A distribution is a mathematical description of probabilities or frequencies.

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Measuring the uncertainty of the average of average rates

Is it possible to determine the mean value of a point by averaging the average rate of ranges that contain that point, and if so, how can the uncertainty of that value be accurately determined? I ...
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31 views

Looking for the distribution of the difference of two Gaussians in a weird relationship

I have a covariate $B$ (let's say age) and two different responses $T_1$ and $T_2$. The bivariate distributions of $B,T_1$ as well as $B,T_2$ are bivariate normal and known: $$ ...
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Consistency of non-parametric estimators for CVAR

Is the estimation of the CVAR (conditional value at risk) using known non-parametric methods different from the estimation of any other random variable? If the answer is yes, are any non-parametric ...
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29 views

Derive the conditional probability $P\left(X \in A \middle| \, Y \in B \right)$

I am trying to derive the following form of conditional probability: $P\left(X \in A \middle| \, Y \in B \right)$. Problem formulation: Let $g$ be a complex r.v. normally distributed as ...
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1answer
18 views

What are the recent real life use or applications of the Cauchy Random Variable?

We have a short assignment on the described question and I already have gone through a lot of trash results from Google. I can't seem to find any. I don't know where else to post this question. ...
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46 views

Distribution of $e$ if $g=\tilde{g}+e$, $g=|f|$, $f \sim \mathcal{N}(0,1)$ and $\tilde{g}$ is the quantization of $g$

Let $f \sim \mathcal{N}(0,1)$ be a normal random variable with zero mean and unit variance. Let $g=|f|$. Let $\tilde{g}$ be the quantization of $g$. We suppose that there are $n$ possible levels of ...
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4 views

Discretization for a bayes network model with small sample

I have been playing around with a Bayesian network toolbox for prediction and classification. I have had good success with the examples but I'm now stuck on how I should proceed with my scenario. I ...
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14 views

how can you prove mean is greater than variance in binomial distribution? [on hold]

How will you prove mean is greater than variance in binomial distribution in terms of expectation and moments?
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1answer
32 views

Probability two people arrive at the same time?

Two people arrive at a train station at a random time between 12pm and 1pm. They arrive independently of each other and their arrival times are uniformly distributed. What is the probability they ...
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1answer
51 views

What are some common approaches for estimating variability of right skewed, bimodal distributions?

I have a data set with the dollars in transactions a store has done historically from noon-2pm on Wednesdays. Most of the time, the store does no volume during this time (16 observations with the ...
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235 views

Is the logarithmic transformation sufficient to tame every distribution?

Today I realized a quite known fact. The log transformation of a random variable, drawn from a fat tail distribution, maps into an exponential tail distribution. ...
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62 views

Estimating the distribution of frequencies from a sampling of unique values

Let $L$ be a list of elements with repetitions, and $S$ be the set of elements appearing in $L$. I have two tools at my disposal: I have a sample of $k$ elements taken uniformly in $S$, and for each ...
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18 views

Support of distribution (distribution fitting)

This might be a weird question. I want to know why Matlab still run to produce estimated parameter whenever I input data which doesn't belong to the support of the distribution? E.g. I want to ...
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1answer
25 views

Functional relationship misleads statistical conjecture -how to explain?

This is an educational issue for me (I am not a Statistics instructor, but colleagues tend to turn to me for some first-line help with the subject), but I believe it bears to anyone having to present ...
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24 views

Rejection Sampling Not Giving Correct Distribution

I hope someone can check through all my steps to see where I made a mistake: I wish to create a sample with the density $\ f(x)=\frac{1-x}{(π-2)(x + 1)√x}$ using the [1,0] uniform distribution U, and ...
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23 views

Average waiting time in an exponential distribution

I have come across the following problem in one of my courses: Let's suppose a patient in a hospital is waiting to be picked by one of the two doctors available. The time till a new pacient arrives ...
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1answer
62 views

What fat tail distributions can I fit to my data?

I have 490 data points, which are very unlikely to be I.I.D. Below is a summary in Million dollars. My goal is to fit a distribution so that its 99.9th quantile captures the 70.22M maximum. Min. 1st ...
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1answer
44 views

What is the probability of randomly picking 4 consecutive ladies out of a team of 11 people?

