Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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12 views

How to compare 2 groups with different sizes?

I wish to compare network density metrics. I have 6 densities from 6 different graphs. Each graph has different number of nodes as well different number of edges. I wanted to compare the 6 ...
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How do I compare the means of 2 sets when they have different distributions?

I want to compare the means of 2 sets of data. I have already taken the log and removed spurious outliers. But the 2 sets have different shapes and I don't want to blindly throw them into a linear ...
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What is the distribution of single variable in multivariate normal given the other variables are fixed?

Say we have a multivariate normal: $$\boldsymbol{X} \sim \cal{N}(\boldsymbol{\mu}, \Sigma)$$ then the distribution of each variable $x_i$ is a Gaussian normal, $p(x_i|\mu_i,\Sigma_{ii}) = \cal{N}(\...
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Comparing different uniform distribution estimator against binomial distribution?

There's a coin with true success probability 0.5 that's flipped 400 times, with outcomes $Y1$, . . . , $Y400$. When computing the estimator you get $Y = 1/400 (Y1 + · · · + Y400)$ and have $Y= 0.65$. ...
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Tail distribution

I'm studying extreme event statistics and have seen that the tail of a distribution is 1 minus the CDF. Intuitively, i can't make sense of why that is . Are we setting a fixed x and then at that point ...
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Marginal distribution of a Poisson rate

I have a random sample of Yi~Poisson(θ) with i=1,..,n. Where I assume a gamma(a,b) prior for θ. Where I'm able to find the marginal distribution of Y to be a NegativeBionomial(a,p) where p=(1/(1+b), ...
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dealing with imbalanced FEATURES

I am aware of the "class imbalance" problem... What I am asking here is using some "unbalanced features". Suppose we have a perfectly balanced class label for the dataset, but most of the features ...
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1answer
47 views

Conditional log-concavity and unimodality

Let $X$ and $Y$ be two random variables (or vectors) with continuous and "smooth enough" joint distribution. Assume that the two conditional distributions $X|Y=y$ and $Y|X=x$ are log-concave for all $...
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Determine the MLE of parameter p for the negative binomial distribution [closed]

![Function of p, has a maximum value. This value can be found by taking the derivative of L with respect to p, and setting it equal to 0. I don`t know what the value of L will be in this case? ]1
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1answer
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How to simulate a sample from log skew t distribution in R

How I can simulate a sample from log skew t distribution with lambda equals to 0? I didn't find any packages can do it and I'm not so in order to write a function. Can someone help me to understand ...
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R: About gamma distribution [closed]

It's a very silly question, but I start learning R recently, hope I can get some help from you guys If 60 cars pass the intersection of rd.A and rd.B every minute, find the probability that at most 2 ...
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Expectation of 500 coin flips after 500 realizations

I was hoping someone could provide clarity surrounding the following scenario. You are asked "What is the expected number of observed heads and tails if you flip a fair coin 1000 times". Knowing that ...
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Measuring standard/formula when we know length, mean, highest and lowest values of a set

This is probably a basic statistics question, sorry about that. I have sets of data that I wanna compare. Each set has a list of values from which I know the length, mean, highest and lowest values ...
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38 views

Percents of Random Samples

I have three sets $A,B,C$ of sizes $N_A=2508$, $N_B=36211$ and $N_C=2296$ respectively, containing binary values. I took 200 samples of each set to produce point estimates of the averages: $\hat p_A=0....
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Q-Exponential distribution in Numpy

I am studying a phenomena, which I know is characterised by the q-exponential distribution, with parameters $c=1$, $q = 1.355$ and $b = 0.524$ in the equation $$e_{q,b,c}(t) = c(1 + b(q-1)t)^{\frac{1}{...
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Approaches to Processing exam results [closed]

I am trying to process around 8000 exam results I have put these in a datatable. What I would like to know is how you would go about processing this data from a statistical point of view. I have ...
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1answer
22 views

Mean-center continuous predictors for GLMMs?

