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A distribution is a mathematical description of probabilities or frequencies.

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How to uniquely identify each Employee in an Organisation with a hash value between 0 and 511

let I be a set of random input values, with I = N . Then h meets this quality criterion if (∀1 ≤ i ≤ n)(|h(I) ∩ Pi| ≈ N/n ) if N >> n. Suppose you want to use Employee numbers to calculate a hash, ...
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20 views

Comparing probabilities generated by two different normal cumulative approximations [on hold]

Suppose I have two ways of approximating cumulative normal probability and I want to compare whether the two methods are equivalent. The most obvious way to go about it would be to have a bunch of ...
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0answers
22 views

Unsure about the distribution of the canonical statistic

Iam a bit unsure if the distribution of the canonical statistic below is correct ? I suspect i would need idenpendent variables to show the correct answer. Let $Y_1,Y_2,...Y_n$ be a sample form a ...
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1answer
34 views

What kind of distribution is figure 2 in this study?

What kind of distribution is figure 2 in this study? If it's a Gaussian distribution for the LH hormone, I can't make any sense of the data. The article: Aksglaede, L. et al. (2009): Recent decline ...
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1answer
21 views

Algorithm for selecting largest possible value, when observing online sequence of unknown distribution?

I have been trying to devise an algorithm for a problem that's been bugging me for a while. For some weird reason I haven't been able to find any mention of this problem in the literature, so far. I ...
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0answers
31 views

Hypothesis test for machine failure rates

Let's say I have one collection of machines (made by manufacturer 1). These machines run over a few days and fail at a certain rate. Let's say they run for a total of $h_1$ machine hours and the ...
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1answer
13 views

Clarification on traditional notation for moments

$\newcommand{\E}{\mathrm{E}}$ I have been going over the Hill et al. (1976) paper on Johnson distributions and struggling with some notation that is undefined but I believe might have been considered ...
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1answer
35 views

Find a realistic distribution scenario for requests

For a loadtest I have to figure meaningful numbers for the maximum number of requests per hour and minute. The only thing I have is the number of requests per working day (which is a timeframe of 14 ...
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12 views

Estimating parameters in a mixed distribution

From my samples I have some distributions made up a mixture of 2 to 4 different components. I have the overall density and the proportion of each component in the distribution, but I want to estimate ...
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27 views

Probability distribution model

I have a dataset in the following form: ...
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0answers
9 views

Difference between Beta process and Beta regression?

In a layman language, how the difference can be defined between statistical process and the same named GLM such as poisson processes and poisson regression or beta processes and beta regression? How ...
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1answer
98 views

If $X=Y+Z$ with known pdf of $X$, are $Y$ and $Z$ unique?

Say there are random variables such that $X=Y+Z$ with $Y$, $Z$ independent; knowing the pdfs of $Y$ and $Z$, one can (technically) find the pdf of $X$. Taking it from the other side: if one knows the ...
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Calculating Variance for a Normal Distribution [closed]

I want to add noise to a given time series of data. The noise is to be generated using a distribution technique. For example for an interval of 10 min I have 60 entries which sum upto say 13643Kw. ...
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1answer
24 views

What are the survival and hazard function of a Gumbel distribution?

What are the survival and hazard function of a Gumbel distribution?
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1answer
32 views

What probability distribution can be described as y ~ X * Exp(1) [closed]

The green dots show the product of X and the exponential distribution with rate 1. It looks like it should be some simple probability distribution but I can't figure out what it is! Can you tell me ...
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0answers
60 views

How were statistical distributions discovered?

Let me start, that i know that it's not very difficult to generate a probability distribution. If one takes any positive integrable function and normalizes it, this results in a probability density. ...
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0answers
16 views

CLT for different but independent random variables [duplicate]

Is the Central Limit theorem still applicable if we consider a sum of independent but different random variables? (Each with finite mean and variance) Is there some theorems about this ?
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0answers
17 views

Multinomial distribution: Practical applications [closed]

I'm wondering if you could share your experience in using (or seeing) practical engineering applications of the multinomial distribution (the cousin of the binomial). \begin{align} \displaystyle {n! \...
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0answers
22 views

Unbiased estimates of parameters from pareto samples

If $X_1$, $X_2$... $X_n$ is the sample of the above distribution, so what's the unbiased estimate of $\frac{1}{θ}$
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1answer
32 views

What is the maximum entropy distribution given the median (instead of the mean)?