I was running the morning standup this morning and in contrary to the usual alphabetical order I announced I was going to go in "random" order today, however I then ended up giving all the ladies of ...
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1answer
38 views

What is meant by using a probability distribution to model the outputs for a regression problem?

Often a theoretical text will say something like, 'a probability distribution may be used to model the outputs' or, 'assume a probability distribution such as normal or Lognormal for the outputs'. ...
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85 views

Confidence interval for the confidence interval?

I'm studying confidence intervals, and I'm curious about how one might generate a confidence interval for the confidence interval, if that even makes sense. For example, let's say I draw simple ...
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1answer
45 views

Neural network: two output vectors?

Architecture: I have a CNN which does some classification for me. The output layer y consists of a vector $\vec{y}$ which is of dimension $(1, 1000)$, so it has 1.000 neurons in total (the weight ...
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1answer
37 views

How to consistently distribute numbers on polyhedral dice to ensure maximal fairness?

There are several regular solids made into dice (d6, d8, d10, d12, d20, d30). You have to number each face starting at 1. Given the imperfect nature of dice manufacture, you want to distribute the ...
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2answers
242 views

Why is this definition of the Central Limit Theorem not incorrect?

I found the following definition of the Central Limit Theorem from book Probability and Statistics by Degroot (also from Wikipedia). It simply states the CLT as $$ \lim_{n\to\infty} ...
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continuous vs discrete random walk

For 1D random walk in discrete case the probability of finding walker at position X after N steps(P_N(X)) is binomial distribution(http://mathworld.wolfram.com/RandomWalk1-Dimensional.html), moreover ...
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Urn with balls of two colours with a priori probability of each ball

If we have a urn with $N$ balls of two colours ($D$ red and $N-D$ black balls respectively), then probability of having $k$ red out of $n$ balls drawn at once without replacement follows the ...
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30 views

How to find the probability that a group of people is not allowed to enter a country given some factors?

I have this scenario: There are two countries A and B. A sends a group of N people to B... There is an independent probability of p that a person gets fatigued while traveling to B. And I have ...
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Is there a distribution that covers Pareto's law?

Is there a distribution where (for example) 80% of the results come from 20% of the inputs? (i.e. Pareto's law). Hmm... there's a tag for Pareto Distribution ... is that the answer?
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24 views

Probability of median > 1.5

I was asked a probability question: Given three numbers i.i.d as $\text{uniform}(0,2)$, what is the probability of the median greater than $1.5$? My hunch is that each number has $P(X > 1.5) = ...
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17 views

Estimate number of unique items by number of duplicates in a sample

We have a v. large (1e6) population with unknown number of types of items. We draw a small sample (~100) of a certain size, and find that exactly one item was duplicated. The question is to estimate ...
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32 views

For a U-shaped distribution, how many results must I verify

--edit-- in plain English. I have a distribution with over a million points between 0 and 1 that is shaped like a U with many values falling near 0 and 1. Each point is SUPPOSED to represent a score ...
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8 views

Probability of Pr(N=0) as function of Panjers (a,b) parameters

Is there a way to find the general formula for Pr(N=0) as the function of Panjers parameters a and b for Binomial, Negative Binomial and Poisson distributions? It is possible to show e.g. parameters ...
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34 views

Expected value of normal-wishart, is the solution correct?

I want to compute expected value of $E[μΛ]$ for a normal-wishart distribution how can i compute it? A normal-wishart distribution is defined as below: $$ NW(μ,Λ|μ_0,λ,W,v)=N(μ|μ_0,(λΛ)^{−1})W(Λ|U,v) ...
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26 views

Terminology clarification: Discrete distribution == Categorical distribution?

I'm reading "The Indian Buffet Process: An Introduction and Review" by Griffiths and Ghahramani and wanted to confirm my understanding of one of the terms they use. On page 1188, they say that the ...
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22 views

Impact of data distribution on (statistical/ machine) learning performance: overview

I am trying to get a global view on the different ways how (non-ideal, messy) data distributions can affect different performance dimensions of statistical/machine learners, incl. but not limited to: ...
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16 views

Finding proper cut off for filtering?