I have a dataset with a non-negative, right-skewed response variable and at least one non-negative, right-skewed predictor. Given the non-Gaussian, non-negative distribution of the predictor variable, ...
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1answer
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Why Pareto distribution has pointy head? How its symmetrical version looks like?

I want to use Pareto distribution for the stock price probability distribution. They say (B. Mandelbrot and N. Taleb Mild vs Wild Randomness) it represents the price changes, especially the tail ...
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Comparing 2 mixture models using mixtools

I have 2 mixture models I'd like to compare. Specifically, I want to compare lamda (i.e. proportion/area under each distribution) as it looks like there are differences there. Is this possible? ...
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1answer
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Bayesian Question [closed]

A person belongs to 5 different groups. Group A consists has 10 people, 6 of them male. Group B consists has 20 people, 11 of them male. Group C consists has 30 people, 16 of them male. What is the ...
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Questions about pmf of multinomial distribution with indicator variables

I was reading through the textbook of Introduction to Machine Learning, it introduces $z^{t} = (z_{1}^{t},...,z_{k}^{t})$, where $z_{i}$ is an indicator variable, each with probability $\pi_{i}$, then ...
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What information in general is necessary to fully specify a multivariate distribution?

Given some multivariate probability distribution, we can fully describe it with its density or mass function -- we can associate each point in the space with either a probability density or mass, ...
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1answer
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How do you forecast a time series that is inherently uncertain?

Most time series forecasting models take in fixed (so presumably deterministic) historical values, and then output either: A point (usually mean) forecast + forecast intervals, so $\hat{Y}_{t+1} = ...
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One-way ANOVA method validation

Here is my case: Let's say we have 50 polygons(looks like this:and a point set distributed within these 50 polygons. So that for each polygon, there is an associated point density. What I want to ...
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Does the below Plot refer to a Valid PDF?

I have tried to creat a valid PDF according to some special function I have got the below Plot , I got it for n=6 Integrand Range[n/n], Now My question here Is : Is that below Plot refer to a valid ...
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How to estimate the marginal distribution of binary dependent variable with respect to one predictor using a classifier?

I have a dataset with a binary dependent variable $y \in \{0,1\}$ and a set of predictors $x1,x2,..,t$. Here, $t$ is the time in minutes (in 24 hrs, that is $t \in (0,1440)$). I want to estimate the ...
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Binomial distributions - probability estimation [closed]

X ~ b(8,0.5) and Y ~ b(10,0.5) are two independent binomial distributions. What is the probability X=3, if X+Y=8
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What is the resulting distribution of a data set that was originally normally distributed but has been quantized and had all negative values removed?

I am trying to benchmark a seasonal forecasting model and calculate not just the point forecasts but the forecast densities from the model. To do this, I generated a simulated data set in the ...
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1answer
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Choosing the train data size automatically - Sarimax Time Series Model

I am working on a forecasting application on some credit data. The flow of money looks as follows: I am using a sarimax model since I have weekly seasonality. For ...
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2answers
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What are the uses of bootstrap resampling?

I'm still wrapping my head around bootstrapping but am struggling to think of how it is applied. I have looked at: Explaining to laypeople why bootstrapping works So far, my understanding is that ...
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Exponential with Long Tail?

I am modeling the time until the next visit to the doctor of patients using a survival model assuming exponential distribution for the dependent variable. I have coded the dependent variable (time ...
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Representativeness of sample, distribution of age from sample compared to national sample

Please forgive my entry-level question. I have been slamming my head on the table for well over 3 hours now as I cannot seem to figure this one out. I have a sample of n=450, population is about 17m....
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Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll ...
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33 views

How to change the distribution of classes?

I have two classes [0,1] and I want to evaluate algorithm on different distributions of classes. I did label flipping incrementally such as 0%, 10%,20%,....,90%,100%. Does label flipping change the ...
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transformations of empirical distributions for multi class logistic regression

I am working on a multiclass logistic classification problem where two of the predictors (features) have highly skewed distributions. One is visibility (in m), which looks something like this: ...
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1answer
29 views

What is Half-Inverse-Student-t distribution?

