Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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21 views

Probability finishing on a given turn two independent draw

I have two decks of card. I draw from each deck independently. I need to find a specific card from each individual deck. What is the odd that on turn $n$, I have found the card in each deck (this is ...
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18 views

Constant Mode Equation for a Weibull Distribution

I am trying to build a movement class for a simulated annealing algorithm for predicting an optimal spare parts policy. For better or worse I am looking to the Weibull distribution to move about the ...
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33 views

Conditional expectation of X given X+Y [duplicate]

X and Y are two independent variables, X ~ exp(a), Y ~ exp(a). I need to find E(X|X+Y). I tried to calculate by definition, but it did not lead to success. Maybe there is another, more convenient way ...
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How to measure if a categorical distribution is concentrated in a very few bins

I'm trying to think of a way to measure that a categorical distribution of any size is concentrated in only a few bins, so not uniform. The best way I can think of is checking entropy, but that's kind ...
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191 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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How to use the chi-squared test to determine if data follow the Poisson distribution

The figure below (Figure 1 from p. 646 of this paper) compares observed values against expected values under the Poisson distribution. It then runs a chi-squared test to see if the observed values ...
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119 views

Graphing probability distribution using R and checking other solutions

I am trying to solve questions in my statistics book. There is a question a want you check me and help for the part iv : Consider a population of 100 computer, 45 of whom are broken, and the rest ...
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1answer
40 views

Distribution $f$ that minimizes $JSD(f||q) + JSD(f||p)$

What can we say about the distribution $f^*$ that is the solution to the following optimization problem: $$\min_f JSD(f||p)+JSD(f||q) ,$$ where $p,q$ are given distributions over some set, and $JSD$ ...
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How to match a biased sample to a population?

I have a sample of people which is biased in age, gender, geography. I am trying to measure various continuous outcomes out of them. I have the census data to tell me the reality of the population ...
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1answer
38 views

Can a sampling distribution have only 1 element or is it necessary to have multiple data elements to be a sampling distribution? [closed]

Can we have a sampling distribution of only 1 realization or is it necessary to have multiple data elements to be a sampling distribution?
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162 views

What is the ideal distribution for a GLM for comparing survey data with election results?

I'm relatively new to statistical methods. I'm hoping to learn what kind of distribution I should use for some data I have. My dependent variable is the results a candidate received by county. My ...
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1answer
54 views

Generating Random Variables from the Generalized Beta Distribution

There is a very nice solution to generating random numbers from the Generalized Distribution of the second kind which can be found here. There is a more general form of this which was developed by ...
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What distribution is produced by the correlation of random values sampled uniformly?

I'm trying to figure out what this distribution is so that I can calculate the exact probability of values close to 1 or -1 using its PDF: as produced by the following code in R: ...
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GLM Logit with either Normal or Binomial Distribution

I am fitting several continuous parameters to predict a proportion (0 - 1) outcome. I used a generalized linear model with a link logit and a Normal distribution. I have seen some people recommend ...
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768 views

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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Inverse Mills Ratio for Logit?

For $X\sim N(\mu,\sigma^2)$ , $$E[X|X>\alpha] = \mu +\sigma \frac{\phi\left(\frac{\alpha-\mu}{\sigma}\right)}{1-\Phi\left(\frac{\alpha-\mu}{\sigma}\right)} $$ Is there an analogous expression for ...
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1answer
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How to show that regularly varying distributions are heavy tailed?

Let distribution $F$ be regularly varying with index $\alpha \geq 0$ (denote $F \in R_{\alpha}$), i.e. its tail $\bar{F} = 1 - F$ satisfies $\lim_{x\rightarrow\infty} \frac{\bar{F}(xy)}{\bar{F}(x)} = ...
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How to prove that t = min{t1, t2} follows an exponential distribution if t1, t2 follow another different exponential distributions

I have no idea about how to prove the next: Suppose we have two random variables, $t_1$ and $t_2$, that follow the distributions $\lambda_1e^{-\lambda_1 t_1}$ and $\lambda_2e^{-\lambda_2t_2}$, ...
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1answer
29 views

Model to determine when mean is unlikely to cross threshold

A doctor inserts a needle into a muscle to measure the duration of specific events. For every insertion approximately 5 data points are gathered. The doctor keeps making new insertions until he/she ...
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208 views

Normalizing Data in Multiple Categories

I couldn't decide if this question belonged here or on the Math stack exchange, but I'm posting it here since it seems more directly relevant. Basically, I have a bunch of categories, labeled, say, A-...
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1answer
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Unexpected probability distribution from xgboost binary classification

I am testing different a couple of different binary classification models using xgboost to predict the likelihood to convert. The difference between the 2 probability distributions shown below is ...
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1answer
94 views

Can every multivariate distribution be expressed as a function of univariate distributions of the same random variables?

Can every multivariate distribution $p(X)$ of a multivariate random variable $X = [X_1, X_2, \dots, X_d]^{T} \in \mathbb{R}^d$, be defined as some function of univariate distributions on $X_i$? I ...
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708 views

Probability that the sample comes from a certain distribution

Assume we have a data sample: $x_{1}, \dots, x_{n}$ from $n$ i.i.d. continuous random variables. Then, for simplicity, let us consider two distributions, $f(x)$ and $g(x)$. Is there any statistical ...
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An interesting problem - an "ugly" familly of distributions - what can we do? [closed]

I've recently encountered an interesting problem. Say, we've got a famility of distributions indexed by a parameter $ \theta$. Say it's a family of descrete distributions (you can also tell me what to ...
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1answer
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Compare two samples?

