A distribution is a mathematical description of probabilities or frequencies.

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Artificial Data Generation based on Data Distribution

My data looks something this (for example): Salary | Age | Zip | Class 60000 | 35 | 5 | Yes 50000 | 52 | 4 | No 10000 | 25 | 3 | Yes 70000 | ...
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Standard Error of Ratio of Weibull variates

Assuming that I have 2 distinct random variables that follow a Weibull distribution, what's the standard error* of the ratio of these two random variables? Basically I have $X \sim \text{Weibull}, Y ...
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How to compare the distributions of two variables

The attached figure plots the distributions of two variables. I want to demonstrate statistically how closely the the two distributions match each other. What is the best way of doing this?
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What does raising frequencies to a power do when calculating probabilities? [on hold]

For example I read some code iterating through an array of frequencies: ...
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Looking for a robust, distribution-free/nonparametric distance between multivariate samples

There are many distance functions for distributions out there, but I'm having a hard time wading through them all to find one that is "distribution-free", or "nonparametric", by which I mean only ...
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22 views

Correlation / clustering over lognormal data

I'm working with some financial data and it turns out my data is pretty much lognormal distributed. The question I have is, which produces "better" results: using plain data to find correlation / ...
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Need an effective way to show distribution changes over time and outlier reoccurence

Does anyone have suggestions on the best way to approach this problem? I have a large dataset (over 200k+ per day) in a MySQL database, that consists of a single record per user per day with a ...
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Expected distribution of Likert to test for bias

I have conducted a survey which included a Likert response question. My question is whether or not it is possible to conclude bias like extreme responding and acquiescence bias by looking at the ...
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88 views

Mechanics behind deviation from random distribution

The system we are working on is biological, more specifically the distribution of programmed DNA damage events across a chromosome. This can be thought of as 1D array (the chromosome) across which ...
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24 views

Question about histrogram in R-studio [closed]

Here is my code in R-studio hist(NPV, breaks=40, main="Frequency Distribution of NPV", xlab="Net Present Value (NPV)", col="blue", ylim=c(0,1000)) I have some questions about histogram in R-studio ...
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29 views

Combining the Standard Deviation for Multiple Populations; Small Data Sets

I have been presented with a very small dataset which describes a material property for a particular cast of stainless steel, in this case fracture toughness. The data is: ...
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How to represent distribution dependencies in Bayesian graphical models?

In a Bayesian graphical model, suppose that we have a random variable $B$ whose parent is the random variable $A$. So there is an arrow from $A$ to $B$, and this means that the joint distribution is ...
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36 views

can i make a linear congruential generator with lognormal distribution?

So as one of my class task is make a simulation. I've gathered the data and do distribution fitting to it and the result of the distribution is log-normal. i have the code to generate random number in ...
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42 views

Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable

I am aiming to run simulations in order to estimate the influence of the distribution of $Y$ (independent variable) on a certain binary outcome $X$ (dependent variable). $Y$ must always has a mean of ...
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7 views

Deconvolution on distributions with limited resolution

When you visit your optometrist to measure your refraction he/she tests your eyes with lenses of different focal lengths. These lenses come in steps of 0.25 diopters (D). Studies have shown that the ...
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36 views

Observations from two distribution functions mixed, how to separate them?

Assume I have 100 observations, I know they are from two distribution functions, they are mixed together. Is this possible to find out which distribution they are coming from? Here is an example in ...
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A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution — proof

let $Z \sim N(0,1)$ and $W \sim \chi^2(s)$. If $Z$ and $W$ are independently distributed then the variable $Y = \frac{Z}{\sqrt{W/s}}$ follows a $t$ distribution with degrees of freedom $s$. I am ...
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Statistics tests for monitor changes in data distibution (concept dritf) without knowing real output

I'm currently struggling with concept drift problem in on-line learing. I read some papers "Ikonomovska Gama - Regression Trees from Data Streams with Drift Detection " and check their implementation ...
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24 views

How to find the distribution of data? Can the distribution be sum of multiple distributions?

