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Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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Is there a way to statistically compare the standard deviation of two distributions?

Suppose that a set of 100 items are responded to under two different conditions. Instead of comparing the means, is it possible to compare other things about the distribution of responses, for ...
Dave's user avatar
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How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

I have functions that on iterval [0,1] all seem to look like this: i.e. they have a zero around 0.4 +ve derivative from zero to 0.4 and around zero or slightly negative derivative up to 1. I plan to ...
ufghd34's user avatar
3 votes
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Estimating mean and SD given the median and IQR values

it is possible to estimate mean and SD given the median and IQR? I am involved in a meta-analysis where some trials show outcomes as mean and standard deviation but most show median and inter-quantile ...
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Distribution to describe size of population with random exponential growth

Is there a distribution family that describes the size of a population experiencing random exponential growth (either discrete or continuous)? For context, I am trying to computationally model a ...
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2 answers
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Exercise on finding probability density function

Let $Y_1$ and $Y_2$ by independent and uniformly distributed over the interval (0, 1). Find the probability density for $U = Y_1/Y_2$: Solution: $F_U(u) = P(U \le u) = P(Y_1/Y_2 \le u)$. Looking at ...
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Can a non-symmetrical distribution have the same areas under the PDF in the two sides around the mean?

I was thinking about symmetrical vs. non-symmetrical distributions and I found myself stuck in a thought that I had never thought before. We know that symmetrical distributions like Normal, Laplace, ...
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Distribution of a product of random variables

I have two independent distributions $X$ and $Y$. $X$ is defined by the piecewise CDF $$F_X(x) = \begin{cases} F_X^1(x) & x \in (-\infty, a_1)\\ F_X^2(x) & x \in [a_1, a_2)\\ F_X^3(x) & x \...
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Proof of Strong consistency of Beta posterior distribution

Suppose that we have random variable $X_{1}, X_{2}, ..., X_{n} \sim^{iid} \text{Bernoulli}(p_{0})$ with $p_{0}$ true unknown probability in $[0,1]$. Now, I want to implement Bayesian machinery to ...
Fiodor1234's user avatar
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2 votes
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How do I measure the regularity of the distribution in a list of binary data?

Suppose I have a list list = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1], which gives information about whether a person was sick on a day (1) or not (0), since ...
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Does a Fast WEIBULL transform software exist? [closed]

I am frequently asked to calculate the deconvolution of data series in term of WEIBULL probability functions (usually 2 parameters). I am getting very good results using a EXCELL spread sheath I ...
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Sampling distribution of the proportion of events

For categorical variables with $l \ge 2$ categories, what is the sampling distribution of the proportion of events in each category? These are obviously not independent, since they add up to 1. Does ...
Jessica's user avatar
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Equivalence of inverse transformations under distributional equivalence

Consider continuous, invertible transformations $g,h : \Bbb{R}^d \rightarrow \Bbb{R}^d$ and suppose $g(Y) \overset{d}{=} h(Y)$, where $Y$ is a $N(0, I)$ random variable. Then what can we infer about ...
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How can I show statistically that one of my replicates is likely contaminated?

I have a dataset that looks like the below: five replicate samples, each of which is composed of 4 different fractions that sum to 100%. The fifth sample clearly looks visually distinct from the other ...
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calculating percentage normalisation

Please don't laugh or close this post I am confused as to how I can calculate the percentage normalization occurring post treatment. So, here is a background of the problem, I have reading from ...
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Complex parameterizations of real-valued distributions

Suppose we have some random variable $X$ that takes values in $\mathbb{R}^n$, parameterized by $\theta \in \Theta$ where the parameter space $\Theta$ is finite-dimensional. In almost all statistical ...
Randy Savage's user avatar
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Calculating the joint pdf of linearly dependent random variables $X$ and $Y=X$

Let $X$ and $Y$ be two random variables and $p_{(X,Y)}(x,y)$ be the joint pdf of $(X,Y)$. Suppose that $(X,Y)$ transformed to $(X,X)$. We want to calculate the joint pdf of transformed random ...
Naveen Kumar's user avatar
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How to plot the theoretical Lorenz and Bonferroni graphs for custom distribution [closed]

This is the CDF and donot have closed form quantile function. Any help will be appreciated CDF=((alpha)**(1-exp(theta*x))-(beta)**(1-exp(theta*x)))/(alpha-beta) I ...
Sid's user avatar
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6 votes
1 answer
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Vintage of this lower bound on skewness for positive data with given mean and sd?

