Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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2answers
14 views

Is it appropriate use the Binomial Theorem to analyze the problem of rolling dice?

In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to ...
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Bayesian update vs optimization in multivariate case

Say I have a multivariate normal vector $r$~$N(\mu , \Sigma )$ and I observe that $ y \equiv Pr + \epsilon = Q$ where $P$ is a matrix and $Q$ a vector and $\epsilon$~$N(0 , \Omega )$. Now I ...
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1answer
10 views

Use Effect Size VS p-Value when determining the best fitting distribution?

I have a large sample size of about 50,000 I want to determine what theoretical distribution fits the distribution of my samples the best. What I did is to fit all distributions I know to the data ...
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1answer
10 views

Average expected reward vs expected reward for start-state

Suppose we are given a MDP and a policy $\pi$, where for simplicity we have exactly one possible start state $s_0$. Let $V^\pi(s)$ denote the expected return when being in a state s. Moreover, denote ...
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1answer
132 views

Showing t-distribution from multivariate standard normals

I came across a paper that assumes the following has a t-distribution: Let $W = \frac{\mathbf{a}'\mathbf{X}}{\sqrt{\mathbf{X}'\mathbf{X}}}$ and $\mathbf{a}' \in \mathbb{R}^n$ with $\mathbf{a}'\...
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1answer
31 views

Distribution for simulating machine learning algorithm errors

I want to simulate machine learning algorithm, that solves binary classification problem. This algorithm should output not just $\{0, 1\}$ labels, but probability of class $1$ (that of course is in $[...
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1answer
36 views

linear combination and univariate normal

Show that $(X_1,X_2)$ has a bivariate normal distribution with means $\mu_1, \mu_2$, variances $\sigma _1^2 $ and $\sigma _2^2$, and correlation coefficient $\rho $ if and only if every linear ...
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0answers
12 views

Why is Knuth's definition of random sequence (R4) too weak?

Knuth's $R4$ definition of a random sequence is called "too weak" and he presents an example of why --- second paragraph after the definition on the previous link. Definition $R4$. A $[0..1)$ ...
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7 views

Distribution to Examine Perceived Impact of Aircraft Flyovers [on hold]

I am attempting to model the impact of aircraft flyover noise and had a two question survey filled by students 1) The frequency of disruption of their study sessions per day 2) The perceived noise ...
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1answer
26 views

How probability distributions help a statistical analyst/data scientist

How exactly the probability distributions help a statistician/data scientist in modelling/decision making? Or how using distributions a data scientist derive any inference or make decisions when ...
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1answer
34 views

How to find probability of quantiles given mean and variance? [on hold]

If someone could explain the process for beginning this and the formulas involved I would be grateful. Male height in the Netherlands is normally distributed with a mean of 73 inches and a ...
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1answer
42 views

Why is weighing random observations according to their probability from all distributions wrong?

Is sampling all distributions n times and then talking out i numbers from each sample, where i is probability of that distribution * n, wrong? Suppose $$ 0.3\!\times\mathcal{N}(0,1)\; + \;0.5\!\...
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1answer
34 views

Probability that a set of values came from a distribution

I have a probability distribution. And I have a set of values. I need to figure out how to calculate the probability that these values were generated by the same model as the distribution. I found ...
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0answers
20 views

What is the standard deviation and mean of the reciprocal of normal distribution in terms of that of the normal distribution? [duplicate]

What is the standard deviation and mean of the reciprocal of normal distribution in terms of the standard deviation and mean of the normal distribution?
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2answers
33 views

How exactly does knowing a variable's probability distribution help you when learning about data?