Similar questions have been asked but have not managed to get a conclusion from them. I am comparing two sets of samples, where ratios have been obtained for several analytes per sample. So the values ...
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28 views

What is an auxiliary density/distribution?

I am currently reading an academic paper where, without definition, the concept of an "auxiliary distribution" has been invoked. Additional expressions used are "auxiliary density ...
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793 views

Distribution of the $L^2$ norm of a vector of components drawn from uniform distributions

We consider a random vector $\vec{v} = \left(x_{1}, x_{2}, \dots, x_{n}\right)$ built from $n$ real random variables drawn from a real continuous uniform distribution $\mathcal{U\left(a, b\right)}$, $...
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1answer
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When is the distribution of product of two normal distributed variables near normal distribution?

It is clear the product of normal distributed variables is not normal distributed. For example, if $X \sim N( \mu_1,\sigma_1^2)$, $Y \sim N( \mu_2,\sigma_2^2)$, then $XY$ does not has the ...
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1answer
117 views

Transforming a multivariate normal sample using the sinh-arcsinh transform

Let us say that we have sample from the multivariable normal distribution. I would like to understand how is possible to apply a transformation to this sample to produce sample that has the sinh-...
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168 views

Is there a generalized concept of noncentrality of a distribution?

The theory of probability distributions forms one of the pillars of statistics, and is a foundation for statistical inference. There are more than a few probability distributions, and they are neat-O. ...
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1answer
454 views

A description of the mean of the Geometric Distribution - is it unorthodox or just incorrect?

I have a homework assignment where I'm asked to propose an estimator for the mean of a geometric random variable. This seemed simple enough, given that I've always understood the mean of the geometric ...
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71 views

Support of a probability distribution

Consider a bivariate probability distribution $G$ and a random vector $(X_1,X_2)$. Should $G$ satisfy any specific support restrictions in order to be an admissible probability distribution for each ...
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1answer
56 views

Distribution from -1 to positive infinity?

I'm performing a regression analysis with a proportions that ranges from 0 to positive infinity, but it's currently centered on 1 (values < 1 indicate a negative relationship, values > 1indicate ...
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1answer
218 views

Correlation between spatial distributions

I have three bivariate data sets of different sizes and the same sampling interval. These represent the variation of dry river bed direction with distance at equidistant sample points. When plotted ...
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487 views

Independence of Mean and Variance of Discrete Uniform Distributions

In the comments below a post of mine, Glen_b and I were discussing how discrete distributions necessarily have dependent mean and variance. For a normal distribution it makes sense. If I tell you $\...
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In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?

Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
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How do I identify if, out of three groups, two are more similar to each other than the other, with statistical support, in R

I have seen similar questions but I believe there are some differences in what I wish to do. I have three groups, A,B, and C. I have two variables namely matings, feather reflectance for all the ...
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Best distribution to model leaving time of people at a concert

I'm writing a simple model, modelling the leaving time of people at a concert (ie the time when people leave the venue). Data shows that people are most likely to leave just after the concert finished,...
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What does the beta parameter tell you in the cauchy distribution?

I am doing some bayesian analysis, and I recently used the half-cauchy distribution as a prior for a variable that tracked monthly spending. My thinking is that this is a non-negative number that is ...
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1answer
55 views

Conditions under which $\int_{\mathbb{R}} x f_1(c - x) f_2(x) dx \geq 0$

I have the integral $$\int_{\mathbb{R}} x f_1(c - x) f_2(x) dx$$ where $f_1$ and $f_2$ are both symmetric densities (symmetric about $x = 0$) and $c \geq 0$ is a constant. I would like to know if this ...
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how to find value at or above 90% probability

I would like to know given a lognormal distribution as per attached. How can I find the value x such that there is 90% probability that the a variable will be higher than x. May I know the coding in R ...
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Not all conditional distribution are normal - how to analyze

I tested the response of a weed's biomass (dry weight- DW) to a herbicide sprayed at three different phenological stages (4-6, 6-8 and 8-10 true leaves). The ...
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Is there any probability distance that preserves all properties of a metric?

In studying Kullback–Leibler distance, there are two things we learn very quickly is that it does not respect neither the triangle inequality nor the symmetry, required properties of a metric. My ...
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Meaning of "Overdispersion" in Statistics

I am trying to understand what "overdispersion" means in statistics. Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is ...
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21 views

Is there a generalization of a Bernoulli distribution with respect to $p$'s dimension?

When $X\sim Ber(p)$ then $P({X=1})=p$ and the complement's event probability is $1-p$. What if I want to distinguish between $n$ possible events? I will need $n-1$ variables to describe this, right? I ...
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Independent Sample T-test or Mann-Whitney U test?

I am a very young stats learner, and I need help understanding the justification of a test choice. I have a sample of 39 participants (20 females and 19 males) been measured on task performance, and I ...
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Can enough cross-sectional data eventually substitute for longitudinal studies?

Imagine there is an injection being recommended, and it’s to lower your risk of getting a disease. The injection is new, meaning almost no time has passed to do a proper longitudinal study on its ...
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Example of a parametric family of distributions that always has dependence on among its variables

Inspired by this question, I would like an example of a parametric family of distributions such that there is dependence for all choices of parameters. The family could be infinite or finite, but I ...
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When does zero correlation imply independence? (apart from joint normal)

Is there a class of distributions (other than joint normal) such that the statement is true? In other words, is there a class of distributions under which zero correlation implies independence? Can we ...
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When does zero correlation imply independence? [duplicate]

A lot have been written on why zero correlation may not imply independence. I would like to ask a different question: is there a class of distributions (those that contain joint normal such as ...