...
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Upper Bound and Lower Bound on Means when Distributions are bounded?

Suppose we have two different probability distributions $p, q$ defined on input $x \in [0,1]$. We know that for any value of $x$ in the domain, we have $\exp^{-a} \leq \frac{p(x)}{q(x)} \leq \exp^{a} $...

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