Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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What can we say about $\log \zeta(\mathbf X)?$

I previously asked: Visualisation of L(X). Unfortunately I didn't receive an answer. This question is related to that question with some new elements... Let $\mathcal L^n_+$ the set of all $n$-...
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Comparing similarity between multivariate distributions

I'm a non-mathematician trying to get a better intiution into how we can go about saying if one distribution is closer, or further away from another. For example, if we have a set of patients who each ...
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Formula for producing probability that binomial distribution was created with different odds of producing heads?

Given a binomial distribution of, say, unfair coin flips: 1 1 0 1 0 0 1 1 0 I'm trying to determine: given an x% probability of flipping heads, what are the odds ...
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Calculating a probability of a function of a random variable in a limit

I am reading the paper Luo et al.: Parameterized Explainer for Graph Neural Network and trying to understand the mathematical reasoning after Equation (4) on page 5: How do they calculate $\...
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Likelihood a datapoint belongs to a given non-normal distribution

This problem is encountered by me lot of times. Let's say I have a set of data points (x1, x2,....,xn) whose mean and standard deviation can be calculated. However these data points are non-normally ...
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How to test statistical probability that two distributions of boolean values are different [duplicate]

I'm looking for the name of a statistical test or method to compute the statistical probability that H0 : two distributions of boolean variables are the same. In an example, let's say i have a ...
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How to find the distribution of a function of two random variables?

I have the joint pdf $$f(x_1,x_2)=\begin{cases}\frac{1}{4}\;,\ -1<x_1,x_2<1\\ 0\;,\ \text{otherwise.}\end{cases}$$ I have to find the distribution of $Y=\frac{X_2}{1+X_1^2}.$ I have tried to ...
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How to test the effect between income and economic growth in spss?

am going to test the impact and relationship between income, which is an independent variable, and economic growth, which is a dependent variable, over 10 years in spss? Thanks
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Approximate minimum

I’m measuring some data (cpu usage for a fixed amount of work), which could be represented as: C + noise The noise will never be zero or negative, but on average ...
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What are the rules for Significant Figures, Precision, and Uncertainty, strictly speaking?

In the physical sciences (which are physics, chemistry, astronomy, materials science, etc.), we learned that the uncertainty is ± the smallest unit (which is 1) of the last significant figure if the ...
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Finding the unconditional distribuition of a variable

Im solving Gibbs sampler related questions and Im trying to find the unconditional distribuition of $\beta | \lambda \sim N(0, \lambda^{-1}\Sigma)$ knowing that $\lambda \sim Gamma(\frac{\alpha}{2}\...
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Given the CDF of $X$, find the distribution of $X$ and $P(1 < X < 5)$ [closed]

I know I have to find the distribution of X and then sum the probabilities of the values that apply the rule, but I just can't figure out how to do it.
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Convergence of standarized empirical distribution functions to distribution of standarized sample mean

Suppose we have a family of $i.i.d.$ random variables $\{X_n\}_{n=1}^\infty$, with distribution function $F(\cdot;\mu,\sigma^2)$, with mean $\mu\in\mathbb{R}$ and variance $\sigma^2>0$. By virtue ...
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Python/numpy - conditional sampling of variables, distribution of subsequent value is based on result of previous value

I am trying to generate a random sample of multiple variables which are loosely related to each other. Meaning that "allowed" values of some variables depend on the value which is set for ...
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What is the prior corresponding to a weighted sum of pdfs?

