Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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1answer
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deciles in skewed distributions [on hold]

Does it make sense to use deciles for distribution that are skewed. For example, consider the exponential distribution with lambda >= 1.5 or lambda distribution ...
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1answer
59 views

How likely is sample A and sample B is from distribution C? [on hold]

Let's say I have a sample A: [0,0,0,1] and another sample B: [2,0,5,10,100,3,2,6] I would like to know the probability that A and B are both picked from the same population C. I tried applying a ...
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0answers
22 views

Binomial distribution - Variance (Experimental vs theoretical)

Just been experimenting with creating a simulation for the binomial distribution. I've made an applet in Geogebra that generates the histogram, mean of the experimental data, the variance of the ...
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1answer
28 views

How to do Chi-square test with given distribution

I see that function for Chi-distribution are given on this page: https://wiki.freepascal.org/Generating_Random_Numbers The code (comments added) is as follows (in Pascal - easily understandable): <...
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2answers
89 views

Distribution of the Sum of 2 Rayleigh Distributed Values

Problem I have been trying to determine the distribution of the sum of 2 values sourced from a Rayleigh distribution with the parameter $\sigma$. Unfortunately, I am unable to match a computer ...
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0answers
24 views

Classifying feature vectors just using a probabilistic classificator for the iris dataset [on hold]

I would like to classify the iris dataset and subsequent vectors from an estimation or guess of the iris dataset distribution. I would like to compare the performance with a neural network. I would ...
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0answers
21 views

Dealing with positively skewed data when doing multilevel sem in lavaan [on hold]

I am conducting a multilevel sem model using lavaan, and while I'm able to run the code, not all expected results are showing. I ...
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25 views
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6 views

What could be a good quality index for an OCR scanner? [on hold]

I have an OCR (Optical Character Recognition) that, given the image of a word, tries to detect the letters giving, for each letter, the accuracy as a 0-1% probability. For example suppose that I have ...
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1answer
64 views

Total variation of a distribution

The wikipedia page for Total Variation says that "The total variation of any probability measure is exactly one" (and is therefore not interesting). I don't get why. For example, if I take a ...
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7 views

compounding a gaussian with shifted exponential

Wikipedia states that the exponentially modified gaussian distribution is a compound probability distribution in which the mean of a normal distribution varies randomly as a shifted exponential ...
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0answers
5 views

Gil-Pelaez condition

I'm struggling to understand some passages of proof of Gil-Pelaez condition here described (pag. 1,2), i.e. ** $P_j=\mathbb{Q}(S_T>K)=\frac{1}{2}+\frac{1}{\pi}\int_{0}^{+\infty}Re[\frac{e^{-iuK}...
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1answer
20 views

dmultinom discrepancy [closed]

I am trying to write a simple Maximum Likelihood Estimator based on the following pmf for the multinomial distribution. $$f(x_{1},\ldots ,x_{k};n,p_{1},\ldots ,p_{k})=\frac{n!}{x_1!\cdots x_k!} p_1^{...
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1answer
37 views

What is the relationship between: the first raw moment, location, expected value, mean in general, arithmetic mean for any sensible distribution? [closed]

I am a bit confused by the several sources telling that: the first raw moment is by definition the arithmetic mean expected value of any random variable is exactly the arithmetic mean The expected ...
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1answer
70 views

Identifying a distribution

I am trying to understand what sort of distribution is produced by the following code. Using the following Matlab code we can generate a distribution (normalized such that the sum of the set is equal ...
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0answers
29 views

Bayesian estimation from sum of two random variables

Let's say I have a set of observations $Y=\{Y_1,\ldots,Y_N\}$ where each observation is created as the sum of two random variables, i.e. $Y_i=X_{1,i}+X_{2,i}$. Also, I know that $X_1 \sim Dist_1(\...
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1answer
11 views

Mutual Information between multi-dimensional and single dimensional Variables

I would like to estimate MI between two variables X and Y of shape (nXd) and ...
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1answer
21 views

Is it possible to determine a dice pool from a given range?

