# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### KL divergence of categorical distribution with continuous inputs

I want to simulate a process. I have a probability distribution and I have d classes to choose from. The inputs of my distribution are 3d points and it maps each of these points to a d-dimensional ...

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### Estimating ratio of two PDFs where one of them is noisy

I have a list $L_1$ of positive integers, such as $[1, 2, 1, 3, 10, ...]$. There are repetitions. From this list, I sample (with repetition) according to some method (not relevant to my question), and ...

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### Combining information from multiple distributions

I have 13 classes. For each class, I have a different distribution: e.g.
For each distribution, the y-axis indicates the probability and the x-axis indicates a count value.
Given some input data, I ...

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### R: Question about central limit theorem

Hello everyone :) can you help me please, I really don't understand my teacher's videos and it is the last part of our 20-pages work :O
In the question 1 they ask us to create a Poisson distribution ...

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### the true proportion is within two standard deviations of the sample proportion

A tutorial says
If there's a 95% chance that the sample proportion is within two standard deviations of the true proportion, that's equivalent to that there's a 95% chance that the true proportion ...

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### Determine Normal Distribution based on LogNormal Distribution

Suppose that we have that $Y=e^{aX}$ where $a$ is a positive scalar. We know that $Y$ follows a logNormal distribution with parameters $0$ and $2$. Then is there a way to derive the distribution of $X$...

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### Fitting stock prices to MLE in Python

Given the return prices $r(t) = p(t) - p(t-1)$, fit these to the mle of the following distributions in Python:
t
Exponential
Power law
Mixture Dirac Binomial
So i've got my return prices through <...

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### Is the mean of two symmetric, independent random variables also symmetric?

Does a proof exist that the mean of two symmetric, independent random variables is also symmetric? Or is the conjecture false?
I would be interested to learn about references to this question, or ...

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### Extending normalized probability generating function (pgf) in branching process

My question is in the context of branching processes and simply how to extend a normalized negative binomial probability generating function (pgf) from $\frac{1}{y}[G(s)]^y$ to $\frac{n}{y}[G(s)]^y$ ...

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### Doubt about the formula for āThe on-policy distribution in episodic tasksā

I've read the post how Deriving the formula for "The on-policy distribution in episodic tasks"? but I've a problem.
If I apply the sum for all states $s \in \mathcal {S}$ in
$$
\eta(s) = h(...

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### Formula for difference in order statistics [closed]

Is there a specific formula one can use to compute the differences in order statistics, say $x_i - x_{i-1}$ when the underlying distribution of $x$ is standard normal?
Also what is the asymptotic ...

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### Restricting Binomial Success Rates in simulation

Suppose I am generating 10000 data points with probability P out of N total trials, but I know that P x N can never be below M, where M < N. How would I go about restricting my simulation to never ...

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### Separate individuals with uniformly distributed events from individuals with other type of uneven distributions

I am working on a project where I have a dataset in which the occurrence of some events are mapped into a two dimensional grid for different individuals.
I would like to separate the individuals ...

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### How do we obtain the probability density of a truncated regression with an upper and lower bound

I know my density for $y$ is supposed to be something of this form $$g(y|x_{i},t)=\frac{f(y|x'\beta, \sigma^{2})}{F(t|x' \beta' \sigma^{2}}$$ where the numerator is the density of the normal ...

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### scipy.stats failing to fit Weibull distribution unless location parameter is constrained

Here is a demo set of data points that are drawn from a larger sample. I fit a Weibull distribution in R using the {fitdistrplus} package, and get back reasonable ...

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### Trying to determine which distribution to use for my percentage data for mixed effects model

I am seeing a lot of different answers to percentage data, either beta or binomial with a logit link and not to use poison distribution because it isn't count data. My response variable is retention ...

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### Why does the standard deviation of the sampling distribution of the sample mean needs N >= 20n

I keep seeing sources stating, without proof, that the standard deviation of the sampling distribution of the sample mean:
$$\sigma/\sqrt{n}$$
is an approximate formula that only holds if the ...

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### Error : data must be a numeric vector of length greater than 1 [closed]

Please help me to solve this error, thank you.
pWeiNorLL <- function(q,mu,sigma,c,gamma) 1-exp(-(pnorm(q,mean=mu,sd=sigma)/(gamma*(1-pnorm(q,mean=mu,sd=sigma))))^c)
dWeiNorLL <- function(...