Recently, I have read a paper (Bayesian Bridge Regression , H. Mallick, 2018) which states that since $$ \frac{\lambda^{1/\alpha}}{2\Gamma(1+1/\alpha)}e^{-\lambda|\beta|^\alpha}=\int_{u>|\beta|^\...
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Looking for a predictive prior for what I thought to be Bayesian Analysis

I need a prior with 2 parameters location (μ) and scale (σ) (a transformation of mean and standard deviation). My distribution is over discrete values, equally spaced with distance $c$ between ...
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Generating samples from a distribution while ensuring sample mean equals distribution's mean? [closed]

I am working with a software that for a given distribution and sample size $N$, it produces $N$ data points with a guarantee that the sample mean of these points is equal to the mean of the assumed ...
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Sampling from bivariate conditional distribution

I would like to sample from a bivariate conditional distribution $F(y_1, y_2 |X_1 = x_1, ..., X_p=x_p)$, where the distribution is determined non-parametrically. How can I sample from such a ...
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Create a synthetic dataset from the measures of spread

I have certain measures of spread (p50, p66, p75, p80, p90, p95, p98, p99, p99.9, p99.99, p100, Median, Mean, Min, Max)as my attributes. Can I regenerate a data distribution from these? Use case: I ...
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Transformations for zero inflated non-negative continuous response variable in R

Initially, this was going to be a simple analysis of variance (ANOVA) with a categorical predictor (4 levels) and a non-negative continuous response variable (number of aphids on leaves from four ...
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Is $f(\widehat{x})$ ($\widehat{x}$ is a random sample of $x$) equivalent to $\widehat{f(x)}$ (a random sample of $f(x)$)? [closed]

Assuming $f(x)$ is an injective function, is sampling $\widehat{x}$ from the distribution of $x$ then calculating $f(\widehat{x})$ equivalent to directly sampling from the distribution of $f(x)$? Note ...
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How to find the marginal prior distribution?

Suppose that $\beta$ has the following prior $$ \beta|\zeta \sim f(\beta,\zeta) $$ Then I know that the marginal prior distribution of $\beta$ is given by $$ \int f(\beta,\zeta) d\zeta $$ However, ...
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Nonparametric Order Statistics - Does this Exist?

I was reading about Order Statistics (https://en.wikipedia.org/wiki/Order_statistic) : Apparently, if we have a sample with "k" number of elements (e.g. x1, x2, ...xk) and assume a ...
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Significance test for an image centroid

I have an n x n matrix. Each cell contains a value. The matrix is essentially a heatmap. The null hypothesis is that the greatest values would be at the horizontal and vertical midlines of the matrix. ...
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Particle filter with systematically incorrect motion model

I'm familiar with particle filters from robotics, as a tool for synthesizing information about a robot's motor control with measurements to maximize localization accuracy. Given probabilistic models ...
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Why does Anderson-Darling statistic increase as Frequency is increased for my data?

I have been carrying out sieve analysis to estimate the median particle size of a powder. I wanted to check if the data so far followed a normal or lognormal distribution, as I have come across ...
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How to calculate the combinations probability of X>values given a frequency distribution

Lets imagine I have the following distribution of values: Value N Cases % 0 60 60 1 20 20 2 10 10 3 8. 8 4 2. 2 Assuming independence of events and no order: What is the probability of a ...
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Python : How to Generate positive number with a given standard deviation and mean within 0-1? [closed]

I want to generate a list (or array) of all positive numbers, and all the numbers need to be within 0-1. I've seen one code, ...
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How to prove the mean of a sample approximates well to the mean of the population

Suppose I have a population whose distribution is definitely not normal but both the population and sample size will be large. Is there any way I can prove/ show that the mean of a large enough sample ...
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Probability that a > b when a = b + constant [closed]

X is a random variable with normal distribution of average 260 and sd 50 What is the probability that a >= b when a = b + 15 Brand X computer have a average battery duration of 260 minutes with a ...
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Ranking log-linear distributions and the Lucas numbers

The wikipedia page on rank-size distributions claims: "When any log-linear factor is ranked, the ranks follow the Lucas numbers, which consist of the sequentially additive numbers 1, 3, 4, 7, 11,...
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Help with interpreting a cumulative probability distribution graph in a journal paper

I am from the life sciences field (neuroscience research) and I am reading a journal paper about the formation of dendritic spines. In their experiments, they count the number of protrusions along ...
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Upper bound for random correlation

I recently had a conversation with a college of mine and this question popped into my mind and I am unsure how to solve it. Let's say I have 100 variables. Some of the variables have a pairwise ...
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Noise model to encompass most other noise models

Suppose I have lots of compute and wish to model a wide variety of possible 1D signals, but instead of trialing vast datasets I simply generate lots of random signals. The goal is to find an extremum ...
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How to transform parameters to obtain an "unbounded" Johnson distribution?