First off, assuming this problem - or one similar enough to directly apply - hasn't already got an official theorem or conjecture proving it one way or the other, I'd be content with simply being ...
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9 views

Spatial modelling: raster calculation from covariate estimates of GLMs produce some negative values in raster distribution data

I am constructing spatial distribution models/maps for soil carbon using coefficient estimates from a GLM. The GLM is made up of a mix of continuous and categorical variables and the response is a ...
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0answers
11 views

Why can “one row of this element” in the MCMC output table represent marginal posterior distribution? [duplicate]

Take the table below as an example, which is in Box 8.1 of this book. This table illustrates the converged MCMC output including the first and last five samples for parameters and derived quantities. ...
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1answer
61 views

Why is the population standard deviation approximated as the sample standard deviation?

This question addresses calculating a p value from the mean and standard deviation statistics of a sample. I understand that the -general- philosophy is to divide the sample standard deviation by the ...
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0answers
28 views

On estimators that do not converge to a constant

Say one had constructed an estimator $\hat{\mu}_n$ for a parameter $\mu$ and that such estimator had the property that $$ \hat{\mu}_n \xrightarrow {d} X $$ where $X$ is a random variable with an ...
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1answer
33 views

Binomial Dist problem

I want to know how I would go about computing how many times I would need to flip a coin where $P(H) = 4/5$ to make sure that the proportion of heads that shows up is in between $75$ and $85$ percent ...
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1answer
46 views

Learn this distribution from samples? What is the sample complexity?

$\newcommand{\norm}[1]{\left\lVert#1\right\rVert}$ We have an $n$-variate distribution $X\in\{0,1\}^n | \sum_i^n X_i = k$. Or, in other words, we are guaranteed that only $k$ variables will be $1$ in ...
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0answers
12 views

A/B testing for control and test stores

I have historical data for 1000 stores across US. Now I want to introduce an offer in few of the stores (eg 20 Stores) and see its effect on overall sales of those stores after two months. The way I ...
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13 views

Statistical Process Control with Big Data

At work one of our projects has been to monitor a certain type of mechanical system and identify anomalous behavior. Luckily for us we have access to 5+ years of system performance across many ...
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1answer
33 views

Non norma distribution

I have a non-normal distribution (Kilograms ~ Years), so I can't use ANOVA test to reject the null hypothesis (that the tree means are equal). There is a tendency of weight to be 100kg. Is there a way ...
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1answer
43 views

Does the sum of two independent exponentially distributed random variables with different rate parameters follow a gamma distribution?

short question. Suppose we have two independent exponentially distributed random variables with means $400$ and $200$, so that their respective rate parameters are $1/400$ and $1/200$. Do these ...
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24 views

Distribution $f$ that minimizes $JSD(f||q) + JSD(f||p)$

What can we say about the distribution $f^*$ that is the solution to the following optimization problem: $$\min_f JSD(f||p)+JSD(f||q) ,$$ where $p,q$ are given distributions over some set, and $JSD$ ...
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3answers
66 views

How to visualize an evolution of a distribution in time?

Suppose you have a record of distribution for each day in some period. For example, some distribution which depends on a parameter which evolves over time. Suppose we have dozens or hundreds of days. ...
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2answers
46 views

Developing a 40-100 scoring system (doesn't work as intended) [closed]

I am using r. I have a dataset with this distribution There are 1275 observations with values ranging from ~ -0.07 to mostly 0.08. I have 4 outliers that are over 0.8 (0.12, 0.12, 0.12 and 0.10). I ...
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0answers
13 views

Hypothesis test of distributions from two biased samples using NPMLEs

Suppose $X_1, ..., X_n$ is a biased sample (bias mechanism known) from distribution function $F_1$ and suppose $Y_1, ..., Y_m$ is another set of observations sampled in a differently known biased ...
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10 views

Permuting RV order in stacked Auto-regressive Flows for density estimation

Brief background: Normalizing flows such as detailed in MAF and B-NAF use an auto-regressive formulation such that highly expressive bijective transformations of the RVs satisfy the probability chain ...
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1answer
48 views

Conditional Mean E[X|X>Y] when X,Y are Uniform [duplicate]

X and Y are independent and identically distributed uniform (0,1) random variables. Find E(X|X>Y) Please explain it step by step. I am getting ans 0.5 while the actual answer given is 0.66
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30 views

Please solve the following problem [duplicate]

Need not to solve the whole question just tell me how to proceed $U_n$ will follow cauchy distribution since ratio of standard normal is cauchy.Please specify the parameters I am confused. $V_n$ is ...
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30 views

Sampling disttibution

If $(x_1,x_2,\ldots,x_n)$ be a random sample drawn from a normal population with mean $\mu$ and standard deviation $\sigma,$ then find the sampling of $T=\sqrt{\sum_{i=1}^n (x_i-\bar{x})^2}.$ Further ...
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Symmetric distribution problem (MCQ)

please refer to the question in image source :CSIR NET Mathematical science exam there is only one correct option and answer key says its option 4. since $X_1$ is symmetric so $X_1$ and $-X_1$ ...
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13 views

What does normalized gamma random variable with single parameter means?

