A distribution is a mathematical description of probabilities or frequencies.

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Negative Binomial as weighted average?

I know the Negative Binomial distribution can be considered as the sum of r independent geometric distributions, as described here. Can it also be formulated as a weighted average of, possibly ...
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What is a good way to model this set of time-series data? What might the distribution be? (Personal expenses)

I'm trying to make some sense out of this data, but have been having some trouble. The data is of personal expenses made during the last 90 days. How would one go about the modeling this type of data? ...
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Average/extreme value in distrubtion

If I have a distribution like the one below, is there a way to say to what degree a value is part of the distribution? e.g. if I am considering the value 4.122e-4, it clearly falls within the ...
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Conditions to be in a class of Poisson distribution

Ambulance cars are arriving at a traffic signal in accordance to a Poisson process. The arrival rate of ambulance cars is measured at every 1 hour. $\lambda_k$ is defined as $k_{th}$ hour arrival ...
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How to classify an empirical distribution into a group

How can I check that an empirical distribution function belongs to a group of empirical distribution functions? Imagine I have some customers who have been classified into some groups. Each person ...
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1answer
20 views

Possible to estimate distribution around mean given #samples, mean, highest and lowest?

For a project for which there are multiple bidders, the following is known: Number of bidders: 24 Mean bid: 104 Highest bid: 356 Lowest bid: 20 Given the above, is it possible (however roughly) ...
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48 views

What is the formal definition of an “atomless” distribution?

The use of atomless (continuous) distributions is ubiquitous in applied works. While the general idea is somewhat clear to me, I was looking for a formal definition or some useful references on the ...
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working with entire census data of population distribution

i am working on the total population of a state using census data sets, please what statistical techniques can i use to analyse the data to test if the distribution of population within the state in ...
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62 views

Probability distribution of $aX + b$, where a and b are integers and $X$ is a uniform variable

My textbook has the following introductory example about functions of random variables: Suppose that $X$ is a random continuous variable with a uniform distribution over the interval $(0,1)$. ...
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29 views

Largest set of numbers qualifying Exponential distribution [on hold]

For a given set of numbers $ Y = \{ .... \} $ and a given exponential distribution expressed by $ f(y; shape, scale, family )$, there should be a subset of numbers that can be derived from $ X \subset ...
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use of statistics in analysing census data [on hold]

Good day everyone. Please I need your urgent assistance. I am about to write a research project on the topic: The Application of Geographic information Systems In analysing Census data with regards to ...
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Distribution analysis “too uniform” - need help understanding my result

I have $n>1000$ vectors of size $k=20$, sampled from an unknown source that I would like to find their distribution. They appear uniform, so I run the KS test with $\alpha=0.1$ to check. If this ...
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133 views

How do you find a cutting point / strong slope within one-dimensional data

I have one-dimensional data. I want to find possible natural cutting points (strong slopes) within the data. For instance, if the data is ...
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Visualize Sensitivity Results Using Combinations of Means and Standard Deviations of Two Normally Distributed Variables

I ran a sensitivity of my model, sampling the response space using two normally distributed variables. I used four nested repetition loops to generate this data, recording the average output of the ...
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How to find copula-based conditional probability P(U|V>=v)?

Using the Copula operator $C$, which for any (possibly dependent) RVs $U$ and $V$ represents the joint cumulative DF of their inverse probability transform. That is, $U^* = F^{-1}_U (U) \sim ...
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1answer
38 views

How to compare two spatial points patterns in R?

I have two spatial points data sets (relocations of animal A and distribution of plant B). How can I investigate if animal A is more likely to be where plant B is present? With the animal ...
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9 views

Pareto 2 distribution

I am bit confused between Pareto and Pareto Type II distribution. In the actuar library (page 64), details of pareto distribution are given. However, in the end, it is mentioned that "Distribution ...
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18 views

What is the logic behind the names of distributions?

Why is a negative binomial distribution just a generalized version of a geometric distribution (they are the same when r=1), while a hypergeometric distribution is like a binomial distribution without ...
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28 views

probability distribution of complex Gaussian column vector and conditional probability of complex Gaussian column vector

I have column vector $\vec r=[r_1\ r_2]^T$. $$\vec r =hA\vec s +\vec n$$ where $h$ is a complex number , $\vec n \sim \mathcal{C} \mathcal{N}(\begin{bmatrix} 0 \\ 0 ...
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37 views

Generate independent random values from a bivariate normal distribution

I am trying to independently select two sets of numbers (set 1 and set 2) from a bivariate normal distribution. I want the ...
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8 views

Which measure of central tendency and which frequency distribution should be used to describe the distribution of scores?

For example say that on a test you measured each week the count of days from the previous week the participant had thoughts of suicide.
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44 views

Stopping time distribution of a fun and simple game!

A friend of mine asked the following question, which I haven't found a convincing answer for it yet. I'd appreciate any comment in advance. The game has two players $A$ and $B$, each having $\$5$ ...
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26 views

How do I split a normal distributed sample into groups of percentiles but with an additional random noise component for uncertainty?

I have a sample of students that I want to divide into smaller groups based on a their IQ but with a certain random noise component - how can I do that? I need to cluster the best, the average and ...
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22 views

Differences between Distributions [closed]

I have three samples with different values about same random variables. I want to test the difference between the three distributions (position, shape, etc...) You can suggest a list of tests to do ...
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Is the minimum of the Doksum ratio always unbounded?

