A distribution is a mathematical description of probabilities or frequencies.

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Perturbation of binned random variables

Setup: Assume that we have an interval coded random variable $T$ which takes values in the set of half-open intervals $\{[L_1, U_1), \ldots, [L_K, U_K]\}$, where $U_k$ and $L_k$ are the upper and ...
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46 views

Which mean value should I use

I am to test the transformational shifts in three different directions for 3 different imaging techniques in a group of 30 patients. I am trying to prove one is not statistically different to the gold ...
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Quantifying the similarity of distributions

I'm looking to quantify the similarity / difference of two income distribution pairs and then compare the quantity with other distribution pairs. Any pair of distributions have the same number of ...
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94 views

Can somebody identify this distribution?

I am searching for the name of the distribution associated with this density on $\mathbb{R}_+$: $$p(r|\lambda) = \frac{2\lambda ...
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Sampling Size for a large Dataset

I am having a dataset of size upwards of 200 million rows. I have no knowledge of the distribution of this dataset. Would like to perform some analysis on this - like look at the ...
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Sampling from a multivariate distribution

Given $X = [X_1 X_2 \ldots X_n]^{\top}$ is a vector of independent bernoulli random variables and $A \in \{0, 1\}^{m \times n}$ is an arbitrary boolean matrix. Define a random variable $Y$ as $$Y = ...
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estimating the upper bound on a uniform distribution from max order statistic

I have a question. Suppose that $X_1,\ldots,X_n$ are iid $U(0,\lambda)$ and let $X(n)$ denote the nth order statistic. Suppose $\lambda$ is unknown and should be estimated from the sample. Take ...
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What is the limiting distribution of the sample mean?

My question is relatively simple: what is the limiting distribution of the sample mean? But there are some technicalities I want to discuss. context: I was asked this problem in an exam, and I feel ...
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1answer
39 views

General questions on MCMC

This is a continuation of the following question. The previous link was related to rejection sampling. This is related to MCMC. General questions on rejection sampling 1a. As far as I understand, ...
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General questions on rejection sampling

I am new to Bayesian methods. I was going through a chapter on sampling. I have a few questions related to it. Please help me get these clarified. As far as I understand, rejection sampling will not ...
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13 views

Relation of distributions

I want to predict a distribution using multiple related distributions. One method is to use multiple regression (the model specification is that the dependent variable, yi is a combination of the ...
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10 views

Role of Chi inverse distribution in the confidence interval of standard deviation

Suppose X = [11.17, 9.52, 10.69, 9.84, 10.84, 9.88, 10.28, 12.23, 18.4] is a random variable with mean and standard deviation as 11.48 and 2.77, respectively. If I calculate the lower and upper ...
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How to determine the sample size, if standard deviation, population mean, sample mean and precision is given?

Determine the sample size if sample standard deviation is 6, population mean : 25, sample mean = 23 and the degree of precision is 99%
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Why do we estimate population parameters using statistic?

I had been studying statistics, I have a doubt that I couldn't find the answer of. Its related to estimating population parameters using statistic. Suppose we have a population size of 10000, we want ...
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2answers
54 views

What distribution is this? Activated process

A particle randomly hops a discrete distance from one position to another. I have measured, for 200 hops, the time between each hop. Here is the histogram: What distribution is this? To look at, ...
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423 views

Does mean = median imply that a unimodal distribution is symmetric?

For a unimodal distribution, if mean = median then is it sufficient to say that distribution is symmetric? Wikipedia says in relationship between mean and median: "If the distribution is ...
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[SOLVED]Is there a name for this simple discrete distribution? [duplicate]

I'm just wondering if there's a name for the distribution described by the following p.m.f $$p(n) = n(1-s)^{n-1}s^2$$ where $n$ is an integer from $1$ to $\infty$ and $0\lt s\lt1$. Thanks.
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1answer
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Salary Range Determination When Given Percentiles

Can one determine an accurate salary range (minimum, mid and maximum) if only provided the 25th, 50th and 75th percentiles?
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1answer
47 views

How to test an extra small sample is from discrete distribution?

My sample size is less than 7. The discrete distribution has 5 values, skewed, bell-shaped. How to test that the sample is from this distribution?
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SPSS: How to split distribution evenly to analyze subgroups

I have a normally distributed SPSS dataset with 1400+ cases. I want to create sub-groups based on "age in months" that are distributed evenly. The dataset ranges from 12 to 60 "age in months". ...
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1answer
39 views

What is the difference between a distribution and a semi-distribution?

I hope the question to be clear. The name "semi-distribution" certainly implies some meaning, yet, I'm unable to conclude what really means. I found the term on this paper: ...
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Conditional and joint pmf of sequences of random variables

I have random variables $X_1...X_N$ which are Poisson($\theta$) distributed. I also have inclusion indicators $Y_1...Y_N$ which are Bernoulli($\pi$) distributed. These indicate whether $X_i$ is ...
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1answer
66 views

Gaussian is conjugate of Gaussian?

Someone told me that, Gaussian distribution is conjugate to distribution because a Gaussian times a Gaussian would still be Gaussian distribution ? Why is that ? Say the following situation: $X\sim ...
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1answer
19 views

joint probability distribution with a constant

If $X \sim N(0,1)$, then what is the joint probability distribution of $(X+1,X)$? An attempt: $f(x,x+1)=f(x|x+1)f(x+1)=f(x+1)$, so $N((0,0),(0,0;0,1))$. Note sure though...
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Regression with non-zero mean errors

I want to fit a linear regression model of the type $$y_j= x^{\top}_j\beta +\epsilon_j,\,\,\, j=1,\dots,n,$$ However, the distribution I am using for modelling $\epsilon_j$ does not have mean zero, ...
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376 views

What's the difference between Gaussian and Bernoulli?