I need to find the distribution of the demand data to generate the demand. I tried to fit distribution using tools in excel and python. But for all the distribution, p-value was high (in simple terms ...
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30 views

Gibbs sampler for a particular distribution

I'm trying to implement Gibbs Sampler for the distribution: $$\pi(x,y)=e^{-10(x^2-y)^2-(y-1/4)^4}$$ So, like the first step, I need to find: $$\phi(t) = \int_{-\infty}^{t} e^{-10(x^2-y)^2-(y-0.25)^4} ...
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102 views

Arbitrary function approximation in one dimension

Suppose we have some arbitrary function $f: X \mapsto Y, X \in \mathbb{R}, Y \in [0, 1]$. It may be smooth but it may not. I am looking for some way to approximate this function given samples drawn ...
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66 views

I need to find the distribution of data, which is from a retail chain network. No distribution fits the data

I need to find the distribution of data, which is from a retail chain network( demand of product across all stores). I tried to fit distribution using EasyFit (which has 82 distribution to check the ...
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How can I calculate the posterior mean of a two-point distribution?

I am trying to reproduce some of the results in this paper. Specifically, there is a two-point distribution with one probability mass concentrated at $pfd_A \times pfd_B$ and the other mass ...
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average behavior of different data sets

I have $n=100$ different data sets, each of which are distributed as what it seems to be a power-law distribution with different exponents, i.e. $x^{-\gamma_{i}}$ for distribution $i$. What I am ...
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Scaling behavior of the Width of a distribution

I'm considering the following distribution on the interval $[-1,1]$: $$p(x)=\frac{1}{N}(1-x)^{n-p}(1+x)^p$$ where $N$ is a normalization factor while $n, p \in \mathbb N $ and $2\leq n$ and $ 1\leq ...
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Are two sets of multiple choice survey responses different?

I have survey data with 2 distinct types of respondents: tall people and short people. They've answered a series of questions about their preference for certain foods. I'm trying to determine what ...
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How to fit discrete data that have mode 0 to a log-normal distribution?

I am trying to figure out how to fit a log-normal distribution to discrete data that have mode 0, in particular, without first removing the zeros. For example, paper citation data are said to be ...
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23 views

Distribution of output from accuracy {forecast}?

I'm trying to work out a method for "online" or live model evaluation for models used in forecasting. One approach is to use the R package strucchange, but it ...
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Choose $m$ out of $n$ distributions s.t. the union of them likely contains top $k$ elements

I have $n$ sets of items. Each item in each set has a certain score. I want to select top $k$ items out of all available (i.e., out of the union of $n$ sets). However, explicitly calculating the union ...
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Independence of Sample mean and Sample range of Normal Distribution

Let $X_1,\dots,X_n$ be i.i.d. random variables with $X_1 \sim N(\mu,\sigma^2)$. Let $\bar X =\sum_{i=1}^n X_i/n$ and $R = X_{(n)}-X_{(1)}$, where $X_{(i)}$ is the $i$ the order statistic. Show that ...
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29 views

Normal with mean unequal to zero squared

It is a well-known fact that if $x_i \sim N(0,1), i = 1, \dots, n$, that then for $\nu \in \{1=1,\dots, n\}$ it holds that $\sum_{i=1}^\nu x_i^2 \sim \chi^2(\nu)$ I was wondering what now would ...
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218 views

Finding the point of maximum probability in a mixture of gaussians

I have a model that estimates probability of an object to be located in a 2d space. Using a mixture of gaussian with a set of criteria that I chose I got interesting results, and now I am faced to a ...
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Laplacian distribution in arbitrary and limited ranges

I'm writing a computer program that applies Laplacian noise to data, in which λ is unbounded, and my statistical competence is limited. If data is a generic numeric value that is ok, but if domain ...
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What distribution is this? (and how to simulate a sample from it in R)

This is the information given: 10% of the population is colour blind. Let $X$ be the number of colour-blind people in a sample of 20. The distribution is $X \sim Poisson(20, 2)$ - is this correct? ...
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Showing Expected Value and Covariance of an expression?

