A distribution is a mathematical description of probabilities or frequencies.

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Find distribution of underling feature

Let's say I have a dataset compose of value for the variable W. The distribution of W doesn't follow any obvious know distribution. I have a model that gives W as a functions of E and K. W = f(E, K). ...
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19 views

Anomaly detection: multivariate Gaussian distribution

I am trying to do anomaly detection on a heterogeneous dataset (There are unknown groups present in the dataset). I want to try multivariate Gaussian distribution based approach, but I was thinking of ...
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21 views

Modeling continuous abundance data with a GLM in R: how to select the correct distribution family?

I have abundance data (counts) that I have standardized by area sampled, making them continuous. I would like to explain them with my two independent variables using a GLM but I am having trouble ...
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115 views

Curious distribution

While checking my Android App Rating I saw this It's almost a quadratic progression! Is there any explanation for such a rating?
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16 views

Probability-generating function of two independent Poisson random variables [duplicate]

Let $X_1, X_2$ be two independent Poisson random variables with mean $\lambda_1, \lambda_2$, and $S_2 = a_1 X_1+a_2 X_2$, where the $a_1$ and $a_2$ are constants. Is it correct, that ...
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44 views

What coefficients do I use for a binomial distribution problem?

I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having ...
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1answer
14 views

Picking a probability distribution for observed intensities

I have an experiment that measures "intensity" (in this case, electron density of a molecule) on a grid. The values it gives are non-negative,. I'd like to write a likelihood for this observation ...
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16 views

Place balls in bins with specific distributions algorithm [on hold]

I've searched for an answer for my problem on the forum but is still not answered. Let's say I have N balls and want to place them in M buckets without replacement, BUT.. These buckets have all ...
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83 views

Inverse CDF sampling for a finite mixture

The out-of-context short version Let $y$ be a random variable with CDF $$ F(\cdot) \equiv \cases{\theta & y = 0 \\ \theta + (1-\theta) \times \text{CDF}_{\text{log-normal}}(\cdot; \mu, \sigma) ...
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179 views

Outlier Detection on skewed Distributions

Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions ...
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13 views

Moment generating function of univariate skewed-t distribution

Is there a moment generating or a characteristic function for a univariate skewed-t distribution $y\sim ST\left(\xi,\omega^2,\alpha,\nu\right)$ as defined by Azzalini
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24 views

Families of distributions with bounded variations

For what family of probability distributions $f(x)$ do we have the following property? $$ \forall x, \quad \int f(u) - f(u+x) du \leq L\| x \| $$ for some $L$. Can we say anything about the ...
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How to determine the random variable distribution to fit the generalized linear model in R? [on hold]

I have a trouble with a sample from a random variable. I cannot determine its distribution. I would like to calculate the generalized linear model then with this variable treated as the dependent ...
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1answer
33 views

Independent and Identically Distributed(i.i.d.) Random Variables

The assumption that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods . However in practical applications of statistical modeling the assumption may or ...
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19 views

Compare distributions for equality

I am looking for a method to compare two distributions for their equality. E.g. assume I have a distribution of specific elements which I found theirs positions not being equally distributed (blue). ...
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34 views

Proof of probability density function? [on hold]

Is there any website or any book which you can recommend to me for learning the proof of all PDF (distribution function)?
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25 views

Fitting a GEV distribution - non-negative only

I am fitting a GEV distribution to some rainfall data, but the software I am using (Matlab and Easyfit) are giving a distribution which includes negative numbers (i.e. negative rainfall). Is there a ...
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1answer
23 views

Reparameterization of probability distribution (spike and slab)

I try to understand a statement in this paper: http://papers.nips.cc/paper/4305-spike-and-slab-variational-inference-for-multi-task-and-multiple-kernel-learning.pdf In particular, I am talking about ...
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1answer
30 views

Possible to morph a bimodal distribution into a normal distribution slowly?

Is it possible to slowly turn a bimodal distribution into a normal distribution slowly by shifting some parameter K? The reason I want to do this is because I want to conduct a scenario analysis and ...
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1answer
33 views

Is there a way to characterize the position of a point in a distribution that takes higher moments into account?

When summarizing a location in a distribution, we can take the mean into account by simply calculating $x-\mu$. We can take the standard deviation into account by calculating a Z score ...
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26 views

Problem with multivariate lognormal distribution in R

I'm using the R package compositions for the multivariate lognormal distribution. this is the only package I found that supports it. However I'm not sure how this ...
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1answer
78 views

Reduce a Weibull model to an exponential one

I have this problem: Let $\ X\sim Weibull(\theta_1;\theta_2)$ with the sample: ...
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1answer
52 views

Can a CDF from data cross with another CDF

Given two data sets of positive real numbers X and Y, both of the same size, and 0<=Y<=X for each row; can the empirical CDF of X ever cross the empirical CDF of Y?
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Comparing values of random variables from sampled distributions

This is a novice question, which I struggling to answer. I want to find P(A>B) where A and B are random variables from two different distributions. Although two distributions that I have are not ...
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2answers
82 views

Detecting Bimodal Distribution

I have histograms of audio signals where they have bimodal "normal" distribution. What I want to do is to detect these subpopulations inorder to have a threshold, this is meant to divide the values ...
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1answer
28 views

multi stage binomial “process”

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$ X_1 \sim \text B(K,p) $$ , p is the ...
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37 views

Polynomial transform of a Gaussian Random Variable

I have been trying to find how the PDF of a polynomial transform of a Gaussian Random Variable could be found. Eg: If \begin{equation} \ X\sim N(\mu,\sigma^2) \end{equation} Then what would be the ...
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26 views

Multiplication of two random distribution

I am trying to find the resulting PDF , when two random functions are multiplied. First function obeys normal distribution and second function obeys cauchy distribution. Can anybody tell me how to ...
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Compare non-gaussian distributions and evaluate sampling process

I have a 150,000 datapoints (continuous values between 0 and 1) and I am running a process that averages groups of smaller samples based on some other data values and results in ~100,000 datapoints. ...
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1answer
79 views

Which of these distributions approximates better to a Poisson distribution?