Given that the median seems to be a more robust statistic than the mean/average, I was wondering if there is a solution of the maximum entropy distribution given the median (or the median and some ...
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1answer
32 views

Probability Distribution and Transformation

Let X have the following distribution function F(x)= 0 for x<0; x/3 for 0<=x<=2; 1 for x>2. Let Y=X^(2) To find P(Y<(X)) Do we simply substitute X^2 for Y and divide to get P(X<1) ...
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2answers
50 views

Confidence Intervals meaning [duplicate]

Lets say I know population std. deviation $\sigma=5$ and sample size $n=60$. Now lets say my sample mean is $\overline{X}=98$. I already know from central limit theorem that 95% of the time the sample ...
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0answers
14 views

How to obtain an approximation to a PDF that cannot be obtained analytically?

Let $W$ be an RV with a Weibull $\mathcal{W}(a,b)$ distribution. Then$^*$ the PDF of $X=\log(1+W)$ is $$ f_1(x) = 10^x \left( 10^x-1 \right)^{a-1}ab^{-a}\ln(10)\exp\left[ -\left(\frac{10^x-1}{b}\...
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1answer
28 views

Standard Error of the ratio of multinomial and negative binomial variables

What is the correct way to compute a standard error of the ratio between random variables following multinomial and negative binomial distribution? I asked a question about computing variance in the ...
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0answers
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“distance” between two histograms (frequency counts) of ordinal data (Likert scale)

I've got a bunch of survey questions that use a 5-level likert scale for the response. (Strongly disagree, Somewhat disagree, Neither agree or disagree, Somewhat agree, Strongly agree). I can take ...
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1answer
25 views

Hellinger distance for two shifted log-normal distributions

If I am not mistaken, Hellinger distance between P and Q is generally given by: $$ H^2(P, Q) = \frac12 \int \left( \sqrt{dP} - \sqrt{dQ} \right)^2 .$$ If P and Q, however, are two differently ...
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34 views

Generating random data that satisfies two conditions

I am looking to generate a synthetic set of data. For clarity I will use a simple example and then elaborate. Suppose that I would like to create a set of data concerning the color and size of a ...
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1answer
56 views

Conditional distribution of $(X_1,\cdots,X_n)\mid X_{(n)}$ where $X_i$'s are i.i.d $\mathcal U(0,\theta)$ variables

Let $(X_1,X_2,\cdots,X_n)$ be a random sample drawn from $\mathcal U(0,\theta)$ distribution. It is a common exercise to prove that the maximum order statistic $X_{(n)}$ is sufficient for $\theta$ as ...
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1answer
24 views

How to find the maximum probability of an hourly based variable ?

Let's say my dataset is composed by the time (hour) of when a user uses his TV, over a month. I may have something like this : ...
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0answers
35 views

Distributions over continuous distributions [closed]

I know a few stochastic processes that are described as 'distributions over distributions'. For example, the Dirichlet process draws discrete distributions from a default model (see e.g., p3 of these ...
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2answers
73 views

Batch loss of objective function contains exp becomes nan

I am trying to solve a survival analysis problem, where all data are either left-censoring or right-censoring. I use an objective function which contains the CDF of Gumbel distribution. I have $m$ ...
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1answer
50 views

Comparing the distribution of few integers

Suppose every person in a group ranks the quality of two products. The quality can be ranked as 1 (very good), 2, 3, 4 and 5 (very bad). I have a list of those observations. which is the right way for ...
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2answers
37 views

statistical test to compare a distribution of values versus a fixed number

I have over a 100 observations of human decisions. If my hypothesis is correct, they should all be a fixed number, or around that fixed number (allowing for small errors around that fixed point). How ...
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15 views

