A distribution is a mathematical description of probabilities or frequencies.

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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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Distribution of the duration of a markov-process in a specified state during a specified time

I have a continuous time markov chain with two states $A$ and $B$. The transition rate $A\rightarrow B$ is $\lambda$ and $B\rightarrow A$ is $\mu$. Imagine that $P(X{t_0}=A)=1$ (the process starts in ...
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How to calculate non centrality parameter?

Suppose $Y\sim N_p(\mu,\sigma^2I_p)$. Let $A$ be a symmetric idempotent matrix. I want to show $Y^{T}AY$ follows a chi-sq distribution with some non centrality parameter. Suppose ...
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How to create a realistic distribution of cities? [migrated]

I'm not sure if this is the right community to ask this, so let me know if it's not. I'm wondering if there's been some empirical research as to how villages and cities are distributed around other ...
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20 views

Correlation between normally and non normally distributed variables [on hold]

If one of the variable is normally distributed and the other non normally distributed ... how do u correlate them ? for instance in my case i've two hormones ... one shows a normal distribution while ...
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1answer
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Why is $\sin(\theta)$ not U-estimable in this example?

For completeness I give the definition of being U-estimable: An estimator $\delta$ is called unbiased for $g(\theta)$ if $E_{\theta} \delta(X) = g(\theta) \ \forall \theta \in \Omega $. If an ...
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1answer
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Sampling Distribution question [on hold]

Q: In a certain neighbourhood it is known 12% of school leavers are un-employed if a random sample of 150 school leavers are chosen what is the probability the sample contains: Required: A) At least ...
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Regression with dependent variable which ranges from -1 to 1

I performed a series of Pearson correlations which give me as expected values between -1 and 1 (actually very few below zero). I'd like now to see if some factors are linked to these correlation ...
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Frequency of the most frequent word using Zipf's law

I modeled my corpus using Zipf's law, so that: $$f_r=c/r$$ Where $f_r$ is the frequency of a word at rank $r$. I calculated $c=90000$. How can I calculate the frequency for the most frequent word? ...
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Understanding Zipf's law calculation for probability of a word

So, I am analyzing a a corpus of ~1,000,000 words and I am trying to understand how I can use Zipf's law. I found on some textbook slides the following formulas: $$f_r = c/r$$ $$p_r = k/r $$ where ...
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1answer
165 views

Interpretation of eigenvectors of Hessian inverse

I'm reading a paper in which they use the eigenvectors of the inverse Hessian of a continuous probability distribution to characterize dimensions along which the distribution is most and least ...
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1answer
250 views

Molecules movement distribution puzzle

Let's say I have blood samples of whiteblood cells ($x$) and viruses ($v$). Space has been discretized in $LL$ spaces. They have a $p_v$ probability of interacting when found in the same space. I want ...
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test ranking differences across three groups

I have three groups A, B, C, with participant ns of 20, 89, and 165. Each participant ranked her or his concern with 14 items (potential impediments to success). Scale was 0-1-2-3, 3 = most concern. ...
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1answer
59 views

Gamma Distribution and Life of Component?

I came across an old exam question as follows: If the life of one computer component (in years) has Gamma distribution with mean $6$ and variance $18$, how can we find the probability that this ...
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Gaussian Mixture and K-Means ?! a big challenge?

This is taken from Tom. Mitche Material as Old-Exam. I think the (2) is true and not (3). Who can verify me?
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Relationship between Poisson and Exponential distribution problem

I'm struggling to understand why I can't use an exponential distribution to solve this question: Astronomers treat the number of stars in a given volume of space as a Poisson random variable. On ...
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3answers
233 views

What exactly is a distribution?

