A distribution is a mathematical description of probabilities or frequencies.

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Distributions change when data is transformed to higher dimensions?

Suppose that I have a skewed data set with the positive class being 5% and negative class the rest 95%. I want to classify the data using SVM with RBF kernel. Should I worry about the distribution ...
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117 views

How to add noise to a random variable whose range is the unit interval?

I have a list of values sampled from a beta distribution that therefore lie in the interval [0,1]. I would like to add (e.g. Gaussian) noise to these values, but of course there is the problem of the ...
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18 views

Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
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58 views

PDF of a sum of dependent variables

This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
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28 views

How can we reduce the non-central hypergeometric distribution from a multivariate to a univariate version?

Is it possible to combine the odds for two or more groups of balls in a multivariate version of Fisher's non-central hypergeometric distribution to give a univariate equivalent? For example, this ...
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9 views

Weather data analysis [on hold]

I am assigned to analyze weather data for bias correction. I am seeking help for analyzing distribution of the observed minus forecast values . What is the correct way of analyzing this distribution ...
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145 views

What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?

I have four independent uniformly distributed variables $a,b,c,d$, each in $[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be ...
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1answer
55 views

PDF of sum of ordered weighted exponential RVs

Let $X_{(1)}, X_{(2)}, ..., X_{(N)}$ be the order statistics of an iid exponential RVs with parameter $\lambda$, where $X_{(1)} \geq X_{(2)} \geq ...\geq X_{(N)}$. Any hints on how to find the PDF of ...
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Student t distribution: standardization [duplicate]

I got a question concerning the standardization of a student t distribution. I see that the "plain vanilla" t distribution has density $f(x|\nu)=\frac{\Gamma(\frac{\nu+1}{2}) ...
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1answer
27 views

Which metric should I use to rank these distributions?

I have a number of 1D distributions, which, when plotted show a distinct ranking in terms of the "spikiness" of the data. I would like to apply a relatively fast metric that would allow me to rank ...
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2answers
31 views

How to test if 2 means are significantly different for non-normal non-paired data

I have 4 averages from 4 samples and I want to test if the means are significantly different. When I look at the QQ plots and the shapiro wilk test (all have very low p values) the data is not normal ...
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Matching a query distribution to a family of template distributions

I was turning over a hypothetical question in my head: Suppose I have a set of template probability distributions, let's say each giving the probability of the occurrence of certain objects like ...
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30 views

Slope analysis where one group is not normally distributed

I am currently doing analysis of five separate drug groups and their changes in levels of prescription over time. Having done linear regression on excel I am comparing the 'steepness' (m) of the ...
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1answer
65 views

Why do we need confidence intervals?

I am following a video lecture on Statistics, which introduces the concept of confidence intervals in the following way: "A bank vice president is interested in the average checking account balance ...
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1answer
30 views

Is my data normal graphical vs. analytical test

I am trying to determine if my data is normal. I am using R. I run the jarque bera test that has a NULL hypothesis of Normality ...
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Independence of the products of two independent normal variables with a Rademacher variable [closed]

Let $X$ and $Y$ be two iid $N(0,1)$ random variables, and let $Z$ be a Rademacher variable i.e. $P(Z=1)=P(Z=-1)=0.5$ distributed independently of $X$ and $Y$. Let $U=XZ$ and $V=YZ$. Are $U$ and $V$ ...
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What would be an efficient way of representing a known discrete distribution with a number of samples?

So, say that I have a known discrete probability distribution, for example: [1] [2] [3] [4] [5] 0.08072 0.0642 0.2853 0.3206 0.2492 What I want to ...
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Distribution of number of files in folders on personal computers?

At a company I work for, we're trying to simulate running software on an enterprise-scale system. We would like to put files in folders, to simulate a customer environment. At the moment, we uniformly ...
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1answer
25 views

Is there an analytic distribution for the sum of random variables distributed IID inverse gamma?

How about their ratio? I have looked at the related distributions section on Wikipedia and tried playing with the pdf's by hand. I could have been a little more specific about the case that is ...
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1answer
67 views

Calculating a p-value from permutations

I have 500 genes I am interested in. I want to test whether they are enriched in a certain dataset (Y). Y is a list of cancer genes that are called cancer genes at different levels of likelihood. I.e. ...
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2answers
31 views

Discrete survivor function expressed in terms of hazard

Let $T$ can take on values $t_1,t_2,\ldots,$ with $0\le t_1\le t_2,\ldots,$ and let the probability function be $$f(t_j)=Pr(T=t_j),\quad j=1,2,\ldots$$ The survivor function is then $$S(t)=Pr(T\ge ...
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1answer
88 views

Generate data with skewed distribution and known percentiles, mean and median

I'm trying this one again as my imprecise use of language unfortunately confused my last attempt at this question... I am trying to recreate some data from a publication. The study was on levels of ...
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1answer
40 views

Square root of an inverse gamma distributed random variable

I work on the grouped t copula and try to replicate part of the following paper: "The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk ...
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17 views

Observed vs. predicted values distribution misfit

After realising the problem with my predictors thanks to the comments in my previous question, I've tried to fix that somehow. However, I can't figure out how to transform my predictors and/or my DV ...
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1answer
87 views

Distribution of the quotient of two gamma random variables with different rate parameters?

I have a question about how to derive the distribution of the quotient of two random gamma variables drawn from two different Gamma distributions with the same shape, but different rates. For example, ...
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Combining and normalizing gridded parameters of different distributions with the same units

I have a grid that has two parameters for each cell. One parameter, let's call it K, is the same for all grid cells. The other parameter, let's call it M, has values of M, 2M, and 3.5M, with each ...
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Predicting with Posterior PMF(discrete non-pram dist) ? Predictive posterior distribution?

