A distribution is a mathematical description of probabilities or frequencies.

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Sampling from $k$ urns until drawing at least $n$ marables from any of them

What distribution describes sampling with replacement from $k$ urns with probabilities $p_1,\dots,p_k$ (where $\sum_i p_1 = 1$) until drawing $n$ marbles from at least one of them? It's not negative ...
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How Many Random Choices Before They Have All Been Picked About The Same # Of Times?

Given a set of numbers 1 through X, how many times do I have to randomly pick a number before all of the numbers have been picked an equivalent (roughly) amount of times? For example: Given numbers 1-...
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141 views

Truncated normal distribution over a union of intervals

Suppose I want to find a truncated normal distribution, but instead of it being defined on an interval $(a,b)$, where $-\infty<a<b<\infty$, I want it to be defined on an interval $(a,b)\cup(c,...
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What is the point of using an initial estimate when sigma-clipping data?

I am reading a paper that is discussing sigma clipping some velocity data, lets call it a set $V$, and it says: The center at each iteration of the $3\sigma$ clipping is the biweight average, and $...
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2answers
38 views

Obtaining distribution from histogram

I have an array of values, with those values I plotted the histogram, calculated mean and variance. I want to know the corresponding distribution from the histogram obtained. How is it possible? Could ...
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53 views

Variance of a distribution of multi-level categorical data

I am currently analyzing large data sets with various characteristics (such as city). I wanted to find a measure which would essentially say how much or how little of a variance there was across the ...
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1answer
19 views

Derive z- or t-statistic from p-values of regression coefficients from a probit/logit model

I have the results from an empirical study reporting the results for a probit and logit model. They just report the p-values of the regression coefficients. I want to derive the corresponding $t$-/$z$-...
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How to identify parameters of distributions of a mixture when many samples are sum of the samples?

I have a list of values which are samples from 4 different normal distributions. The list also contains sum of two or three sample values. I would like to identify parameters of the distributions. An ...
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38 views

Distribution of the sum of the two dependent bivariate gaussian distributions and related questions

This is something I was thinking about and I decided to modify a question from a mid-term to ask this. Suppose $X_{1}$ and $X_{2}$ are two bivariate gaussian variables, decribed as $$ X_{i}=\begin{...
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8 views

Evaluate various censored estimators goodness-of-fit with and without ground truth

I would like to evaluate the goodness-of-fit for non-parametric estimators (Kaplan-Meier, Nelson-Aalen and their smoothed variations) of the survival function on a number of datasets. For some of them,...
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57 views

K-S test is too sensitive

I'm trying to compare two samples to see if they come from same distribution. I'm not just interested in the measures of central tendency but in the overall shape and nature of the distributions. ...
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Actuarial question [on hold]

A family buys two policies from the same insurance company. Losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10. One policy has the ...
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28 views

How to compute frequency distribution in R? [migrated]

Actually there are many functions which I don't know what to use to calculate it X = rnorm(100) Lets assume I have a normally distributed vector called X. I don'...
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19 views

2d points distribution with shifted centroid

How can I have a distribution with centroid being away from center? i.e. points distribution starts out dense, and then goes on to become sparse, but with NO sudden transition? Pl find the image ...
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10 views

Limit-bound continuous data, how to compare multiple distributions?

We are doing a simple experiment looking at the effect of smell on taste. 200 subjects are given a liquid to taste and asked to rate the favorability of the taste on a scale from 1 to 20. The subjects ...
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47 views

What distribution describes this process?

I have three clinics that are testing for Zika virus. We know the proportion of positives aggregated across all clinics, i.e., the first clinic has identified 20% of all positives across the three ...
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25 views

Probability of a Blizzard - Poison vs Binomial vs Bayesian

My goal is to model data I have collected to compute the probability of a severe blizzard occurring in a given set of states (region). Assume the US is broken into 3 regions that categorize the ...
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13 views

Using differential entropy for characterizing a number

I have to come up with a score representing the information related to a number pulled from a a text (IM text). When correctly identified the numbers in our Ims follow a distribution composed of two ...
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49 views

Variance of the modulus of a random variable

Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. What is the upper-bound on the variance of $Y=\left|X\right|$? My gut feeling says that $\operatorname{Var}(Y) \leq \operatorname{...
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How to best describe a bunch of 2D histograms/distributions?

For chords of several music genres, I have subjective ratings from subjects that show how pleasant they found each chord (x axis below) and also how consonant (y axis). A scatter plot (or rather a ...
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Measuring the spread of values in a matrix

Given the following matrices: Matrix 1: \begin{bmatrix}1&1&1\\1&1&1\\1&1&2\end{bmatrix} Matrix 2: \begin{bmatrix}0&0&5\\0&5&0\\0&0&0\end{bmatrix} ...
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Goodness of fit tests in R

I have a population of 663 random balls drawn. The interval of this population's values is [1,27]. I want to do a Goodness of fit test to proof if it has a gamma ...
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KL Divergence between an i.i.d sequence and non i.i.d sequence

I have two sequences of probability density functions $Q=\prod_{i=1}^{n} q(x_i)$ (independent and identically distributed, i.i.d )$P=p(x_1,\cdots,x_n)$ (non i.i.d). How can I calculate the KL ...
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39 views

Working with percentages of positive variables

Say we run an experiment and observe the following impact on a variable of interest (one row per experimental unit): ...
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75 views

Permutations and probabilities for indistinguishable balls into indistinguishable fixed-sized buckets

I'm neither a statistician nor a mathematician so apologies if this question is asked and answered elsewhere or if I've misdescribed my problem. I am trying to figure out in a thread in stackoverflow ...
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Can I compare chi-square values for goodness of fit tests to see which observed distribution deviated most from its null distribution?