Sorry for such a basic question. I know very little of Probability and Statistics, and am wishing to learn. I see the word "distribution" used all over the place in different contexts. For example, ...
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1answer
30 views

How to find the distribution? [closed]

If $ L=2Y_1 +3Y_2 −2Y_3 \ \text{and} \ Y_i \sim N(\mu=1,\sigma=1) $ I'd appreciate any tips on how to find the distribution of this.
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38 views

Degenerate distribution

If $X \, \sim \, \mathcal{N}(m,\sigma^{2})$, I know that $\displaystyle \begin{bmatrix} X \\ X \end{bmatrix}$ is not a Gaussian vector since its entries are not independent. However, what can we say ...
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Test for differences in distributions; three samples; multimodal distributions

Here is a question on how to test for differences in distribution between three samples of multimodal distributed data. I have conducted a dictator game (http://en.wikipedia.org/wiki/Dictator_game) ...
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1answer
63 views

R and Regression: How to determine distribution of residuals?

I have residuals from a linear regression model on my data set. I want to find an appropriate distribution of my residuals. Say, I assume my residuals are Skew-T Distributed, how can I find the ...
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The distribution of a product between a Lognormal and a Beta is …?

I have to random variables expressed as $1 \times 1000$ vectors. One of the vectors $B$ is Beta distributed while the other $L$ is lognormal distributed. Upon element-wise multiplication, I get vector ...
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R gplot for normal distribution - add data to graph [migrated]

I'm trying add to my plot some data that will facilitate users. My distribution graph comes from this code: ...
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Population version of Kendall's Tau Equation

I am reading about concordance and Kendall's Tau. I understand both concepts from an intuitive level. The empirical formula for Kendall's tau is given by: $$ t = \frac{c-d}{c+d} $$, where c is the ...
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33 views

Custom Distribution in R [on hold]

I am trying to create a "custom distribution" in R based on historical data. More specifically, I have some 10 years of daily stock price and P/E data. What I want is to pull that data into R, ...
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PMF for sum of hypergeometric distributions

Basically, my question is the same as this one, except I need more than the $k = 0$ special case: Given a sum of independent random variables each following a hypergeometric distribution, is there ...
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1answer
48 views

Closed form for $\mathbb{E}[\ln (1-p)]$, for $p \sim Beta(\alpha, \beta)$

We know that if $p \sim Beta(\alpha, \beta)$, then $$ \mathbb{E}[\ln p] = \psi(\alpha) - \psi(\alpha + \beta) $$ where $\psi(.)$ is the Digamma function. Is there an easy form for $ \mathbb{E}[\ln ...
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Strategy for geometric die guessing game

The first day of statistics class, we played a betting game to visualize the basics of probability distributions. It worked like this: The teacher begins by rolling a die repeatedly until the number ...
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hypergeometric vs. binomial for sales modeling

Suppose you are selling Product X. You have a customer base with $N$ people. You want to measure the "natural buying probability" (which happens because a customer sees Product X in ads), so you ...
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By how much the mean and variance in size of beans changes after sampling with replacement?

You have a bag of $n$ beans of different sizes. The mean and standard deviation of the size of these beans is $\mu_1$ and $\sigma_1$ respectively. The probability of drawing a bean is an increasing ...
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2answers
32 views

Distribution of p(x) in empirical model

I am having a hard time to exactly name what I am looking for (I am quite sure it already exists out there...) so I'll start with a concrete example: I have a population of discrete colours (red, ...
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42 views

Dependent Bernoulli trials confidence interval

I would like to know if there is a way to build a confidence interval, for a random variable which has a Bernoulli distribution, based on its history. I mean if the order of its states is 11100 (i.e. ...
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15 views

Mode for group data

What would be my fx if my distribution table is like this: ...
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1answer
45 views

KL divergence between two univariate Poisson distributions

I found this awesome thread which shows KL divergence between two univariate Gaussians. I was wondering if the same formula worked for KL divergence b/w 2 univariate Poisson distributions. Or should ...
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2answers
34 views

Variance of a function of the sample variance

I'm looking for the sampling standard deviation of $\hat\sigma^\gamma$, where $\hat\sigma$ is a sample standard deviation. For simplicity, lets do the sample variance of the sample variance and take ...
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Linear combination of two random non-normals that is still a member of same family

It is well-known that a linear combination of 2 random normal variables is also a random normal variable. Are there any common non-normal distribution families (e.g., Weibull) that also share this ...
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Can a Multinomial(1/n, …, 1/n) be characterized as a discretized Dirichlet(1, .., 1)?