I had a set of data (149876 rows and 1200 columns)and I have found outliers points for each row. Now I want to determine a proper threshold for filtering my outliers. The distribution of my data is ...
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Predict the average stay of customers

This is my data: customers subscribing to a service and more or less regularly having activities on that service. I want to calculate an average length of stay for the customers using the service. I ...
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Distribution of samples from a uniform distribution [duplicate]

Let's say we are taking $n$ samples from a uniform distribution, that spans from $0$ to $1$. According to the central limit theorem, the mean of the $n$ samples will follow a normal distribution with ...
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27 views

Distribution with known mean and bounds, but unknown standard deviation

Let's say I wanted to construct a distribution where based on more anecdotal evidence then actual given data sets. For example. lets say I think that I think the value $K$ is anywhere between 9% and ...
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Fitting distributions to data

I have a dataset of 1000 observations of a continuous quantity, and I am trying to find a distribution that fits them best. At first I tried the Cullen and Frey graph, with bootstraping, to get an ...
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1answer
41 views

What is the probabilistic view on clustering? [closed]

Say that we got a set $\mathcal{X} = \{x_1, x_2, \ldots\}$ of samples. You want to partition $\mathcal{X}$ into $k$ subsets, where $k$ is unknown besides the fact that $k \ge 1$. How clustering ...
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62 views

How to calculate $E(x)$ and $V(x)$ when $g(x)\sim f(g(x))$

Let assume that we are interested in a variable $x$. We know that e.g. $g(x)=x^2$, $g(x) \sim Uniform(a,b)$ or any other distribution. From that I can calculate $E(g(x)) = (a+b)/2$ and ...
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81 views

Probability of failure in a finite population

I regularly inspect finite populations for failures (we make custom products in batches of ~500-800). Currently, we inspect every product for failure, which is quite a bit of work. I want to reduce ...
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56 views

Finding the conditional distribution of 2 dependent normal random variables

Here's the situation $X \sim N(\mu, \sigma^2)$ and given $X=x$, $Y \sim N(x, \tau^2)$ I need to find the distribution of $X$ given $Y=y$ From what's given, I know the pdf's of $X$ as well as ...
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853 views

Why is the logistic distribution called “logistic”?

What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
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43 views

Find cumulative probability from given formula

Given a formula to calculate instantaneous probability of an event. f(i) = 0.0222 * e ^ (-­i / 11.5) For instance 0.0222 * e ^ (­-4 / 11.5) is the probability of ...
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23 views

Modelling the distribution of rare events. How to validate?

I have been asked to create a model for the distribution of the number of items any previous customer might buy from a shop. Each customer will get a distribution of their own based of their past ...
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1answer
105 views

Distribution of $|q|^2$ if $\Re[q]\sim \mathcal{N}(\mu_1,\sigma^2/2)$ and $\Im[q]\sim \mathcal{N}(\mu_2,\sigma^2/2)$

Let $q$ be a complex random variable such that: $\Re[q]\sim \mathcal{N}(\mu_1,\sigma^2/2)$ and $\Im[q]\sim \mathcal{N}(\mu_2,\sigma^2/2)$. What is the PDF and CDF of the squared norm $|q|^2$ ?
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26 views

ANOVA (assuming different distributions) vs Kruskall-Wallis and post-hoc tests

During stats courses on Uni I learnt (if I remember correctly and hopefully don't put my teachers to shame) that if you want to compare multiple groups with eachother you look at the residuals of an ...
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51 views

Pdf of the square of a standard normal random variable [closed]

I have this problem where I must find the pdf of $Y = X^2$. All I know is that $X$ has the distribution $N(0,1)$. What kind of distribution is $Y = X^2$? Same as $X$? How do I find the pdf?
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Is a time frame of time of day circular data?

I have data points with time of day. But I only took data between about 6:00 AM and 18:00 PM. If I want to test these data for distribution do I have to take a circular test? Or should I take a ...