A distribution is a mathematical description of probabilities or frequencies.

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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
29 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
70 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
28 views

How to find the distribution? [on hold]

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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1answer
34 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
59 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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8 views

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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12 views

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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Custom Distribution in R

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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1answer
26 views

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
44 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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2answers
36 views

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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14 views

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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40 views

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
31 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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Statistics Dot Plot Help [closed]

The report “Who Moves? Who Stays Put? Where’s Home?” (Pew Social and Demographic Trends, December 17, 2008) gave the accompanying data on the percentage of the population in a state that was born in ...
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41 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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1answer
15 views

Mode for group data

What would be my fx if my distribution table is like this: ...
2
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1answer
41 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
33 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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1answer
218 views

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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32 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
199 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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0answers
33 views

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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188 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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Lower Quartile Value [SOLVED] [closed]

What will be the lower boundary of my lower quartile if its value is lower than the lowest cumulative frequency? LL = lower limit, UL = upper limit, f = frequency, CF> = less than cumulative ...
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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
142 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
135 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 ...
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28 views

Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
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2answers
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PDF of a sum of dependent variables

This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
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Expressing a multivariate probability distribution as a univariate equivalent

Is it possible to combine the odds for two or more groups of balls in a multivariate version of Fisher's non-central hypergeometric distribution to give a univariate equivalent? For example, this ...
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2answers
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What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?

I have four independent uniformly distributed variables $a,b,c,d$, each in $[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be ...
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1answer
58 views

PDF of sum of ordered weighted exponential RVs

Let $X_{(1)}, X_{(2)}, ..., X_{(N)}$ be the order statistics of an iid exponential RVs with parameter $\lambda$, where $X_{(1)} \geq X_{(2)} \geq ...\geq X_{(N)}$. Any hints on how to find the PDF of ...
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Student t distribution: standardization [duplicate]

I got a question concerning the standardization of a student t distribution. I see that the "plain vanilla" t distribution has density $f(x|\nu)=\frac{\Gamma(\frac{\nu+1}{2}) ...
2
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1answer
29 views

Which metric should I use to rank these distributions?

I have a number of 1D distributions, which, when plotted show a distinct ranking in terms of the "spikiness" of the data. I would like to apply a relatively fast metric that would allow me to rank ...
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2answers
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How to test if 2 means are significantly different for non-normal non-paired data

I have 4 averages from 4 samples and I want to test if the means are significantly different. When I look at the QQ plots and the shapiro wilk test (all have very low p values) the data is not normal ...
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Matching a query distribution to a family of template distributions

I was turning over a hypothetical question in my head: Suppose I have a set of template probability distributions, let's say each giving the probability of the occurrence of certain objects like ...
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Slope analysis where one group is not normally distributed

I am currently doing analysis of five separate drug groups and their changes in levels of prescription over time. Having done linear regression on excel I am comparing the 'steepness' (m) of the ...