I am an elementary/wanna-be statistician/data scientist from South Korea. I have been studying a variety of theories of mathematical statistics and different probability distributions. (I apologize ...
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0answers
9 views

test to know in what percentage 2 empirical probability distributions resemble [on hold]

I have two empirical probability distributions, and I would like to know the percentage of similarity between them. Just for the sake on an example imagine that I have a normal distribution and a ...
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1answer
18 views

Resources for Probability

I'm currently studying joint distribution functions (discrete and continuous) with their expectation, variance and covariance etc. I would like to get as much practice as possible. Can you suggest ...
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11 views

Finding the expected value of Laplace distribution truncated to interval [on hold]

Hello I am experiencing difficulties finding the solution for the following Problem: Find the expectation of X where X has a Laplace distribution truncated to interval [5, 9].
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1answer
25 views

Maximum likelihood estimator in Uniform distribution [on hold]

For Random sample with uniform distribution in Tetha< x< Tetha +1 What's the maximum likelihood function how can we maximize it?
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13 views

Finding the expected value of Laplace distribution for specific interval

Hello I am experiencing difficulties finding the solution for the following Problem: Find the expectation of X where X has a Laplace distribution on [5, 9]. I understand how to find the expectation ...
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0answers
10 views

Improving a landau-gaussian convoluted fit using ROOT

I am using the landau-gaussian convolution fit (available here - https://root.cern.ch/root/html/tutorials/fit/langaus.C.html) for my data but I fail to understand the behaviour of the fits. For some ...
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0answers
17 views

Distribution of the minimum and maximum order statistics under a partial ordering

Let ${\bf{x}} = (x_{11},x_{12}, x_{13},\ldots,x_{nm})$ and $f({\bf{x}})\propto 1_A({\bf{x}}) \prod_{i,j} {x_{ij}}^{\alpha-1} (1-x_{ij})^{\beta-1}$ for $i = 1,\ldots, n$ and $j = 1, \ldots, m$. That ...
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1answer
20 views

relation between location of a sample mean in sampling distribution and the standard error

Can someone explain the following statement with an example We'll describe the location of the sample mean by calculating how many standard errors it is away from the center of the sampling ...
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1answer
12 views

Distribution for difference in scores for a game

Imagine a game where the winner is the first player out of two to win 10 independent rounds. We can model the game as series of realisations of a Bernoulli random variable with parameter $p$. Lets say ...
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2answers
157 views

Distributions with simple truncated expectations

For a project I'm looking for continuous distributions which have a somewhat simple closed form for upper-truncation expectation ($E[x|x>c]$). Here are two examples I've found so far: Exponential ...
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0answers
40 views

Methodology to distinguish single and double exponential distribution

I have a set of n data points $x = [x_1, x_2,...,x_n]$ that follow an exponential distribution or a double exponential distribution (two different $\lambda$ parameters). In order to check which ...
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0answers
24 views

What does it mean when a distribution is “INDEXED” by something? [duplicate]

I am doing some reading and am seeing phrases such as the following. For context, I am learning about Bayes Inference and prior/posterior distributions so theta is the parameter: In such problems, ...
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1answer
23 views

How do I find the standard deviation that results in a specific probability coverage in a truncated normal distribution?

Given a truncated normal distribution $X$ with mean $\mu$, lower limit $a$, and upper limit $b$. How can I pick a standard deviation $\sigma$ such that $P(\mu -x\leq X \leq \mu+x)=y$ for some ...
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1answer
32 views

Drawing curve from events that have probabilities

I'm having some problems plotting my data, and understanding what I can do with it I have a dataset that looks something like: ...
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1answer
55 views

What is the name of this distribution?

I came across this: a categorical distribution with $K=10,000$ parameters (categories), and we take only few samples from this distribution, say $N=400$ (the point is $N < K$). Now, obviously, not ...
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2answers
28 views

Estimating parameters for the product of a lognormal random variable and a uniform r.v

Suppose I have a random variable which I suspect is the product of a lognormally distributed random variable $X$ and an independent uniformly distributed variable $U(0, 1)$. (The variables are the ...
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1answer
31 views

Literature on Bayesian stuff with Normal Distribution?

I am writing something on Bayesian Analysis involving the normal distribution. I know that the conjugate prior is the so-called normalized Gamma inverse distribution, I know the update rule for the ...
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0answers
8 views

Determining Boundary between True Positive/Negative Results

I have a large dataset of distributions similar to the histogram below. Each distribution is a part of an independent set that's being assessed one-by-one, and I'm looking to automate the process. ...
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0answers
76 views

Confidence Band for a function of the derivative and the value of the cumulative distribution function?