So this question is slightly messy, but I'll include colourful graphs to make up for that! First the Background then the Question(s). Background Say you have a $n$-dimensional multinomial ...
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Distribution with fixed mean and closest to a given distribution

I was wondering if this problem has been tackled in some way in the probability/functional analysis literature: Given a pdf $f$ such that the expectation is zero and $\mu\in\mathbb R$, find the ...
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33 views

How likely is it, that a value belongs to a given distribution?

I'm struggling with this question: I created 100 random data sets and the results are normal distributed. This data will be my null hypothesis. Now I want to check, if an observed value belongs to ...
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1answer
61 views

Approximate distribution of product of N normal i.i.d.? Special case μ>10σ, σ>0

Given $N\geq30$ i.i.d. $X_n\approx\mathcal{N}(\mu_X,\sigma_X^2)$, and $|\mu_X|\geq10\sigma_X$, $\sigma > 0$, looking for: accurate closed form distribution approximation of ...
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1answer
200 views

PDF of dependent variables

In my recent question an answer was given, and I am able to compute it myself. Still, I'd like to understand where does that answer come from. Hence, what's the approach to handle dependent variables ...
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65 views

Approximate distribution of product of N normal i.i.d.? General case

Given $N\geq30$ i.i.d. $X_n\approx\mathcal{N}(\mu_X,\sigma_X^2)$, and NO assumptions about $\mu_X$ and $\sigma_X$, looking for: accurate closed form distribution approximation of ...
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Compute a PDF in Mathematica/mathStatica [closed]

Let $X,Y$ be iid uniform in $[0,1]$ RVs, and $U$ has a PDF $f_U(u)=\frac{1}{4}\ln\left(\frac{4}{u}\right)$, $u\in(0,4]$. Mathematica itself is able to compute the PDF of $X+Y+\sqrt{(X-Y)^2+U}$ (see my ...
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190 views

Approximate distribution of product of N normal i.i.d.? Special case μ≈0

Given $N\geq30$ i.i.d. $X_n\approx\mathcal{N}(\mu_X,\sigma_X^2)$, and $\mu_X \approx 0$, looking for: accurate closed form distribution approximation of $Y_N=\prod\limits_{1}^{N}{X_n}$ asymptotic ...
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Squared Normal RVs Divided by Sum of Squared Normal RVs

Suppose we have $d$ random variables $X_1, X_2, \cdots, X_d$ sampled from the standard Gaussian N(0, 1) i.i.d. What's the distribution of the following identity? $$\frac{X_1^2}{X_1^2 + X_2^2 + ...
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Mixture modelling to cluster populations.

I am grouping probes on a microarray that are spaced irregularly that map to different annotations. Some of these annotations appear to contain multiple populations in terms of the average probe ...
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How do you find the population size N based on the highest n values?

For example assume $N$ people performed a selection test like GMAT. Assume the distribution of the scores is a normal distribution (but parameters are not known). If you have a list of the $n$ highest ...
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1answer
151 views

Overdispersion in GLM with Gaussian distribution

To check for overdispersion in GLM with a Poisson distribution one can compare the residual deviance with the residual degrees of freedom. If they are equal the Poisson error assumption is appropriate ...
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Distributions change when data is transformed to higher dimensions?

Suppose that I have a skewed data set with the positive class being 5% and negative class the rest 95%. I want to classify the data using SVM with RBF kernel. Should I worry about the distribution ...
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2answers
142 views

How to add noise to a random variable whose range is the unit interval? [closed]

I have a list of values sampled from a beta distribution that therefore lie in the interval [0,1]. I would like to add (e.g. Gaussian) noise to these values, but of course there is the problem of the ...