I am trying to understand a paper related to mmWave communication. The author says (in a rephrased manner) the following The transmission channel $h_l$ follows Nakagami fading with parameter ...
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4answers
1k views

Why is the concept of the Null hypothesis associated with the student's t distribution?

There are dozens of continuous probability distributions like Gaussian (normal), Variance-gamma, Holtsmark, etc. Yet, the concept of the Null hypothesis is basically associated with Student's t-...
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2answers
59 views

Sum of squared variables equals Chi-squared implies that the variables are standard normal?

It is known that if iid $Y_1,...,Y_n \sim N(0,1)$ than $\sum_i Y_i^2 \sim \chi^2_n$. However, if we know that (independent) $Y_1,...,Y_n$ have $\sum_i Y_i^2 \sim \chi^2_n$, can we say that $Y_1,...,...
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0answers
25 views

Distribution of the idle time in a queue

I have iid random variables $D_t \sim \mathcal{N}(\mu, \sigma^2)$ and a constant $Q$. Define a random variable $Z_t = (Z_{t-1} + Q - D_t)^+$. Essentially $Z$ is the waiting time distribution in a ...
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1answer
134 views

If $X$ is a normally distributed random variable, then what is the distribution of $X^3$? Does it follow a well-known distribution?

I am trying to estimate the power production ($P$) from a wind turbine. The instantaneous power of a wind turbine varies with the cube of the wind speed ($v$), so $P = v^3$. If $v$ is normally ...
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0answers
33 views

Limiting Distribution of $n\left[Y_n\right]$ where $Y_n$ is the minimum of a sample of size n from Uniform$\left(0,\theta\right)$ distribution

Suppose $X_1,X_2,\dots,X_n$ is a random sample from Uniform$(0,\theta)$ for some unknown $\theta > 0$. Let $Y_n$ be the minimum of $X_1,X_2,\dots,X_n$. (a) Suppose $F_n$ is the CDF of $nY_n$. Show ...
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1answer
43 views

Order statistics uniformly spaced?

Suppose you have $n$ i.i.d. random variables $X_i$ that take values in $[0,1]$, and have an absolutely continuous distribution. Let $X_{(1)}\le X_{(2)}\le \dots \le X_{(n)}$ be the random variables ...
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2answers
38 views

“Merging” different normal distributions

Consider two different classrooms, A and B, containing 25 and 30 students respectively. Grades obtained in classroom A are distributed normaly, with mean Ma and variance Va, while grades obtained in ...
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0answers
38 views

Characterizing a distribution

I have a set of words which in a given year has a frequency of occurrence k. I can observe that these words follow frequencies k1, k2, k3,....kn in the following year. If I have some data in the form ...
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0answers
21 views

Confusion about the average of two non-normal distributions and expected values

I don't really come from a stats heavy background and am having trouble understanding what the right approach to this question is: A question states that 'a company is trying to increase the ...
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0answers
17 views

Tail of the CDF of noncentral chi-squared RV

The pdf and cdf of the non-central chi squared RV (under the scenario I am studying) is given as follows: \begin{align} &f(x)=\frac{1}{v} \exp\left(\frac{-(a+x)}{v}\right)I_{0}\left(\frac{\sqrt{xa}...
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0answers
22 views

Gauss's Original Gaussian Distribution Proof Help

I am refering to the proof of the guassian from the famous document: https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/stahl96.pdf I have attached the pictures below of the ...
4
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1answer
24 views

Stable and efficient computation of binomial expectations

Suppose we want to compute the expected value of some function $f(X)$ where $X \sim \text{Bin}(n,\theta)$. Taking $\mathbf{f} = (f_0,...,f_n)$ to be the function values over all possible outcomes of ...