# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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. ...
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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### 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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### 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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### 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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### 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 ...