A distribution is a mathematical description of probabilities or frequencies.

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Distribution comparison across different treatments

if I have a table like this In which, site = different sites of measurement (tissue or organ) type = different types of virus And I want to ask something about the data 1.What test can I use to ...
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Human movement distribution [on hold]

Can anybody help me with the mathematical distributions to use to model user movement (user travel pattern) in a city or a given geographical area. I don't have any data; my question is limited to ...
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Is there a PDF for a generalized non-central chi-squared distribution [duplicate]

Is there a PDF for a distribution defined as a sum of squares of random variables pulled from a family of normal distributions with different standard deviation? Is there a way of analytically ...
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Can ayone help me in solving the below Problems of probability distribution?

Patients arrive randomly and independently at a doctor's surgery from 8·0 A.M. at an average rate of one in Five minutes.The waiting room holds 2 persons. What is the probability that the room will be ...
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Bayesian probabilty [migrated]

I need to know how to find the Bayesian probability of two discrete distributions. For example the distributions are given as follows: ...
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55 views

Determining probability distribution for datasets with missing values

As a part of my exploratory data analysis (EDA) prior to further analysis, I'm trying to determine a probability distribution of my pilot dataset's variables. A particular feature of this dataset is a ...
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Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points

Suppose I have two points $(p_1,x_1)$ and $(p_2,x_2)$ where $p_i$ is a probability on the beta CDF and $x_i$ is a value on that same CDF. How would I go about determining the beta distribution shape ...
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Automatic identification of distribution of data

Some statistical tools offer methods of automatic identification of the distribution of data, such as the one shown in this post. Generally, is this approach reliable? If not, what's a better ...
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How to find the distribution of the weighted sum of independent Bernoulli random variables for positive non-integer weights

How do I find the distribution of the weighted sum of independent Bernoulli random variables if the weights are non-negative real numbers? I have N number of independent Bernoulli distributed random ...
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Have Narrow Distribution - Need Standard Distribution

I am building a model in R using GLM based on this predictor variable. As you can see, the data is concentrated in the center of the distribution, and then falls off sharply. Is there a ...
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24 views

Acceptance rejection method for a binomial distribution

I have a R-code for acceptance rejection method for a beta-distribtuion but would like to use it for a binomial(30, 0.4) distribution instead. Here is the code: ...
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Get the distribution of a dataset

this is a conceptual question. In data mining, the problem often arises that scientists/data engineers are using an expert guess for the underlying distribution of their data. Often their assumption ...
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Normalization to non-degenerate distribution

I am reading de Haan's Extreme Value Theory (2006). In the discussion of distribution of sample maximum, he said "in order to obtain a non-degenerate limit distribution, a normalization is necessary". ...
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Comparison between MAD and SD

I am reading Huber's Robust Statistics (2nd). On page 2 and 3 he gave an example. The basic facts are summarized here. Let $(X_n)$ be a sequence of random variables and define two measures of spread ...
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How to determinate standard deviation above and below mean classes programatically

I have an array of float from wich I calculate the mean and the standard deviation. The user can specify a number of class varying between 2 and 8. The min and max values of each class is calculated ...
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65 views

How many eligible bachelors in a city?

This is a very simple question posed to me by a friend of mine. I know it's a statistical analysis problem, but I suck at math. Given the total population of $x$ within a metropolitan area, what ...
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34 views

How to take cumulative sum of a 2D distribution?

How can I take the cumulative sum of a 2D distribution, starting from the highest value in the distribution? Background: my 2D distribution is the probability of different combinations of wave ...
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23 views

What is the difference between dexp and pexp [duplicate]

I understand probability distribution but I am having a hard time getting a grasp on probability density function, specifically difference between dexp (density of exponential distribution) and pexp ...
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How to describe a distribution of statistics in a meta-analysis?

I'm conducting a meta-analysis using water-quality data collected from multiple lakes in multiple regions. Due to the differences in the sampling programs, each waterbody has been sampled an unequal ...
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sample generative model from a chain/tree

I have a tree of states and I would like to sample from this tree based on pure birth process; however, I don't know how exactly I can do this; so far I have done this; I simplified my problem; the ...
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Cumulative distribution function: what does $t$ in $\int\exp(-t^2)dt$ stand for?

I'm trying to teach myself how to quickly translate many different types of equations into VB, T-SQL and MDX code. Since I'm trying to build a skill, not just solve a single isolated problem, I'm try ...
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How does Standard Deviation (Error) change with sample size change in this scenario. Explanation needed for a nonprofessional

I have this question that I want figured out. A person's Blood pressure was taken 4 times,the mean of these 4 observations came out to be say 120mm of Hg And the SD was 2.5. Now we have taken 4 more ...
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32 views

Test means of populations with lots of zeros, is sampling the way to go?

I am trying to test whether means of two populations with lots of zeros are different. Here is the following python code example: ...
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Best distribution to handle a ratio of counts as a response variable

A quick statistics question (apologies for the added biology): I have two sets of counts (for the expression of two different isoforms of a particular gene), and to generate the response variable in ...
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Generating hyperbolic variates

How do you simulate from the hyperbolic distribution? The Wikipedia article on it does not describe how to do so. I know that the hyperbolic distribution is a special case of the generalized ...
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Distribution of (maximum) run length

I am curious about the distribution of (maximum) run length given k independent trials when $p(X=1)=p_1, p(X=2)=p_2, ..., p(X=n)=p_n.$ For example, for a coin tossing for 3 independent trials, ...
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How to best plot a heavy vs light tailed distribution in R

I want to create a plot that overlays a heavy vs light tailed distribution as an example and am trying to figure out the best way to do this. I can plot gamma distribution which is light tailed and a ...
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How do I compute the density of this data set that is made up of two different 3D-distributions?

