A distribution is a mathematical description of probabilities or frequencies.

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How to test whether a distribution follows a power law?

I have the data of how many users post how many questions. For example, [UserCount, QuestionCount] [2, 100] [9, 10] [3, 80] ... ... it means each of the 2 users posts 100 ...
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X vs x Notation in law of large numbers

This may be a silly question, but I can't find a concise answer. I've been studying Convergence of Random Variables in Wasserman's All of Statistics, which starts out by explaining: $X_n$ is a ...
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138 views

Deriving the bivariate Poisson distribution

I've recently encountered the bivariate Poisson distribution, but I'm a little confused as to how it can be derived. The distribution is given by: $P(X = x, Y = y) = ...
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Comparing file sizes day on day for outliers, what test to use?

I am quite new to statistical analysis, and have to crunch through several thousand folders/files each day to, at a first glance, see if the file size indicates an error (too large/small etc). The ...
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114 views

Question about Dynkin Lehmann Scheffe Theorem

I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question. I am using Bickel and Doksum's "Mathematical Statistics" ...
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Estimating a distribution from a dataset with multiple parameters

How would you go about solving the following problem? You're an insurance company who writes workers compensation policies. You want to build a probability distribution for the number of annual ...
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8 views

Distribute chips over matrix [on hold]

Suppose I have a 2x2 matrix A. Each element in this matrix can have a value between 0 and 1. So for example element A[1,1] can be 0.6 and element A[0,1] can be 1.0 while the other two elements A[0,0] ...
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29 views

How to separate distributions from weighted dataset?

I’m trying to separate two component distributions of an apparent finite mixture from a weighted dataset (determined by a weighted.histogram). I've a set of data and weights only for a part of the ...
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How to get percentiles from empirical density in R?

The density() function in R allows me to enter observations and get an empirical density that I can plot x and y values. I like it because it allows me to weight observations according to how ...
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How to normalize bimodal (or multimodal) distributions?

If I have multiple data series, a = [a1, a2, ... a100] ~ bimodal with mu_a1, mu_a2, sigma_a1, sigma_a2, b = [b1, b2, ... b100] ~ bimodal with mu_b1, mu_b2, sigma_b1, sigma_b2, c = [c1, c2, ... ...
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Approximation of Gauss Hypergeometric function [on hold]

I have a non-convex optimization problem due to this Hypergeometric function: $_2F_1(a,k;a+b;z)$. I am looking for an approximation of this function with convex function(s).Any idea ? Thanks!
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62 views

Algorithm for rating books: Relative perception

So I am developing this application for rating books (think like IMDB for books) using relational database. Problem statement : Let's say book "A" deserves 8.5 in absolute sense. In case if A is ...
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Efficient scale & shape parameter estimation for generalized secant hyperbolic distribution needed

the (symmetric) generalized secant hyperbolic distribution GSHD is very flexible but I found not much at all on how to estimate its 3 parameters. Given the location, I need to obtain scale & shape ...
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77 views

Distribution function of maximum of n iid standard uniform random variables where n is poisson distributed

I am studying probability theory on my own and am trying to work the following problem in the book - Let $X_1, X_2, . . .$ be independent, $U(0, 1)$-distributed random variables, and let $Nm \in ...
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23 views

Approximation by uniform distribution

Imagine I have a random variable $X$ drawn from the sample space $S$ such that $Prob[X = x] = p_x$. Let $A \subseteq S$ be a subset of values from the sample space. My question is if we have a lower ...
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49 views

Derive the mean of a discrete probability distribution

I am reading inference statistics by casella and berger. They are deriving the general formula for the probability distribution like that: I do not get the step before the result. I would ...
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Tail index using hill estimator in R [migrated]

As part of my data analysis (of heavy-tailed data) I wish to calculate the tail (for both left and right) indices of around 100 time series of company returns. My data is stored in a large zoo object, ...
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32 views

Multivariate Hypergeometric Distribution with “or more” Successes

I understand how to calculate multivariate hypergeometric distributions. For example, if you have an urn with 2 red marbles, 4 white marbles, 8 blue marbles, and 12 orange marbles, the probability of ...
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Standardising data within-subjects when analysing distributions

Analysing behavioural data, Spivey, Grosjean and Knoblich, (2005) wanted to show that their results came from a unimodal distribution, rather than from averaging over subpopulations in a bimodal ...
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1answer
24 views

Which distribution to parametrize price histogram with exponential tail?

I have plotted price histograms which seem to follow and exponential tail very well. However, I would also like to parametrize the initial peak in the low price range. Can suggest what ...
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25 views

What is the distribution of inverse Wishart times a Fisher-Von Mises?

Suppose $p$-dimensional vector $x$ takes a Fisher-Von Mises distribution with parameters $\kappa, \mu$, and $M$ is inverse-Wishart with $n$ degrees of freedom and matrix parameter $I_p$, the $p\times ...
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62 views

Unimodal or bimodal data (MATLAB)?

I am trying to figure out what I did wrong or what I could do to get accurate results. I have n vectors of data, and I am trying to decide whether each dataset is unimodal or bimodal. I assumed that ...
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22 views

Range of successes for multivariate hypergeometric distribution [duplicate]

I'm trying to calculate the probability of drawing specific cards in a deck. I know that I can use multivariate hypergeometric distribution to calculate for a defined success. I'm wondering how I ...
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1answer
27 views

How can I determine if two features, given a set of data, are the same feature or not?