I am calculating a value that is computed by dividing the derivative of the cumulative distribution function by the value of the distribution function at that point. It is of the form: $J = \frac{F'(...
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19 views

How to test data with R fitdistrplus against rician and Rayleigh distribution? [closed]

As the title says I'm trying to test a dataset against Rician and Rayleigh distributions using Rs fdistrplus package. According ...
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0answers
33 views

Most likely time car reachs maximum and minimum speed

Assuming the acceleration of a car behaves like a normal distribution, wich we dont know the mean nor the std deviation: at minute 0 a car is driving at 50 km/h and at minute 10 his velocity is 60 km/...
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1answer
26 views

Number of samples to estimate Cauchy probability distribution?

I wonder how many samples (approximately) are needed to fit the parameters of a Cauchy probability distribution. I'm guessing probably more than with a normal.
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475 views

Is the value of a probability density function for a given input a point, a range, or both?

This post says A PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. Is it true? this is the PDF of ...
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1answer
39 views

Where the square comes from in chi-square test?

Chi-squared distribution with $k$ degrees of freedom is defined as: the distribution of the sum of the squares of $k$ independent standard normal random variables. Why the sum of the "squares" of the ...
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0answers
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Joint CDF of $Z = X_1 + X_2 + X_3, Y = X_3$

Given order statistics $X_1 < X_2 < X_3$ I am trying to find the Joint CDF of $Z = X_1 + X_2 + X_3, Y = X_3$. i.e. $P(Y \le y, Z \le t)$. I am leaving out the specific distribution as I have ...
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0answers
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How to generate data in order to fit the i.i.d. assumption in many machine learning applications? [closed]

In many examples in data science and machine learning, the training data and the target is assumed to be generated in an i.i.d. fashion. Example: https://www.ijcai.org/Proceedings/07/Papers/121....
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1answer
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1answer
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Mahalanobis distance - understanding the formula [duplicate]

I've read quite a few explanations on this topic, liking this one the most: https://mccormickml.com/2014/07/22/mahalanobis-distance/ But there is still one thing I don't understand. I understand ...
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0answers
26 views

A set of duplicated normal random variables [on hold]

I am working on the following problem. I have a set of $n$ random variables $$X=\{x_{1},x_{2},...,x_{n}\} \sim N(\mu, \sigma)$$I also have a set of $n$ random variables $$Y=\{p_{1},p_{2},...,p_{n}\} \...
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0answers
13 views

Why probabilities are measured over intervals (instead of points) for continuous probability distributions? [duplicate]

In case of discrete probability distributions, we find probabilities of different points/values over exactly those points, but in case of continuous probability distributions, we find probabilities of ...
3
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1answer
61 views

Finding joint distribution of $(X + Y,X^2 + Y^2)$ where $ X,Y$ are independent standard normal variables

Find joint distribution of $W = X + Y$ and $Z = X^2 + Y^2$ where $X,Y \stackrel{\text{i.i.d}}\sim\mathcal{N}(0,1)$. I am trying to do this by the change of variable method. So first I need to get $X,...
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0answers
20 views

What is the distribution of a point to a random line?

Let's say that we have a random vector that represents a line [A,B,C] so that, Ax + By + c = 0. A, B, and C are independent Normally distributed random variables, with different mean and variances. if ...
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2answers
66 views

How reparameterize Beta distribution?

Consider $X \sim N(\mu,\sigma)$; I can reparameterize it by $X = \epsilon\mu + \sigma; \epsilon \sim N(0,I) $ But given Beta distribution $X \sim Beta(\alpha,\beta)$; is there easy way (closed form ...
8
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3answers
102 views

Getting all answers correct by taking the same exam for fewest times

Rain never studies, so she is completely clueless during the midterm even though it consists of Yes/No questions only. Fortunately, Rain's professor allows her to re-take the same midterm as many ...