Questions tagged [distributions]
A distribution is a mathematical description of probabilities or frequencies.
6,549
questions
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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 ...
2
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1answer
15 views
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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0answers
19 views
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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0answers
11 views
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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0answers
15 views
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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0answers
16 views
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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0answers
15 views
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 ...
3
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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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0answers
13 views
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
1
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1answer
21 views
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 ...
0
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0answers
20 views
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 ...
24
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7answers
6k views
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 ...
0
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0answers
8 views
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 ...
1
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0answers
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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0answers
12 views
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}{...
0
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0answers
13 views
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 ...
1
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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, ...
2
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1answer
44 views
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 ...
0
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0answers
15 views
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?
...
-3
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1answer
23 views
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 ...
0
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1answer
13 views
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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0answers
30 views
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, ...
2
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1answer
37 views
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} = ...
1
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0answers
12 views
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 ...
0
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0answers
15 views
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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0answers
14 views
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 ...
0
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0answers
8 views
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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0answers
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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 ...
0
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1answer
19 views
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 ...
2
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2answers
53 views
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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0answers
23 views
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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0answers
12 views
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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0answers
11 views
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 ...
0
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0answers
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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0answers
39 views
+50
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:
...
2
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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?
4
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1answer
93 views
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$$
What is the distribution of $Y$? Does it have a closed form? Can it be sampled ...
2
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0answers
27 views
+50
What Statistical principles are being violated by comparing specific Trainer Fatality Rates to Race Track Fatality rates?
A Hall of Fame Trainer of Thoroughbred Racehorses has been banned from a Race Track because 7 horses under his care have have been injured while training or racing in the past year.
Critics cite a ...
2
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2answers
103 views
Can IQR ever be larger than standard deviation?
As I understand it the IQR specifies the dispersion of the data by taking the difference between Q3 and Q1 (i.e., the range that the middle 50% of the data lies), while std specifies dispersion using ...
1
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1answer
24 views
The coefficient of variation as a measure of “narrowness” of a distribution
In this lecture about statistical mechanics, page $10$, the author said that for a peaked distribution, like the one below,
the width of the peak is proportional to $\frac{\sigma}{\mu}$, where $\mu$ (...
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0answers
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Comparing conversion rate in A/B testing
I have a website, and I want to see if offering a 5% or a 10% discount in an advertisement increases the click-through rate. Essentially an A/B test but with 2 alternatives, so an A/B/C test.
In the ...
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0answers
11 views
Distribution of noncentrality parameter in noncentral t-distribution
Let $X$ be a random vector $X \sim N(0, \Sigma)$, where $\Sigma = \frac{1}{n} Id$. Find probability
$$
P(|T| > a)$$
where $T$ has noncentral t-distribution with noncentrality parameter $\delta = \...
1
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0answers
31 views
Uniform distribution problems
I was confused about this problem
Two emergency response units， unit A and unit B， patrol uniformly and independent a 10-km stretch of moad. An emergency incident occurs on the road and its position ...
1
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0answers
14 views
How do you prove that samples are equally distributed even when taken without replacement? [closed]
I was reading Casellar and Berger's book and came across this well-known property. Although, in the book, the proof for any Xi is not provided. Does anyone know how to follow up on it? I'm curious, is ...
5
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0answers
93 views
Moments of $Y=X_1 + X_2 X_3 + X_4 X_5 X_6 +\cdots$
The $X_i$'s are i.i.d. and $X$ denotes any of these random variables. We assume here that $|E(X)|<1$ to guarantee convergence. I am interested in particular in the third moment $E(Y^3)$. For the ...
3
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2answers
139 views
If $|E(X)|< 1$ and $E(X^2)<1$, can we have $1 - E(X^2) = (1 - E(X))^2$?
Of course $X=0$ works, but I am looking for a non-singular solution. I haven't made much progress to solve this problem. However, let $\mu_2 = E(X^2)$ and $\mu_1 = E(X)$. For the equality to hold, we ...
0
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0answers
12 views
A Multinomial Geometric distribution? What is this distribution called?
In a problem I am dealing with I repeatedly interact with a distribution of the following form,
$$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 $p$ ...
1
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0answers
15 views
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 ...
2
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0answers
28 views
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 ...
2
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1answer
42 views
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 ...