Starting from this sentence: The trait theory considers for example introversion and extroversion as two extremes of a single continuous line: the population will be distributed in a Gaussian ...
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Multivariate nonparametric divergence (or distance) between distributions

For example, we could say I have two fruit classes (oranges and apples) and for each one I measured different statistics of interest, for example: width, height, sugar, water... of a lot of fruit ...
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How the PDF of random-variable is affected if the original transformation is translated?

Let $X$ be a continuous random-variable with probability distribution $f_X(x)$. Let $Y=g(X)$, where $g(\cdot)$ is some transformation and we also know $f_Y(y)$. Question How the probability ...
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Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
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To model an unknown bounded probability density function by a Gaussian mixture

I have points in dimension 10 coming from an unknown probability distribution. The nature of data strongly suggests that this distribution is bounded. But the boundaries are not precisely known and ...
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How normalize this distribution probabilities [closed]

I have these probability distributions, how can I normalize then calculating the Kullback Leibler divergence ? ...
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1answer
72 views

which distribution should be used in this question?

A basketball player succeeds in making a basket three tries out of four. How many times must he try for a basket in order to have greater than 0.99 probability of making at least one basket? In this ...
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In a two-way ANOVA, how can the F-statistic for one factor have a central distribution if the null is false for the other factor?

Consider the two factor additive ANOVA model $$\begin{align} X_{ij} &=\mu_{ij}+e_{ij} \\ \mu_{ij}&=\mu+\alpha_i+\beta_j \end{align}$$ where as usual $\sum_{i=1}^a \alpha_i=0$ and ...
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nonparametric method to calculate the probability how alike two samples are

I have two samples with each couple of hunderd observations. I want to calculate a probabilty how much they look alike. I'm aware of tests like kolmogorov smirnov but I don't think I need this. I ...
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Statistical help for a disability device [closed]

I'm from the Museum of Human Disease at the University of NSW. We are developing a word creator for people who have severe quadriplegia and can only use their tongue. These people have lost the use of ...
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1answer
26 views

Use the properties of linear combinations to derive means and standard deviations

I'm studying different sampling distributions, and have run into a difficult problem with linear combinations. How may I use the properties of linear combinations of random variables to derive the ...
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1answer
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Transformation of normal distribution

Suppose I have a normal distribution $A \sim \mathcal{N}(\mu,\sigma^{2})$ with a known cuttof point (percentile) on this distribution called $o$. Based on this point the distribution needs to be ...
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Using STDEV and RANGE to subset data to desirable subjects

I am running several subjects through a mixed model regression and have encountered problems in which several of the subjects have an undesirable distribution for the specific study I am performing. ...
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1answer
41 views

Inconsistency between sample median and theoretical median for skewed normal using rsnorm in fGarch

I am using the rsnorm function within the R fGarch package to generate random samples from a skewed normal distribution. ...
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1answer
61 views

Truncated Von Mises-Fisher distribution

I am putting a von Mises-Fisher prior on my data. The data does lie on a unit sphere, but the only problem is that my data is always positive. So I feel like I am wasting my prior on unnecessary ...
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Can I use K-S test to distinguish distributions?

I am using the kolmogorov smirnov test to differentiate between distributions. My example is below where I am comparing DATA2 and DATA3 to DATA1. From the image, I was hoping to quantify that DATA1 ...
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how can i work out the percentage of rows with matching values in 2 different columns? [migrated]

I'm trying to find out the percentage of my users which return to my site by comparing their 'Joined' date and their 'Last Seen' date. In more literal terms, I have a table which looks a bit like ...
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covariance matrix of residuals from a fitted model to decorrelate residuals

I fit a geeglm model with clustered data and now I would like to decorrelate the residuals of the model in order to run model diagnostics. I read that if I can obtain the covariance matrix of the ...
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Question about piecewise exponential distribution

This is an excerpt from the following paper. I am particularly interested in knowing how the authors got the displayed equations. We let [Z] denote the distribution of a generic random variable ...
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Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
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1answer
43 views

What is the statistical distribution of a Poisson process when the windows size is different?

I have a discreet random variable X known to be Poisson distributed. This represents the number of observations in a certain time window, day one day. Assuming there are no other factors dependent on ...
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1answer
45 views

Weird pdf of a quadratic function of a N(0,1) variable: miscoding or big rounding error?

I would like to calculate the pdf of a random variable y defined by : y=c+b*x+a*x^2 The pdf is a non-central chi-squared distribution. For a>0, it should be equal ...
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When is distribution of $|X+Y|^2 $ equivalent to $|X|^2+|Y|^2$?

I am trying to compute the distribution of the following $$Z=\bigl(X+Y\bigl)^2$$ BUT I have that both $X$ and $Y$ are Nakagami with parameter $m$. (A Nakagami random variable is the square root of a ...
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Distribution of transformation of normally distributed variable

Apart from lognormal, is there any other convenient distribution that is obtained from transformation of a normally distributed variable and has the support of [0,+infinity)?
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log-linear models and exponential models?

What is usually referred to as "log-linear models"? Is a log-linear model an exponential model where the normalization constant is 1? (since its logarithm needs to be a linear function.) Or is there ...