In the paper of Vanhatalo et al 2018, section 5.3 page 15, they use Half-Inverse-Student-t distribution as a prior: I have never heard of such distribution and I have problems finding it. What is it?
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1answer
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Infinite discounted sum of betas

Let $0 \leq \gamma < 1$, $X_i \sim \text{Beta}(\alpha, \beta)$, and $$Y \sim \sum_{i = 0}^\infty \gamma^i X_i$$ What is the distribution of $Y$? Does it have a closed form? Can it be sampled ...
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What Statistical principles are being violated by comparing specific Trainer Fatality Rates to Race Track Fatality rates?

A Hall of Fame Trainer of Thoroughbred Racehorses has been banned from a Race Track because 7 horses under his care have have been injured while training or racing in the past year. Critics cite a ...
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2answers
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Can IQR ever be larger than standard deviation?

As I understand it the IQR specifies the dispersion of the data by taking the difference between Q3 and Q1 (i.e., the range that the middle 50% of the data lies), while std specifies dispersion using ...
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1answer
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The coefficient of variation as a measure of “narrowness” of a distribution

In this lecture about statistical mechanics, page $10$, the author said that for a peaked distribution, like the one below, the width of the peak is proportional to $\frac{\sigma}{\mu}$, where $\mu$ (...
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Comparing conversion rate in A/B testing

I have a website, and I want to see if offering a 5% or a 10% discount in an advertisement increases the click-through rate. Essentially an A/B test but with 2 alternatives, so an A/B/C test. In the ...
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Distribution of noncentrality parameter in noncentral t-distribution

Let $X$ be a random vector $X \sim N(0, \Sigma)$, where $\Sigma = \frac{1}{n} Id$. Find probability $$ P(|T| > a)$$ where $T$ has noncentral t-distribution with noncentrality parameter $\delta = \...
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Uniform distribution problems

I was confused about this problem Two emergency response units, unit A and unit B, patrol uniformly and independent a 10-km stretch of moad. An emergency incident occurs on the road and its position ...
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How do you prove that samples are equally distributed even when taken without replacement? [closed]

I was reading Casellar and Berger's book and came across this well-known property. Although, in the book, the proof for any Xi is not provided. Does anyone know how to follow up on it? I'm curious, is ...
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Moments of $Y=X_1 + X_2 X_3 + X_4 X_5 X_6 +\cdots$

The $X_i$'s are i.i.d. and $X$ denotes any of these random variables. We assume here that $|E(X)|<1$ to guarantee convergence. I am interested in particular in the third moment $E(Y^3)$. For the ...
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If $|E(X)|< 1$ and $E(X^2)<1$, can we have $1 - E(X^2) = (1 - E(X))^2$?

Of course $X=0$ works, but I am looking for a non-singular solution. I haven't made much progress to solve this problem. However, let $\mu_2 = E(X^2)$ and $\mu_1 = E(X)$. For the equality to hold, we ...
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A Multinomial Geometric distribution? What is this distribution called?

In a problem I am dealing with I repeatedly interact with a distribution of the following form, $$p(n_1, n_2, \ldots n_M)=\binom{\sum_{i=1}^Mn_i}{n_1\cdots n_m} w_0\prod_{i=1}^Mw_i^{n_i}$$ where $p$ ...
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Powerlaw Distribution and old nodes [closed]

I am working on the size of discussions (number of replies, replies to the replies) on Twitter data, and I am observing Power-law distribution for small and medium-size discussion but it is not valid ...
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Test for non-normal data with homogeneity of variance

I'm new to the platform and would like the following question to be answered: I have performed a latent class cluster analysis with 28 variables and 9000 observations, for which I am currently ...
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1answer
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How to estimate log-normal distribution parameters from a set of data?

I don't have any background in statistics, so maybe I may say things that are incorrect. I have to model the production of waste deposition at each container of a set of containers and I have access ...