Thanks in advance for the help. Suppose I have a set of data of the form [feature, rating]. For the sake of argument lets assume feature can be movie A or movie B and rating is a ranked, continuous ...
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62 views

Posterior distribution of a random variable

Im not understanding the following; suppose $y \sim N (\mu,\sigma^2)$ and we have a prior $\mu \sim N (\mu_0, \sigma^2_1)$ Then we can figure out the posterior distribution. What i dont understand ...
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51 views

Moment generating function if the PDF is $f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$

Let $z$ a random variable with PDF : $f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$, where $0\leq z \leq d$, $F$ is the Hypergeometric function, $k$ is a positive integer, $-a+k+1 ...
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26 views

Stratified random sampling and its distribution

I'm learning stratified random sampling and I'm having hard time to solve this problem. consider the following population of six units: ...
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43 views

Is it possible to build a curve with a given skewness and kurtosis?

I have data in the following form: Day Kurtosis Skewness Total Inflows 163 .3 .5 435670 I'm attempting to do some modeling of an inflow ...
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1answer
25 views

Radial distribution to cartesian coordinates

I'm trying to go from a radial distribution in polar coordinates to cartesian coordinates. I'm using Matlab and have tried pol2cart, but are having some trouble getting a matrix with probabilities. ...
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32 views

Conditional or Joint Probability under Various distributions

In various statistical models the baseline equation (like in Naive Bayes $$\mathrm{classify}(f_1,\dots,f_n) = \underset{c}{\operatorname{argmax}} \ p(C=c) \displaystyle\prod_{i=1}^n p(F_i=f_i\vert ...
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19 views

Compare one distribution with multiple other distribution

I've a distribution of numeric scores computed using real data ( my reference distribution ). After that I generated 100000 random distributions of numeric scores computed using points picked at ...
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42 views

Variable bounds from infinity to negative infinity - Change Limits

I have a variable whose values vary between $-\infty$ and $\infty$. I'd like to change its limits from $0$ to $1$. I want to give extremely low values when the values are less than $-1$ or greater ...
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33 views

How to combine distributions

If I have two continuous distributions $f(x)$ and $g(x)$, there are several mathematical ways to combine $f$ and $g$ to get new distributions. Which correspond to what statistical interpretation? For ...
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71 views

How to calculate the scale parameter of a Cauchy random variable

Let $(X_n)$ be iid random variables and suppose they have mean 0 and follow Cauchy distribution. I know I can set the location parameter to 0. My question is how to find the corresponding scale ...
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1answer
53 views

What transformations preserve the von Mises distribution?

The von Mises distribution is entirely defined on the circle with a density given by $$f(x) = (2\,\pi\, I_0(\kappa))^{-1} \exp(\kappa \cos(x-\mu))\ ,$$ where $x$ is in an arbitrary real interval of ...
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45 views

What are the chances of something *not* occurring?

Suppose I'm gambling using a strategy of doubling my bet whenever I lose to recoup my losses from previous bets. If my initial bet is 1/2048 of my capital, I can bet 10 times before I run out of ...
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29 views

How to rigorously test if variables are drawn from a certain distribution

Say I have a list of numbers $X = \{x_1, x_2, \dots, x_n\}$, and I expect them to be drawn from a certain distribution. For my case it is the Binomial distribution $P(x) = \binom{n}{x}p^x(1-p)^{n-x}$, ...
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Identify points significantly outside a regression model

I would like to update my previous question "Methods to determine reliability of measurements using median and median absolute deviation". I have data from biological experiments, that look like ...
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1answer
62 views

Cramer-Rao bound for $\chi^2$ distribution parameter estimates

I've struck an unpleasant problem with the noncentral $\chi^2$ distribution. I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ ...
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18 views

Reference for Sampling distribution with varying sample sizes

I am looking for a reference on the sampling distribution associated with a population where each sample used to produce the sampling distribution is not of a fixed size n. Instead each sample will ...
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58 views

Skew normal approximation of Poisson distribution

What is the skew normal approximation to Poisson($\lambda$)? Am I doing this wrong?
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17 views

Estimating Parameters of truncated generalized pareto distribution by probability weighted moments

Is it possible to estimate parameters for a truncated Generalized Pareto Distribution (Wikipedia Article) by probability weighted moments? If not, why is that so? I am aware that it would be possible ...
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1answer
70 views

Difference between standard deviation and standard deviate

I was reading this paper http://comjnl.oxfordjournals.org/content/20/4/359.full.pdf and in the last paragraph of the first page, Rule 1 is given as $\alpha_{j+1} > \bar{\alpha} + k s_{\alpha}$. ...
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43 views

Linear regression without intercept - sampling variance of coefficient

I am comparing linear regression with and without intercept for the general sampling case. For this, I have $n$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y ...
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Generating density function from $\phi(t)= 1-|t|$

Given: $\phi_X(t) = \left\{ \begin{array}{l l} 1-|t| & \quad \text{if |t| ≤ 1}\\ 0 & \quad \text{otherwise} \end{array} \right.$ Find the density of X. Attempt: ...
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Is $\phi(t) = \frac{1}{2}[cos(t) + cos(t\pi)] $ absolutely continuous?

X is a real-valued random variable with characteristic function: $\hspace{20mm}$$\phi(t) = \frac{1}{2}[cos(t) + cos(t\pi)$, $\hspace{10mm}-\infty<t<\infty$. Is the distribution of X ...
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71 views

How can one construct a cumulative probability distribution function from 2 others?

I dip into project time estimation and can't find intuition. What is the cumulative probability distribution of an event when two independent tasks both complete successfully (when performed in ...
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39 views

Unknown null-distribution, known alternative distribution

I'm rather new to statistics, so please bear with me. I would like to be able to say "to within 95% confidence, this data is exponentially-distributed." In this case, I know how the data should be ...
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68 views

Check if a certain procedure is random or not

I am not a statistician, but I have a personal project and I need a help. I will simplify the project a lot to make it more clear and easier to understand. Then in base of your answers, I can fit it ...