It turns out there is a lower bound on the skewness $g_1$ of any strictly positive set of data having a given mean μ and standard deviation σ: $$ g_1 > \sigma/\mu - \mu/\sigma. $$ Although ...
David C. Norris's user avatar
7 votes
3 answers
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What is meant by the probability of a sample having a value of $x$ is $ng(x)$?

Reading from Wikipedia: The probability of one sample having a value of $x$ is $n g(x)$. Assuming that the notation is consistent throughout the page, I would take $g$ to either be the probability ...
Galen's user avatar
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What are the degress of freedom in the summary output for GLMs in R?

I am currently self-studying GLMs with the book "Generalized Additive Models An Introduction with R" and I am a bit confused regarding the degrees of freedom in the summary output for GLMs ...
Dude3400's user avatar
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differential entropy for comparison distributions

I want to use differential entropy to compare the outcome of Bayesian updating (multidimensional probability distributions) for different datasets. My parameters are different physical parameters i.e. ...
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Estimation of population parameters on the basis of multiple samples regressions

I am working with a population of approximately 1 million subjects for whom I have repeated measures of expenditure (expend). My objective is to evaluate the link between 2 variables (let's say A and ...
Marc-Florent Tassi's user avatar
2 votes
3 answers
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How to work out the expected rate of success when there is a guaranteed success on the nth attempt?

I'm looking to work out how to find the expected success rate when given the rate of success but, also after n-1 failed attempts, there the success rate is 100% for the nth attempt. Intuitively I ...
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Calculating the mean and error for correlated measurements involving different estimators and quantiles

My goal is to find a way to report a mean $\pm$ error for different estimators and quantiles of the same distribution (same measurement). I am measuring the width of a distribution (Gaussian core and ...
nyw's user avatar
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11 votes
2 answers
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(THEORY) Do Tree models output probabilities?

I have a question purely theoretical about decision trees outputs for classification. I have heard a lot of people say "the output of tree models are not probabilities", and having studied ...
Felipe Araya Olea's user avatar
4 votes
3 answers
92 views

Posterior expectation of normal distribution with "truncated" observation

Consider the following problem of estimating an unknown parameter from normal samples: Suppose that $\theta \sim N(0, \tau_\theta^{-1})$, where $\tau_\theta \ge 0$ is the prior precision. Consider two ...
keepfrog's user avatar
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Extract credible/confidence interval of a threshold in a Bayesian posterior draws distribution [closed]

I have a Bayesian model created through bayer package in R on which I need to calculate confidence/credible intervals for a ...
cccnrc's user avatar
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4 votes
1 answer
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Approximation function for MLP and LSTM

I have total of 6300 samples, 5800 of which are training data, and 500 of which are testing data. We compare the performance of LSTM and multilayer perceptron (MLP) with one hidden layer in terms of ...
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how to measure significance of improvement between two methods during modeling

Hello everyone I have two methods for developing models. I use a set of input features (set1) for training model1 and another set of input features which have (set1 features + extra set2 features). I ...
Rhea Bedi's user avatar
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Computing a Confidence Interval for E[X] when PMF is given

I am given a Probability Mass Function for a discrete random variable. From the PMF I computed the Expected Value $E[X]$, the Variance $V[X]$ and the Standard Deviation $S[X]$. Here is an example (the ...
rusiano's user avatar
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3 votes
1 answer
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Intuition behind relation between Gamma and Standard Normal distribution

I read if $Z$ is a random variable with a standard Normal distribution and $X=Z^2$ then $X \sim \operatorname{Gamma}(1/2, 1/2)$. I understand the math (manipulations of formulas) behind it. What about ...
Gabriele Bettineschi's user avatar
1 vote
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Distribution of the model vs. Distribution of the Residuals

Let's say I'm going to do an analysis where my response variable has a gamma distribution. I perform the analysis pointing to the distribution in my model (eg. using the lme4 package, m1<-glmer(Y~...
Graciliano Santos's user avatar
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estimation of multivariate probability

Let $(X_{1}, \dots, X_{n})$ be a multivariate distribution and I can generate the sample from it. Next, assume that I have to compute $$ P(X_{1}\in A_{1}, \dots, X_{n}\in A_{n}), $$ where $A_{1}, \...
ABK's user avatar
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7 votes
4 answers
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Estimating Probability Density for Sample

I have a dataset of over 20,000+ samples. The objective here is to define a distribution for the sample so that I can plot all possible outcomes. However, I am unable to find an appropriate ...
Ahmed Jyad's user avatar
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Beta regression-dealing with small number of 0,1 values

I have a small dataset for 100 participants. The dataset includes repeated 'tests' over a course of a week. A test can have the binary outcome of pass or fail, and the same number of tests are not ...
snalmznh's user avatar
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Distribution of the random variable $\mathbb{P}(Y|X)$

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space and let $X:(\Omega, \mathcal{A})\rightarrow(\mathcal{X}, \mathcal{F})$ and $Y:(\Omega, \mathcal{A})\rightarrow(\mathcal{Y}, \mathcal{G})$ ...
guest1's user avatar
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Does the mean of the maxima of a set of distributions converge?

