A distribution is a mathematical description of probabilities or frequencies.

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fitting parametric survival curves on Kaplan Meier probabilities in aggregate data

Lets suppose I have aggregate survival probabilities (NOT individual level data) from Kaplan Meier curves. I would like to curve fit different "types" of distribution like exponential, weibull, ...
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Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
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Parametric distributions over orthogonal projection matrices?

Consider the set of rank m orthogonal projection matrices in $\mathbb{R}^{d\times d}$, for some $m<d$. With appropriate measure-theoretic considerations, one can define multiple distributions on ...
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11 views

Complicated joint distribution with constraints on the ratio

I'm trying to create random draws of pairs of numbers based on desired distributions of the numbers and the ratio of the two numbers. Let me explain in more detail, although I apologize if my notation ...
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1answer
31 views

Compare distributions (with replicates) and visualization

The experimental set-up is an almost typical control vs treatment, in which we are counting how many reads map to a particular class of genes in each condition (RNA-seq), done in triplicate. An ...
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1answer
19 views

What are some standard bimodal distributions?

I have plotted this curve using the default kernel density estimate function in R I am looking for some standard distribution which could be close to this. Is there any standard bimodal distribution ...
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44 views

Using Dirac Delta functions for estimating a probability distribution

I'm having some trouble understanding this slide. It's mentioned in the context of gaussian distributions. I sort of understand the Dirac delta "function". The main difficulty I'm having is with ...
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1answer
30 views

Hazard function of a gamma distribution

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

Finding the distribution of a pormanteau test

I am trying to find the distribution of a pormanteau test for lack of fit estimating an ARIMA(1,0,1) with white noises and fitting an ARIMA(1,0,1). I know this is not the best way to obtain a certain ...
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44 views

How to model this?

I've had this problem in my head for about a year now, and have never quite been able to find an angle to tackle it from whenever I come back to it. I'm sure there is a way to model this ...
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8 views

mean of a frequency distribution [on hold]

he manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the mean ...
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2answers
52 views

How to get the derivative of a normal distribution w.r.t its parameters?

We normally calculate the derivative of normal density w.r.t its parameters, mean and variance. But can we calculate the derivative of normal distribution wrt the parameters(not the variable, I know ...
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26 views

Bayesian Model For Churn

I need to evaluate how long a customer stays with the company given a retention offer she accepted $r\in\{r_1,\dots,r_k\}$ I'd like to use Bayesian inference for modelling churn. What prior ...
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1answer
30 views

Information from plot of sorted values of a vector

Can we get any meaningful information (especially regarding its distribution) from a simple plot of sorted values of a vector? For example, what would following plot convey: ...
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17 views

Given a set of data, how can I know which distribution those follows? [on hold]

The data contains 2000 observations. I also want to know which R package could solve this problem.
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47 views

Standard Error of the ratio of Binomial variates

What's the right way to compute the Standard Error of the Mean of the ratio of two random variables that follow a binomial distribution? I asked a similar question here using Weibull distributions ...
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15 views

Diagram for spotting distributions, like “contradicting” results

Let's say we have two results that are related to each other: Result 1 was a questionnaire about food and had two options "I dislike Cake" and "I like Cake". The result is displayed as a ratio: ...
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16 views

How to test hypothesis on the composition of CAPM portfolios

I'm facing two different portfolios in CAPM framework derived as $$\hat{\omega}_P=\hat{\Sigma}^{-1}\frac{E(r)-r_f}{H}(\hat{\mu}-\iota'r_f)$$ on the same assets but, for example, on different time ...
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1answer
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1answer
43 views

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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3answers
73 views

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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22 views

What does raising frequencies to a power do when calculating probabilities? [closed]

For example I read some code iterating through an array of frequencies: ...
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2answers
75 views

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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1answer
23 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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16 views

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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14 views

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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1answer
122 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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35 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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1answer
50 views

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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1answer
39 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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1answer
44 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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1answer
38 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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3answers
151 views

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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25 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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1answer
33 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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1answer
105 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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1answer
68 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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20 views

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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43 views

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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24 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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18 views

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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2answers
54 views

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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1answer
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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1answer
220 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 ...