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### Probability of observing a number of special balls from a larger set

Suppose there is a collection of $n$ balls of which $m$ are special. What is the probability of drawing $k$ special balls, when $p$ balls are drawn?
To give it a try I considered the following ...

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28 views

### Understanding Hypothesis tests for a Pareto distribution

I'm writing an essay that's looking at the presence of the Pareto Principle in data. Unfortunately, as a consequence of interest, I've picked a topic that involves statistical analysis well above what ...

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### Find distribution that minimises a function of its moments [closed]

Imagine a probability density function $f(x)$, defined for positive $x$, and let's note its $n$th non-centred moment $x_{n}$. The mean $x_{1}$ is fixed (and positive).
How can I find $f(x)$ that ...

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### Machine learning a discrete probability distribution that is parametrized by a set of real-valued parameters

Assume I have a probability distribution $p_\theta(\sigma)$ defined over discrete binary variables $\sigma$, $p_\theta(\sigma) : \sigma \to [0,1]$. This probability distribution is parametrized by a ...

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### How pvalue is calculated internally here ? And what is the data point for which it is calculating pvalue

I got a into a question while going through poisson distribution.
Here it is:---
A nuclear pump failed 5 times out of 94.32 days.
Give a 95% confidence interval (CI) for the failure rate per day
So ...

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### Binomial distribution - Question with exercise

I have the following exercise which they give us a hint that the binomial distribution is likely to apply.
A company manufactures car components. The quality control scheme for a particular type of ...

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+200

### Probability distributions associated to the logarithm numeration system

The most elementary logarithmic numeration system is defined as follow. Any random number $X \in [0, 1]$ can be represented uniquely as
$$X=\log_3(A_1 + \log_3(A_2+\log_3 (A_3 + \cdots)))$$
with $A_k \...

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### Statistical test for non uniform counts

I have data on counts for about 1000 categories in a sample. I want to get an estimate if the counts are somewhat uniformly distributed across 1000 categories, or most of the counts are cominf from ...

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### Compare the variances of multiple categorical distributions in a repeated measure design

I ran three model-building procedures with different parameters on the same sample and obtained the selection of my optimized hyperparameter for each outer fold (each of the analyses had 100 outer ...

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### Factorization of joint distributions [closed]

Proving the following factorization formulas.
(a) P(x, y, z) = P(x)P(y|x)P(z|x, y),
(b) P(u|v1, . . . , vn) = P(u, v1, . . . , vn)/P(v1, . . . , vn)

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### Learning Distributions: What is the best way for a neural network to predict continuous output distributions from continuous input distributions?

I am dealing with a problem, where I have 3 probability distributions from which I want to predict another set of 3 distributions. The distributions in the input and output describe the same 3 ...

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### Simulation and sample size [closed]

How to make simulation for very large sample size?
Stats:Experts believe that social distancing can reduce transmission of COVID-19 by about 60%. If the total COVID-19 cases all over the world are ...

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### Excel's BINOM.DIST different from R's dbinom [closed]

I am verifying some data in Excel and found that Excel's BINOM.DIST function yields somewhat different results from R's dbinom function. The table below shows the first 11 differences when the total = ...

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### How to prove a multivariate r.v. does not follow the nonparanormal distribution?

Background
You may find the definition of the non-paranormal distribution at the 2nd paragraph in p.2296 of this paper.
In short, $(X_1, \ldots, X_p)$ is non-paranormal if there exists a set of ...

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### What is the expected value of x log(x) of the gamma distribution?

Let $w(x) = x \log{x}$
$x \sim Gamma(\alpha = 3.7, \lambda = 1)$
Find $E[w(x)]$
I have set up the following integral:
$\int_0^{\infty} x\log{x} \frac{\lambda^{\alpha}}{\Gamma(\alpha)} x^{\alpha -1}...

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### Sum of exponential of uniform random variables?

Let $F_{i}$ and $\phi_{i}$ are uniformly distributed independent random variables in the range $[-50,50]$ and $[-\pi/4,\pi/4]$, respectively.
If $N = 10$ and
$$Z = \sum_{i=0}^N e^{j(F_{i}+\phi_{i})}...