I want to find the expected value and variance of: \begin{equation*} Y(t) = e^{-\alpha t}X(e^{2\alpha t}) \end{equation*} where $X(t)$ is a Brownian process with parameter $\sigma$. I know the ...
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What conclusions can I draw from an empirical probability distribution?

I have 240 samples and their relative frequencies (calculated from empirical observations), hence I have the probability distribution. It looks like this (hypothetical values): ...
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Fitting measured, real-world data to theoretical distribution: How to test goodness?

I have a large sets of real-world user data (30k, 80k, 90k measurements). To be precise those are simply session lengths for a specific system. I want to create a theoretical model of this, to ...
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How to Use fitdist to Fit Johnson Familiy of Distributions in R? [migrated]

I would like to fit a a Johnson distribution to some data using the fitdistrplus R package, in order to compare with other distribution fits. The approach I have taken is to use the SuppDists package ...
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Samples from a multivariate t distribution

Hi I have the following problem. I draw a sample of a multivariate t-distribution with some fixed covariance matrix, so that the realizations are correlated, and $\nu=4$. Now I repeat this $n$ times, ...
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Benford's law: analyse individual variables or the entire dataset?

In his 1995 paper, Hill points out that random samples from random samples will usually give rise to data that satisfy Benford's law. He mentions a newspaper frontpage as an example where data may ...
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Stable distribution might not be a distribution generalizing normal distribution?

I am writing a paper using stable distribution in which this distribution would outperform normal distribution due to more parameters, specially in terms of log-likelihood and mean squared error. ...
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65 views

Does linear regression assume all variables (predictors and response) to be multivariate normal? [duplicate]

I stumbled on this really nice blog. http://www.statisticssolutions.com/assumptions-of-linear-regression/ It has mentioned- "the linear regression analysis requires all variables to be multivariate ...
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Testing a proportion in an online setting

I work in an online security setting. My goal is to detect if the number of locked accounts per time unit is stable or not. I've tried several approaches, detailed below, but I am not satisfied yet. ...
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53 views

Dividing or subtracting : Normal PDF's? of independent random variables [closed]

There is clear rule how to multiply OR sum Normal PDF's i.e. https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables $N_1(\mu_1,\sigma^2_1) + N_2(\mu_2,\sigma^2_2) = ...
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Determining continuous vs discrete data sets?

When I collect data for my work, I get a set like the following: [ 133, 183, 185.16, 188, 143, 128, 135.5, 100.55, 117.96, 95.5 ] These points are part of a ...
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108 views

Distribution and knowledge about a state of the environment

Let's assume I have a frequency distribution for train travel times, estimated based on one month of empirical data: [1:00h, 1:20[ : 20% [1:20h, 1:40h[ : 50% [1:40h, 2:00] : 30% Edit: The data ...
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what distribution might be a better fit?

I am trying to fit the data (the green curve) with a mixture of normal distribution. I obtained the fitted distribution (the purple curve) from norMixEM(), but the result is not very satisfactory. My ...
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209 views

How does linear regression use the normal distribution?

In linear regression, each predicted value is assumed to have been picked from a normal distribution of possible values. See below. But why is each predicted value assumed to have come from a normal ...
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Probability of binary outcome based on observed values of correlated variable

How should one approach the following problem? Suppose an object has an unknown binary attribute X in {0, 1} (for example it is only possible to be either ...
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Spatially inseparable data - what to do? [closed]

I'm new to machine learning and trying to solve this problem. In all tutorials, samples and so on the data is usually plotted in 2D and you can see some kind of structure which then the algorithm ...