Sorry in advance if my question is abit awkward, I'm somewhat confused because most of the tutorials on the Internet mention that you should use Posterior-predictive dist to predict new data. The ...
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2answers
79 views

asymptotic distribution of a statistic

Say we have iid sample of size $n$ with $X_i \sim Exp(\lambda)$ and the task is to find asymptotic distribution of the statistic $$T_n := \frac{\bar{X}}{s}$$, where $s^2$ is the unbiased sample ...
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How to Assess the Fit of Thousands of Distributions?

I have thousands of subjects, for each of whom I have a fitted gamma distribution, with the parameters estimated from each subject's data. It is easy to look at the distribution for one subject (say ...
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43 views

Show that $Y_1 X_1 + Y_2 X_2$ $\,{\buildrel d \over =}\,$ $(Y_1^2+Y_2^2)^{1/2}X_1$

I would like verification of my solution to the following problem. QUESTION: Let $X_1, X_2 \,{\buildrel iid \over \sim }\, N(0,1) $ and let $Y_1, Y_2$ be two independent random variables ($X_1, ...
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31 views

Naming unique distributions

Assume the number of flowers at a study site follows a poisson distribution. Then assume insects arrive and destroy the flowers. The number of flowers killed follows a negative-binomial distribution. ...
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86 views

Regression results have unexpected upper bound

I try to predict a balance score and tried several different regression methods. One thing I noticed is that the predicted values seem to have some kind of upper bound. That is, the actual balance is ...
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109 views
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How to select the best fit without over-fitting data? Modelling a bimodal distribution with N normal functions, etc

I have an obviously bimodal distribution of values, which I seek to fit. The data can be fit well with either 2 normal functions (bimodal) or with 3 normal functions. Additionally, there is a ...
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29 views

Large-sample distribution of the Autocovariance function

I'm trying to understand property 1.1 below ($x_t$ is white noise), from Theorem A.7(also below). From the formula for the $W$ matrix, using the more convenient one, I get $W_{pq}=0$ when $p\neq q$ ...
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1answer
60 views

How to describe a function of two normal distributed random variables

I consider the generic problem $W(X,Y)=-2\ln(\frac{(X-Y)^2}{2(X^2+Y^2)})$ where $X$ and $Y$ are normally distributed random variables Can I make any statements about the distribution of $W$?
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quantile function for elliptical distribution

Does the Quantile (inverse cdf) function exists for an elliptically distributed random variable? We know that an elliptical random variable can be transformed into a spherical distribution, so it is ...
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2answers
77 views

Comparing frequency distributions

Quick rundown of my data: I have depth measurements from fish with implanted transmitters from two sites (reference and hypoxic) and two seasons (spring and summer). All data is in an Excel ...
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3answers
79 views

How to measure the “confidence” that one set of values is greater than another?

I have a relatively simple task. I have collected several hundred samples from several groups (group here is arbitrary and not relevant to my question). These samples are scored on a continuous ...
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Subdistributions and superdistributions of exponential families

Suppose you have an n-parameter distribution f(x) such that, for some particular set of parameter values, it is an m < n parameter distribution g(x) which is a member of an exponential family, and ...
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1answer
48 views

Confusion about the sample distribution.. Can you please enlighten me?

I thought that the sample distribution was an approximation of the distribution of the underlying phenomenon. But then the book says: We will denote the sample size by $n$ ($n \le N$) and the ...
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Which distribution should I better use to predict the response in {0,20} applying GBM? [duplicate]

I want to predict the response that is in {0,20}. I am using GBM to make the prediction. ...
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Does the generalized beta distribution of McDonald and Xu constitute an exponential family?

Does the generalized beta distribution of McDonald and Xu, J. Econometrics 66 (1995) 133-152, constitute an exponential family? Can it be written in a way that makes this more obvious? Alternatively, ...
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Constructing a continuous distribution to match m moments

Suppose I have a large sample drawn from a continuous distribution, size n, and 2 < m << n moments from that sample. Alternatively, suppose I have been given those moments by an angel, ...
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1answer
30 views

What is the famous data set that looks totally different but has similar summary stats?

The is a famous example of data with similar summary stats like mean, standard deviation etc but that look totally different. It's named after the famous statistician that produced it. Can someone ...
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How to evaluate enrichment of features in groups of samples?

I have a matrix composed by features on rows and samples on columns. Each value in the matrix correspond to a value of activation of the feature $i$ in the sample $j$. I want to evaluate enrichment ...
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Confidence interval for variances

I have a lot of variances $\sigma^2(x)$ as these: Now I have two task: remove the vertical outliers and compute the confidence intervals (for all cases, this is only one case). I think that their ...
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Inference about parameter $\theta$ be same?

Let $\mathbf x$ be a sample point and $T(\mathbf x)$ be a statistic of $\mathbf x$. Similarly, let $\mathbf y$ be a sample point and $T(\mathbf y)$ be a statistic of $\mathbf y$. In the book ...
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Transformation of Random Variable - Normal Distribution

Let $X$ be one observation from a $N(0,\sigma^2)$ population . What is the distribution of norm of $X$, i.e., $|X|$ ? My attempt : $$f_X(x;0,\sigma^2)=\frac{1}{\sqrt{2\pi ...
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Transformation Theorem & Piecewise Function

I am a total statistics newbie and I hope that you can help me with the following problem: Let $X \sim \mathcal N\left(\mu, \sigma^2\right)$ be a random variable. Define a new random variable $Y$ as: ...
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Analyzing questionnaire data with control group

I have 12 questions weighted on a 5-point Likert scale. 20 people responded to each question, so we have 20 rows and 12 columns, with each cell ranging from 1 to 5. Questions 1-4 measure a random ...