I have a series of goodness-of-fit tests using chi-square a few of which are below, $$ \begin{array}{r|r|c} \text{df} & \chi^2 & \text{Reject } H_0 \\ \hline 49 & 1744.68 & \text{Yes}...
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How can I check the quality of my probabilities?

I have a data set where the number of accidents are given together with the probability (assumed to be correct) that the number of accidents is less than 4. The task is to calculate the probabilites ...
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Limiting distribution with two additive terms converging in distribution

I have a question related to the asymptotic distribution of an estimator $\hat{\beta}$ that tries to estimate the true parameter vector $\beta$ and can be written as $\sqrt{N}(\hat{\beta}-\beta)=\...
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What is the intuition behind the Population Stability Index?

The "Population Stability Index" for two distributions $P$ and $Q$ is defined as the Symmetrised Kullback-Leibler divergence: $$ \mathrm{PSI}(P,Q) = D_{KL}(P||Q) + D_{KL}(Q||P) = \sum_i(P_i-Q_i)\log\...
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Fit parametric distribution to time-series data

I have a time-series of daily revenue data for a number of years and I would like to perform a parametric distribution fit to the data. Given that distribution fitting requires i.i.d. data, I presume ...
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1answer
28 views

What does the height represent in a probability density function? [duplicate]

I know the integral represents the probability, but what does the height represent? It can’t be the number of times that a feature appears, because the function is continuous. I understand that it is ...
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Sampling without Replacement and Non-uniform Distribution

There are $N$ items, numbered $1 \ldots N$. The probability of selecting item $i$ in one draw is $p_i$. Items are drawn without replacement, so after each draw we need to do a re-normalization. Now, ...
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51 views

What does it mean for two random variables to be equal?

I understand that 2 variables may be independent and identically distributed, but I am unable to understand what it means for them to be equal. I came across a statement of the birthday paradox and ...
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What error distribution can I use for GLMM with continuous data but not normal due to too many 0s?

I am having problems with building a generalised linear model with random effects. I am modelling how a sensitivity ratio between various taxa and cyanobacteria (logSR) is effected by the taxa and ...
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What error distribution can I use for GLMM

I am having problems with building a generalised linear model with random effects. I am modelling how a sensitivity ratio between various taxa and cyanobacteria (logSR) is effected by the taxa and ...
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13 views

density plot / kernel

Can anyone explain in more narrative and less technical terms what exactly a density plot is? It seems like it shows the probability of getting a certain value in each histogram bin based on the ...
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Are there examples of non exponential family distributions with sufficient statistics?

In Casella Berger's Statistical Inference, they observe that it is rare to find 'a sufficient statistic with dimension smaller than the sample' (section 6.2.1). Although rare, are there examples of ...
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PDF from difference of two Weibull distributions

How should I derive a PDF from the difference of a couple of given two parameter Weibull distributions ? The convolution integrals become very difficult to evaluate. PS : The parameters are not ...
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Confusion regarding conditional distirbution of the product of gaussian process with a normal

I am getting confusedregarding a simplae problem. say $Y = WX$ where $X$ is a q X n matrix with each row a Gaussian process denoted as $\mathcal{GP}(M(\mathbf{X_i}),C(\mathbf{X_i},\mathbf{X_i}))$, in ...
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Case control study - possible options

Lets assume that I have a two populations ${A, B}$ and they are different in terms of some features such as country. Both samples have fairly large number of ...
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1answer
21 views

What is the mode of Dirichlet-Multinomial (Polya) distribution?

What is the ML estimate of the parameter $e_i$ for the Dirichlet-Multinomial (Polya) distribution defined below? $p(\mathbf{x}|\mathbf{e}) = \frac{N!}{\prod_i^d x_i!}\frac{\Gamma(A)}{\Gamma(N+A)}\...
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How to smooth distribution with Gaussian kernel?

I have a theoretical cross section(just a function $f(p^2)$) which depends on $p^2$(where $p$ is impulse). I know that equipment give we $p_{exp}$ with normal distribution $N(p_{real}, \sigma)$. So, ...
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25 views

How to calculate the central moment giving function of a distribution

Is there a function which gives the central moments instead of just moments of a distribution and if so how to calculate this function for a distribution e.g. the normal distribution.
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Are there any non exponential family distributions with conjugate priors? [duplicate]

I believed I had been taught that only exponential family distributions have conjugate priors but I have recently read that ' all exponential family distributions have conjugate priors', leaving the ...
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Limit of Bernoulli R.V.s is a singular distribution

Working through an exercise in Probability (the question can be found in Lamperti). Let $X_1,\dots$ be independent Bernoulli random variables with $\mathbb{P}(X_i=1) = p$ and $\mathbb{P}(X_i=0)=1-p$. ...
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How to test the distribution of the transcripts per million (tpm) values and analyze ASE (allele specific expression) differences between haplotypes?

I have the TPM (transcripts per million) values generated for my RNAseq data. My overall goal is to identify genes that show allele specific expression differences. In the table below the TPM values (...
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Fit tail to monotonically decreasing data

I am trying to fit several distributions to monotonically decreasing data, and pick the one that fit the best based on several criteria, e.g. mle estimate. I am able to do this by fitting a curve to ...
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Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
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Make two distributions equal

Question in short: How can I make two histograms equal by explicitly downsampling the buckets? More detailed version: I have realizations of sequences of two discrete random variables both giving ...
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Number of parameter in a distribution and Accuracy

I have some data sets defining a random variable (already checked). and I tried to fit those data to different distributions. I have found a bunch of distributions that fit and have not been rejected ...