Understanding Borel Sets in Relation to Distributions

Following up with my last question, I am self studying the book Elementary Stochastic Calculus with Finance in View. The author has lost me in some of the terseness of his explanation of distributions....
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3answers
270 views

A question about Histogram-to-distribution transformation

I have done a simulation with 1 million runs on Matlab. I have got a histogram for this. Using Matlab command hist(X), (where X is the 1 million samples as results ...
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1answer
41 views

Distribution vs Distribution Function

I am currently reading through Elementary Stochastic Calculus with Finance in View and I am going through the probability review section. Intuitively I know the difference between a Probability Mass ...
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0answers
33 views

Check whether a random sample comes from an elliptical distribution?

How can I check whether it is a reasonable assumption to say that a multivariate sample $x_1,...,x_n$ comes from an elliptical distribution, such as a normal distribution or a t-distribution? In the ...
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1answer
22 views

R glmer: distribution for strongly right skewed data

I have the following dataset with daily home range sizes (meter95, meter50) per individual: ...
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1answer
54 views

Why does Uniform Distributions have no outliers?

I was reading about the relation between Kurtosis and Outliers on Wiki and got across a line 'An example of a platykurtic distribution is the uniform distribution, which does not produce outliers' [...
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1answer
20 views

Is this notation for a lognormally distributed variable misleading?

I have gotten into the habit of notating a lognormally distributed random variable $X$ as: $$X \sim \ln\mathcal{N}(\mu,\sigma^2)$$ I am now starting to question where I picked this habit up and ...
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0answers
26 views

Generating random correlation coefficients (Pearson $r$)

I'm trying generate some random correlation coefficients ($CC$) using the Fisher's $z$ transformation. An R implementation is shown below. However, it looks like ...
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1answer
16 views

Is there a canonical probability distribution on an ordering/permutation

What is a good way of defining a non-uniform probability distribution on a permutation of k objects? For example, suppose the parameter was an ideal ordering, and the probability of an ordering was ...
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0answers
15 views

Using Anderson Darling test statistic vs p value to infer Goodness of Fit

I have been reading articles recently that discourage the use of p value for hypothesis testing (https://www.sciencenews.org/blog/context/experts-issue-warning-problems-p-values) Rather than using a ...
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0answers
35 views

How to compare two point estimates between two samples

I have two samples, composed by independent observations and a set of features. Each sample can be represented as a binary matrix ($A_{ij} \in \{0, 1\}$) of observations x features. I want to find ...
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2answers
52 views

why does the distribution of height follow Normal Distribution?

The height of a class of students in a school is said to follow Normal Distribution. We know that the domain of a random variable that follows Normal distribution is said to range from minus infinity ...
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0answers
8 views

Confidence intervals for estimated means in multimodal Gaussian Mixed model

I am trying to define animal behaviors by using a distribution of turn angles from 0-180 obtained from animal locomotion. My plan is to use the angle distribution to determine a range of angles to use ...
2
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1answer
17 views

How to calculate the probability that a feature falls into a certain class

There are classes A,B,C,D,E. Variable x has different means for each of these classes, but there is overlap in the range of x among classes. Item counts are different between classes, eg. there are ...
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2answers
46 views

Convolution of a less typical distribution

$X_1$ and $X_2$ are independent and identically distributed (i.i.d) random variables defined on R+ each with pdf of the form $f_X(x) = \sqrt\frac{1}{2\pi x}exp[\frac{-x}{2}]\quad ,\quad x>0, \quad ...
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Problems Estimating Parameters for the Inverse Gamma Distribution

I am trying to estimate the parameters of an inverse gamma distribution such that a given amount of probability mass lies above and below some specified threshold. If $x$ is an inverse gamma ...
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0answers
27 views

The probability of photon collision

I was reading a textbook and I couldn't figure out something that seemed really obvious: Assume that the space is uniformly and randomly filled with stars, and the mean radial distance between the ...