A sequel to this question. I have a dataset where: $\frac{4}{5}$ of the points are drawn from: $(x, y) \sim \mathcal{U}_{2}(0,30)$, $(z) \sim \mathcal{U}_{1}(14.5, 15.5)$. $\frac{1}{5}$ of the ...
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Will I go to UC Berkeley?

I forget where I got this data (I think from About.com College), but here are some statistics regarding University of California, Berkeley admissions: the 25th percentile SAT Reasoning Test score was ...
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What is the correct notation if two random variables belong to the same distribution?

I want to explain that both the real and imaginary part of a complex variable follow a zero-mean complex Gaussian distribution. How can I write that? For one variable I'd write $a \sim ...
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Finding distribution function [duplicate]

Let $X_1,X_2,...$ denote iid random variables such that $X_1$ is continuously distributed with density $p(x)$ and distribution function $F(x)$ where $F(0) = 0, F(x) > 0$ for all $x > 0$, and ...
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54 views

Multivariate normal distribution has peaks

I'm trying to calculate a bivariate normal distribution in matlab(with mvnpdf), but the pdf I obtain has a strange shape with several peaks. This is the code I use: ...
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Mean and variance of a general multivariate skew normal distribution

I have a problem about a general multivariate skew normal distribution. There is a $p\times 1$ vector, $\mathbf{y}=(\mathbf{y}_1',\mathbf{y}_2',\ldots,\mathbf{y}_n')',p>n$, which has the density as ...
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how calculate inflation observed and expected p-values from uniform distribution in QQ plot

I am trying to quantify degree of inflation (ie. how best the observed data points fit to expected). One way is too look at QQ plot. But I would like to calculate some numeric indicator for inflation ...
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Simple measure for comparison of rainfall regularity

In meteorology we have the concept of monthly rainfall, which is just the sum of daily rainfall over that month. Now, given this extreme example: Situation 1: ...
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Normal Quantile Quantile Plot Normalization [duplicate]

How can I deal with this data set so I can analyze it using basic data analysis? edit: I am trying to get rid of that little tail at the bottom. I already took a log of the data because it was ...
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distribution of matrices

Can any one help me please with this problem :: I would like to know the distribution of the following : $|h' G(G'G)^{-1}|^2$ or $(G'G)^{-1}Ghh'G(G'G)^{-1}$ where $h$ is a Gaussian vector and $G$ is ...
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Where is the uniform distribution with one parameter ($U(\theta, k \theta)$) useful for modelling?

I recently came across the distribution $U(\theta, k \theta)$ (where k is known) in the context of statistical theory (as a nice toy example for finding MLE and the likes). However, I was wondering ...
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[Revised]Proving the expected \bold{density} of being the Nth order statistics is decreasing in sample size

(Sorry that I've previously formulated the question in a wrong way, which confused everyone including myself. This is a better version of the question. Thanks!) Here's another order statistics ...
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Are there any inverse distribution graph that looks like this?

I want to generate random numbers according to a distribution curve like the inverse cummulative normal curve. But the curve should allow parameters to adjust the parameters as shown in the image, ...
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Distribution of altered Mahalanobis distance [duplicate]

Let's say I have a set of i.i.d. samples $X_1,\ldots,X_N \sim N_p(\mu, \Sigma)$. Now define \begin{equation} d^2_i(b)=(X_i - b)'\Sigma^{-1}(X_i-b) \end{equation} which is essentially the Mahalanobis ...
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How to sample from the distribution of a Gaussian scale parameter

I would like to be able to sample the standard deviation of a multidimensional Gaussian distribution of dimension $n$; that is, given some $\phi$, I would like to sample $P(\sigma | \phi) \propto ...
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Haar prior for von Mises distribution

Ok, Let me tell you that this is the very first time that I have no idea with the question below. I can not find a solution or anything that will lead me to it. I say this to prevent comments "what ...
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37 views

Distribution based on rate of distinct values

I am investigating the following problem: I have a large set of values, many of which are repeated. Measuring the number of distinct (or unique) values shows that their number grows much slower than ...
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Distribution of sum of squared normal distributions with different means and variances? [duplicate]

Let $ Z=X_1^2+X_2^2\cdots\cdots X_j^2 $, such that $X_i \sim \mathcal{N}(\mu_i,\sigma_i^2)$. All $X_i$'s are independent of each other and $\mu_i$ and $\sigma_i^2$ are all different from one another. ...
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Area below probabilities

Let $p$ be probabilities and $D$ is the real How can I proof that the areas $$\int p \; d F_{p}(p|D=1) = \int (1-p) \; d F_{1-p}(1-p|D=1)$$ are equal. Where $F_{p}$ is the empirical distribution ...
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limiting distribution of $(n-1)S^2/\sigma^2$

I need to prove that the limiting distribution of $(n-1)S^2/\sigma^2$ is a Normal, where $S^2$ is the sample variance. However, I have no clue on how to do it. We know that $(n-1)S^2/\sigma^2 \sim ...
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Comprehensive list of distributions?

Is there a comprehensive list of distributions, e.g. gamma, Poisson, Gaussian, and when you should use each somewhere? My internet searching has been fruitless.
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Normal distribution to triangular distribution

I would like to know if it is possible to convert a normal distribution into a triangular distribution. If it is, how it can be done? I know the mean and the coefficient of variation of the normal ...
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What do vertical bars mean in statistical distributions?

What do the vertical bars mean in the first and third formulae? $$v_i|z_i=k,\mu_k\sim\mathcal{N}(\mu_k, \sigma^2)$$ $$P(z_i=k)=\pi_k$$ $$\pi|\alpha\sim \text{Dir}(\alpha/K1_K)$$ $$\mu_k\sim ...