This question is related to a recent one I posted. In that question I ask what statistic might best represent the central tendency of the true discrete distribution of a property for a sample for ...
Buck Thorn's user avatar
4 votes
3 answers
115 views

What statistic best estimates the sample mean in case of missing data in a distribution?

I have samples of particles and am interested in the particle lengths. The problem is that the samples are assessed using image analysis. As the particles overlap, the measurements are incomplete and ...
Buck Thorn's user avatar
0 votes
1 answer
29 views

Generating equivalent normal and lognormal distributions

Letting $X \sim N(\mu, \sigma)$ and $Y = e^X \sim LN(\mu, \sigma)$, I want to generate the same distribution using R or some other program. My understanding is that the parameters $\mu$ and $\sigma$ ...
hatmatrix's user avatar
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1 vote
2 answers
90 views

Can we express the Law of the Unconscious Statistician using the CDF instead of the PDF? [duplicate]

I have only seen LOTUS given either in terms of the density $$\mathbb{E}[g(X)] = \int g(x) f(x) dx$$ or in terms of the Lebesgue-Stieltjes integral $$\mathbb{E}[g(X)] = \int g(x) dF_X(x).$$ I have ...
Galen's user avatar
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1 vote
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Conditional expectation of a multivariate normal distribution

Let $(X,Y,Z)$ have a multivariate normal distribution: \begin{align} (X, Y, Z) \sim N\left(\begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 & \rho_{xy} & \rho_{xz} \\ \rho_{xy} &...
parasu's user avatar
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0 answers
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By means of what distribution can I match the first n moments for arbitrary (i e. any) values of those moments?

Suppose I have the first n moments from some data set, either raw, centered or scaled, (or cumulants instead) whichever is more convenient for matching. Is there a continuous, continuously ...
andrewH's user avatar
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1 vote
1 answer
28 views

A set of values ​from a discrete uniform distribution is scaled down by the same factor

Use MATLAB's randi function to generate a set of values ​​that conform to discrete uniform distribution, such as {0,1,2,3,4,5}. If this set of values ​​is divided by an integer 10 at the same time, ...
Cathy's user avatar
  • 107
5 votes
1 answer
326 views

Can a finite decimal number be a discrete variable?

If I have an array {0.1, 0.2, 0.3, 0.4, 0.5}, is this a discrete array? Are the values in it discrete values? (I have this doubt because many materials show that discrete values are usually integers) ...
Cathy's user avatar
  • 107
1 vote
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Choosing a unique visitor on the fly

I've been thinking of this as the "Prize of the Week" problem. Suppose you run a shop, and want to give out a prize once a week to someone making a randomly-selected purchase. You give out ...
Ralph Giles's user avatar
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What is the probability of condition rating 5 following a given condition rating?

I have an asset management system in which assets are given a condition rating from 1 (good) to 5 (bad). Assets are inspected and given a rating every year; new assets start with condition rating 1 ...
camarones95's user avatar
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0 answers
26 views

Predicting if individual has a trait based on their previous locations (distribution of trait at locations is known)

I have been thinking about a problem and I was wondering if anyone has the right name/method/textbook of how this problem should be approached, or if they would be willing to help with finding a ...
oventerrible's user avatar
1 vote
0 answers
18 views

Difference between 3 (not PDF/CDF) distribuitions [closed]

I have multiple (>20) variables that describe 3 different objects, and I wanted to see which variables differ the most across these 3 objects. I was thinking about using KL-divergence/KS-test/...
thfdealer's user avatar
16 votes
2 answers
762 views

Altiplano distribution---Distributions very flat around the center?

(This comes from a Facebook post, reference at the end) "Everybody knows" that the function $x \mapsto \exp\left(-1/x^2 \right)$ is infinitely differentiable, but not (real) analytic, ...
kjetil b halvorsen's user avatar
3 votes
1 answer
79 views

Deriving a conditional joint probability model for the data in a Bayesian linear model

I have been reading Tony Lancaster's 2004 book "An Introduction to Modern Bayesian Econometrics." On pages 116-117, Lancaster derives a conditional joint distribution for the data $p(y,X|\...
user413046's user avatar

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