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### Gaussian closest to a maximum of Gaussians

Let $X_i \sim \mathcal{N}(\mu_i, \sigma_i)$ be independent, normally-distributed random variables. Let
$$Y = a + b \max_i X_i$$
where $a \in \mathbb{R}$ and $b \in (0, 1)$. Which Gaussian ...

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### Parametric model closed under translation, contraction, and maximum

Is there a nontrivial parametric model that is closed under translation, contraction, and maximum? That is, does there exist a nontrivial parametric model $\mathcal{M}$ such that
$$\forall i \in I : ...

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### Smooth sample space

What does it mean that a sample space is smooth and thus we can represent the target distribution with a probability density function?
Source: http://arxiv.org/abs/1701.02434 in section "1. ...

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### Trying to find errors in the distribution and the numerical summary of a graph of test scores

My mathematics and statistics instructor gave me a graph showing the distribution of test scores for exam 1. She said that there are errors in the numerical summary of the graph and in the ...

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### How to estimate the PDF of the logarithm of a uniformly distributed random variable?

This is a question I have to solve and need help with. I know it's usual to give pointers and hints so the OP can follow from there. Thus, I'll appreciate all input that shows me the way to go.
Let $...

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### How can I make a probability paper plot of a log-normally distributed variable?

My company has software that can take a vector of samples and easily create a probability plot of the data and the least-squares or method of moments fit of the data. However, I need to be able to ...

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### Convert Probability Density Function to Normal pdf

Suppose i have a variable that follows a certain distribution. For example $X \sim exp(\lambda)$. If a want to find $P(X > k)$, i just need to integrate the pdf between $k$ and $\infty$. Suppose ...

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### How to derive the distribution of a random variable as the absolute value of a uniform random variable

I'm trying to derive the distribution of a random variable $Y$ given that I know the distribution of a random variable $X$ and the relationship they share.
The $pdf$ of $X$ is expressed as:
$ f_{...

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### Difference between pooled data or panel data for my situation

i am a beginner for panel data econometrics. Need help of experts of the field deciding if it is panel or pooled data or should i use any other methodology.
I have data from wind mill and we use wind ...

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### What is the probability that X=Y<Z

Let $f(x,y,z)=e^{-x-y-z},\,x>0,y>0,z>0$ and 0 elsewhere, be the joint PDF of (X,Y,Z). Compute, $P(X=Y<Z).$
I started the answer as follows.
$\begin{align*}
P(X=Y<Z)=\int_{z=0}^\infty\...

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### Express the posterior distribution: $P(L|X_{1:N})$ using Baye's Rule in terms of the Uniform Distribution

$f(Z; A, B) = \frac{1}{B-A+1}$ if $A ā¤ Z ā¤ B$,
0 otherwise $(1)$
$P(L) = f(L; 1, M)$, (the prior) $(2)$
$P(X|L) = f(X; 1, L)$ (the likelihood of a single license plate number X) $(3)$
We further ...

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### Probability of a binomial random variable being the maximum of a set of binomial random variables

Let $X, Y, Z$ be independent random Binomial variables, each parametrised with different $p_X, p_Y, p_Z$ but the same $n$. I am interested in a formula for determining the probability that the value ...

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### In a statistics paper, how to know which parameterization of a given distribution is being used?

Let's say I'm reading a paper, and the authors write $\alpha \sim \text{gamma}(a, b)$. How do I know which parameterization of the gamma distribution they are using? Is there a convention or must one ...

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### Fitting a distribution. How

First of all, i am not good at this. i need to know what distribution fits in this dataset. i though it could be a poisson due to the characteristics of the data. the data talks about forest fires.
...

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### Probability of filling M boxes with 2 or more elements when sampling S elements from N total elements

Similar to this question, Frequency of Item in Combination.
I am randomly sampling S objects out of N=99 objects into 9 boxes labeled by a single character, "A-I". Question 1: I want to find the ...

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### Understanding NBD transaction process and Pareto dropout process plot conceptually

I am learning to use the BTYD package that uses the Pareto/NBD model to calculate CLV. However, I am struggling to understand certain plots conceptually.
For ...