Consider $\mathcal{F}$ and $\mathcal{G}$ are two continuous distributions and that $\mathcal{G}$ is more dispersed than $\mathcal{F}$ in the sense of satisfying: $$(1)\quad ...
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43 views

3 or, even, 4 parameter distributions [closed]

I have some statistical data for which the pdf has what I think would usually be described as two inflection points. To model this I'm thinking I need something other than the common 2-parameter ...
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Approximation of quadratic form of normal variances, not necessarily non-negative

I am interested in approximating $$ \sum_{i=1}^{n}{w_i u_i^2} $$ where $u_i \sim N(0,1)$ i.i.d. I have seen a few papers on approximating this sum where $w_i \ge 0$, but not in the general case. Why ...
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What is the probability distribution the outer product of which with itself is a uniform distribution? [closed]

Let us take n random variables $x_i$, $i=1,...,n$. Now we take the outer product of this random variables with themselves, $x_i x_j$ to generate $n^2$ numbers. The question is which distribution of ...
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36 views

Sampling from distribution using MATLAB / statistical packages like R

I am trying to read Latent Dirichlet Allocation model for Topic modeling. But I am not able to understand how they sample values from a distribution, draw a distribution from a process. In particular ...
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48 views

The squared-norm of the projection of a Gaussian vector onto an independent $d$-dimensional subspace is a $\chi^2_{2d}$

How we can prove that: The squared-norm of the projection of a $N$-dimensional complex vector with i.i.d. unit-variance and zero mean Gaussian components onto an independent $d$-dimensional subspace ...
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62 views

Multiple regresssion K-S test in R

As suggested, this question first appeared on SO but was now merged across to CV So we can run a K-S test to assess if we have a difference in the distribution of two datasets, as outlined here. So ...
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1answer
154 views

Calculate mean and variance of a distribution of a distribution

I am using hierarchical distributions, of the following form: $\theta\sim N(\mu,\sigma)$ $\mu\sim N(a,b)$ I can calculate the mean, and variance using Mathematica, and find: $\mathrm{E}(\theta)=a$ ...
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Calculating probability of sale from auction data

I have some data representing the last 6 months of closed auction data from a particular website. The data I have includes market value of product, actual sale amount, and date sold. I have about 600 ...
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77 views

Distribution of sum of function of two random variables

Let $\{x_1, \ldots, x_n\}$ be a set of $n$ i.i.d. samples from a distribution $p(x)$. I would like to evaluate the distribution of the sum $$ S = \sum_{1\leq i<j\leq n} f(x_i, x_j), $$ where $f$ is ...
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What's the name for a distribution of the form $10^D$, where $D$ is a known distribution?

In my particular case, I'm generating uniformly random numbers and using them as the power to a base-10 exponent, e.g. in R: s <- 10^runif(10, 1, 10) Is there ...
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34 views

Distribution fitting to given loss data

I am into risk management and deal with Operational risk. As a part of BASEL II guidelines, we need to arrive at the capital charge the banks must set aside to counter any operational risk, if it ...
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Distribution of the largest fragment of a broken stick (spacings)

Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment? More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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Can percentage means be used to calculate %CV?

I am a biologist and very new to statistical analysis for biological data. I need to test the variability between samples within a 96 well plate and between multiple 96 well plates in order to know ...
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53 views

Is the ratio distribution of two normally distributed variables ever normal?

Let $Z = X / Y$ where $X$ and $Y$ are normally distributed random variables. Is $Z$ normally distributed for any $X$ and $Y$?
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How to compare two independent samples using a permutation test? [duplicate]

Suppose I have two independent samples. How can I test if the two samples have been drawn from the same distribution using a permutation test? The sample sizes are equal. The population distributions ...
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3answers
97 views

How well does a single data point fit a distribution?

I have to come up with a way to measure the 'quality' of a distribution for a research project. We collect data over a a period of time $t_0$ through $t_1$ and then estimate the distribution that ...
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Statistic way to find a threshold for NGrams occurrence

I got a vector of Bi-Grams with their occurrences, and I have to calculate tri-grams from the most occurrent bi-grams. Therefore I need to find a statistic way to find a threshold of big-grams ...
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33 views

Non parametric: How to detect different groups

I have data sets for different serial numbers of devices. Those data are not following a normal distribution. I would like to know which serial numbers are behaving differently from the overall ...
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1answer
20 views

How to find the probability distribution of a two-variable metric?

I have a certain metric $f(x,y) \in [-1, 1]$. I would like to study the metric assuming $x$ and $y$ are random variables. The input variables are typically normally distributed in most applications of ...
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190 views

How many distributions are in the GLM?

I've identified multiple places in textbooks where the GLM is described with 5 distributions (viz., Gamma, Gaussian, Binomial, Inverse Gaussian, & Poisson). This is also exemplified in the family ...
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68 views

Median of ratio of independent variates with Beta distributions

Let $X, Y$ be independent random variables where $X \sim Beta(\alpha_1,\beta_1)$, $Y \sim Beta(\alpha_2,\beta_2)$, and $Z = X/Y$. Recall $X, Y$ are supported on $(0,1)$, so $z > 0$. I've ...
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Sum of variances law

I am currently trying to grasp the concept of Variance Sum Law where variance(x + y) = variance(x) + variance(y) I am not even sure if I understand it correctly ...
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161 views

Lindeberg CLT for exponential independent variables

Crossposted in math.stackexchange: CLT for independent, but non-identically distributed exponential variables This problem is self-study for my qualifying exam. Problem Suppose $(e_n)_{n\ge 1}$ are ...
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41 views

What is this prior distribution?

I know that the joint prior distribution is $p\left( {{a^2},{\beta ^2},\gamma ,\delta ,{\varepsilon ^2}} \right) \propto {\alpha ^{ - 2}}{\varepsilon ^{ - 1}}{\beta ^{ - 2}}$. However, I am confused, ...