When applying the R fucntion SuppDists::FitJohnson() to data, the Johnson distribution parameters are automatically calculated, ...
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Find mean value of total N with only relative frequency and mid point histogram [duplicate]

I have the following data of number of vouchers redeemed : How can i calculate the mean value of total vouchers?
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1 answer
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Calculate mean of sample size based on relative frequency in histogram [duplicate]

I have the following data of number of vouchers redeemed : How can i calculate the mean value of total vouchers?
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I learned that CLT is about unbiased statistic, like means. What about sum of distributions (not sampling sums)?

Let's assume I sample many means from any distribution (that has the 1 raw moment). It should resemble the normal distribution. I heard that the same works for medians, variance, range and any other ...
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Systematic differences between estimates resulting from Linear Regression and General Additive Model

Dear stackoverflow community, in a project I am part of we use two approaches to estimate monthly and weekly data means and proportions of indicators of mental health. The latter is primarily intended ...
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Why is the log-normal distribution called "multiplicative? What is multiplicative in it?

Like in the question. What exactly is "multiplicative" in the log-normal distribution? I heard many times, that additive processes are by nature normal and symmetric, and multiplicative are ...
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Sub-sampling a dataset to a different target distribution without replacement - bias correction?

Suppose i have dataset $X$ and $Y$, and i want to sub-sample from $X$ so that the resulting (sample) distribution is as close to that of $Y$ as possible. One thing i can do is subsample with ...
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Intuition behind log in kl distance

So, let's start stating that I already read both Why KL-Divergence uses "ln" in its formula? and What is the role of the logarithm in Shannon's entropy?. However, I still have no ...
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Find a score to assess my predictive models

I have a dataset of numbers that contain several tail events, I fitted a distribution to my data and I am now creating models to try to find the 99% percentile at each position (hopefully the tail ...
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How to calculate the probability distribution of the sum of two dependent random variables?

I need to calculate the PDF and CDF of the polynomial $c_1+c_2 x^2+c_3 x^4$, where $c_1>0$, $c_2<0$ and $c_3>0$ or $c_3<0$ and $x$ is a random variable following the truncated half nornal ...
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Check if growth rate is worse than quadratic?

I was asked to move the question here (https://stackoverflow.com/questions/72692849/check-if-growth-rate-is-worse-than-quadratic) Let's say I have collected a dataset for estimating algorithmic ...
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Can a sequence of PMFs converge to a PDF?

Is there a meaningful sense in which a sequence of PMFs (of a corresponding sequence of real-valued random variables) can uniformly converge to a PDF? Intuitively, it seems like a strange question to ...
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2 votes
1 answer
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Log Cauchy distribution as lifetime distribution

Though I know that the moments of Log-Cauchy distribution do not exist, is it possible to use the Log-Cauchy distribution as a lifetime distribution under Type-II censoring? Because the MLE of the ...
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Is sequence of probability mass functions always uniformly bounded

Say that we have a sequence of discrete random variables, $\left\{X_n\right\}_{n \in \mathbb{N}}$, which converges to a random variable, $X$, with a continuous distribution, e.g., the Normal (Gaussian)...
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What is 'factored models'?

What is 'factored models'? I've seen the term 'factored models' in paper 'The Bayesian Structural EM Algorithm'. But I see it for the first time and it is hard to understand... I tried searching it ...
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Which distribution do reddit link scores follow?

I'm trying to model the distribution of link scores (number of upvotes minus number of downvotes) on reddit, for a single subreddit at a time. For example, here are some histograms of post scores on /...
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