A distribution is a mathematical description of probabilities or frequencies.

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14 views

What is the term for a non-continuous distribution?

Given this graph of ordered samples: It does not seem to be a smooth graph (such as with 1/x) as there is a kink around y=8. This suggests there is a unique ...
0
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1answer
18 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 ...
3
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1answer
31 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 ...
1
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2answers
228 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} ...
0
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14 views

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 ...
2
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45 views

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 ...
0
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1answer
27 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 ...
0
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0answers
23 views

Estimation of beta distribution parameters from two points [duplicate]

I want to estimate the best fit beta distribution from two observed points. So for example ($p_1, x_1$) and ($p_2, x_2$) are known exactly. Where $p_i$ is the true percentile of the $x_i$ point. How ...
2
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0answers
15 views

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?
2
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1answer
22 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) = ...
0
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0answers
14 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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22 views

Google Captcha Housenumber Distribution [on hold]

For sinister reasons :-), I "collect" some Google Captchas (the variant that shows mostly housenumbers, the one or other street name and occasionally some Plasper...damn, now I gave myself away :-) In ...
0
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0answers
30 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 ...
0
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0answers
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 ...
0
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0answers
29 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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0answers
23 views

R fitdistrplus : Seek help in understanding NA in std error [on hold]

I am trying to fit a negative binomial distribution and I am using the following piece of code: ...
0
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0answers
25 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 ...
0
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0answers
27 views

Any suggestions on finding the distribution of $q$ given the distributions of $x$,$y$ and $z$ if $q=f(x,y,z)$? [on hold]

$q$ is a function of $x$,$y$ and $z$ and we know that each of these variables are normally distributed with a known standard deviation. How can I find out how this translate into the variability of ...
0
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0answers
19 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: ...
0
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0answers
13 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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0answers
26 views

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 ...
0
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0answers
10 views

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 ...
0
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0answers
26 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 ...
2
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0answers
36 views

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
40 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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2answers
51 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 ...
14
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2answers
825 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?
1
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1answer
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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1answer
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 ...
4
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1answer
97 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 $|q|^2$ ?
1
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1answer
24 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 ...
0
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1answer
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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29 views

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 ...
0
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1answer
28 views

Why 'Assumption of Uniformity' for Mean?

I am teaching some very basic statistics for grouped data. In a different class a few years ago I made an 'assumption of uniformity' about the data: within bins, data is uniformly distributed ...
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0answers
28 views

Hint for problem including function of random variable?

If $Y=\frac{\ln(U_1)}{\ln(U_1)+\ln(1-U_2)}$ where $U_1,U_2$ are independent $U(0,1)$ random variables, then variance of Y equals. I usually use Jenson's inequality to underestimate or overestimate ...
2
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1answer
53 views

How should I calculate the variance of a circular random variable?

Consider the following function being the PDF of a circular random variable (orientation angle from the zenith) ...
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0answers
18 views

Choosing the good initial value of the Newton-Raphson iteration method for Maximum Likelihood Estimation

I want to estimate the four parameters of Exponentiated Modified Weibull Extension (EMWE) distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation. Because the first ...
0
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1answer
17 views

How to define distribution, given probability generating function?

Given some probability generating function $G_X:(-1,1) \rightarrow \mathbb{R}$, Since $$P_X(k)=\frac{G^{(k)}(0)}{k!}$$ then how does one define the distribution $P_X(k)$ in practice? The difficulty ...
0
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0answers
13 views

random data distribution

I have data with no trivial probability distribution function (kind of random data). I want to feature the data distribution as a sum of commun probability density functions (a sum of gaussian or ...
1
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1answer
33 views

Random unit vectors in $\mathbb{C}^n$ and $\mathbb{R}^{2n}$

Suppose $\mathbf{u}\in\mathbb{C}^n$ is a complex random vector with circular symmetry, uniformly distributed on the unit complex $n$-sphere, so we have $\|\mathbf{u}\|=1$. In other words, $\mathbf{u}$ ...
0
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0answers
10 views

Test to compare categorical distrubutions?

I have data on the number of soldiers in each US military occupation code by home state (also by month for each month over ten years, but let's ignore that). I'd like to test if the distributions of ...
0
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1answer
21 views

How does Anscombe transformation stabilize the variance of a Poisson R.V.?

I was taught that a transformation f(X) is said to be a variance-stabilizing transformation if $[f'(E(X))]^2*Var(X)$ is independent of E(X). For a Poisson-distributed random variable X, E(X) = Var(X) ...
0
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1answer
29 views

Using asymptotic distribution under the null when the null hypothesis is false

This is a general question about hypothesis testing in statistics. A standard hypothesis test as I see it is based on 3 things: Stating a null hypothesis Computing a test statistic for the ...
1
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1answer
18 views

Bhattacharya Distance on Distributions (Matrices) with Different Number of Variables (Dimensions) [duplicate]

We have two matrices, $A$ and $B$, representing two different probability distributions, with dimensions, $m*n$ and $k*n$, respectively. How can we calculate the Bhattacharya distance or another ...
3
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2answers
66 views

How to test H0: “this sample is drawn from a gamma distribution” against HA: “this sample is drawn from two different gamma distributions”

This is a targeted follow-up to " all of these data points come from the same distribution." How to test? I have a sample of strictly positive data. I fit a gamma distribution to it and ...
0
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1answer
19 views

Question on Integrating Over Joint Probability

Let us say that we have a joint probability density denoted as $$P(x_1,x_2,...,x_n)$$ If we are trying to find the probability that every $x_i$ is greater than $0$, is it correct to say that the ...
8
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1answer
104 views

Random overlapping intervals

How can I find an analytical expression $D(n,l,L)$ in the following problem? I randomly drop $n$ "bars" of length $l$ into an interval $[0,L]$. The "bars" can overlap. I'd like to find the mean total ...
3
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1answer
97 views

What is the distribution of sample correlation coefficients between two uncorrelated normal variables?

I want to compare observed bivariate (Pearson's $\rho$ and Spearman's $\rho$) correlations coefficients with what would be expected from random data. Assume that we measure, say, 36, cases across ...
16
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2answers
768 views

“ all of these data points come from the same distribution.” How to test?

I feel like I've seen this topic discussed here before, but I wasn't able to find anything specific. Then again, I'm also not really sure what to search for. I have a one dimensional set of ordered ...