Consider two Poisson binomial distributions (distributions of sums of independent Bernoulli variables) as below: The distribution of the sum of 99 variables with probability 0.01 (of taking the ...
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8 views

Is it possible to train a Convolutional Neural Network with distributions as supervised information

Recently I am working on a project which aims at training a convolutional neural network with some distributions as supervised information instead of discrete labels. I think I can learn some useful ...
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8 views

best distribution fit for risk analysis [closed]

I am using Easyfit software to get best distribution fit for my result. I got the result which a ranking list of best distribution fit that consist of more than 20 distributions. my research is ...
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1answer
23 views

determining significance of term use

Thing one: feel free to RTFM me: I'm definitely looking for search-able terms or background reading. Our situation is this: we have a set of 140 reviewers and 20 elements. Each reviewer reviews each ...
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31 views

Distribution of stackexchange reputation

Should one expect the reputation on stats.stackexchange.com (or any other stackexchange platfor, for that matter) to be similarly distributed to income? That would be a log-normal distribution, I ...
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70 views

Determine distribution of test statistic

I have a set of normally distributed parameters, $\hat{b}_{i}$, with different but known variances $\sigma_{i}^2$, that is $\hat{b}_{i}\sim N(b_{i},\sigma_i^2)$ where the $\hat{}$ indicates a ...
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62 views

distribution of sums from a formula, standard deviation

Given positive integers $a$ and $b$ ($b \leq a$), where $c$ is the set of all combinations of $a$ digit binary numbers, with $b$ 1's, and where $c_1$ is least significant bit, and $c_a$ is most ...
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95 views

What is the meaning of the conditional $y|b$

I think I'm confused about a very simple thing. When we say that some variable is distributed as a Poisson distribution and we write $y \sim \text{Pois}(\lambda)$, is this the same that saying ...
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52 views

Can someone explain what it means for an observation, from a group of data, to be independently and identically distributed?

I don't quite understand what the difference is between an observation being independent and it also being identically distributed. Can someone explain please?
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39 views

How to describe/define tail of a distribution

I have a histogram showing a distribution with a long tail, and I would like to come up with a definition (in words) for the points fall inside the "tail", not based on quantile or standard deviation, ...
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21 views

How to prove NegativeBinomial(r,p) converges to Gamma(r,1) as p->0

Let $X\sim NegBin(r,p)$ and $Y\sim Gamma(r,1)$. How can I prove that $pX \overset{dist}\to Y$ as $p\to 0$. Is this statement the same as $X\overset{dist}\to Gamma(r,1/p)$. Thanks.
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1answer
45 views

How to read results of the Dunn Test from R

How do I read the results from a Dunn test? Specifically, what do the values in the table below tell me? I have non-parametric data in 4 groups, and I first did a Kruskal-Wallis test to confirm that ...
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23 views

comparing two CDFs with different x-ranges?

I was wondering what is an appropriate method to quantitatively compare two CDFs where the x-ranges are different. For example, lets say CDF1 has x values ranging from 0 0.5 and CDF2 has values ...
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2answers
57 views

Testing whether data follows T-Distribution

I am involved in a project where I need to check whether my data follows a T-distribution with N degrees of freedom for a given value of N. I know that Kolmogorov-Smirnoff can be used, but is there ...
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1answer
32 views

confidence interval on expected number of cases in a set given a model

I have a set of units, where unit $i$ has: a binary outcome $y_i$ ("case" or "non-case") a binary vector of treatments $\mathbf{t_i}$, where $t_{i,j}=1$ if unit $i$ received treatment $j$. several ...
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31 views

Sum of percentile rank scores of two or more variables

I need to sum some variables that are on different scales to make a new one. I'm wondering If it's correct to calculate the percentile scores first, and then to sum them up. Imagine I have to ...
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2answers
15 views

Distribution Enquiries

I have a set of cycle time data for a processing counter. Since the cycle time is less than 1 minute, so the time taken are all less than 1 (ie 0.14m). I am trying to fit into distribution, but ...
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1answer
25 views

Compare two distributions of large sizes and unequal variances where one distribution is heavily skewed

My data is from cells that are treated under two different conditions and then their response to the condition is measured by one output variable. The cell populations in the two conditions are quite ...
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48 views

Are there non-trivial settings where the MAD statistic has a closed-form density?

The MAD statistic of an iid sample $(x_1,\ldots,x_n)$ is defined as the median of the absolute deviation from the median: $$ ...
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clustering vs fitting with a distribution

I have a question about using a clustering method vs fitting the same data with a distribution. Assuming that I have a dataset with 2 features (feat_A and feat_B) and let's assume that I use a ...