A distribution is a mathematical description of probabilities or frequencies.

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AIC for 2-dimensional data

Let's consider a univariate (experimental) distribution, and two 1-dimensional models to describe it (e.g., a Gaussian distribution and a mixture of two Gaussians). One then computes for each model $$...
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24 views

General, flexibel distribution [on hold]

What is the most general/flexibel probability distribution. What I mean is, what would be the distribution that, given n parameters, could get more different shapes?
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Independent random variables

Let $L(\xi) = \Gamma(1,1)$. $Y_r=(n-r+1)(X_{(r)}-X_{r-1}), \ r=1,...n$ $(X_{(0)}=0)$ where $X_{(r)}$ - order statistic. Prove random variables $Y_r$ independent and have same ...
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Estimating the Parameters of Multivariate Gaussian from Conditioned Distributions

My goal is estimating the distribution parameters of a multivariate Gaussian $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^n$ from observations that were generated from different conditioned variants of ...
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5 views

Aligning distribution vs aligning subspaces [on hold]

Does aligning the distribution of two datasets via minimization of the maximum mean discrepancy also align the two subspaces that span the data?
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1answer
19 views

How is this chart called? Percentile chart?

Assume I have a chart below how a certain property is distributed (in this case number of cars over 0-100%) over a population: How is such a chart called? Percentile chart? What are the keywords to ...
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24 views

Independence of random variables with known Gaussian conditional distributions

My question regards whether it's possible to know whether two Gaussian random variables are independent when we know only that their respective laws are governed by conditional distributions of ...
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2answers
158 views

Is the multiple of a Weibull distributed variable also Weibull distributed?

A Weibull distributed variable $X \sim \textrm{Weibull}(\lambda, k)$ has probability density function $f(x):$ \begin{equation} f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left(\frac{x}{\...
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192 views

Sampling from an Inverse Gamma distribution

I am using Gibbs sampling in the MCMC estimation of a stochastic volatility model. One of the posterior distributions is an Inverse Gamma distribution.I was struggling with the sampling procedure or ...
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24 views

Does a probability density function fit here? [on hold]

The following is a simplified hypothetical version of my real issue: I'm writing an app that tracks shoe brands in the world using a grid system. The intention is to create a heat map for each brand, ...
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1answer
16 views

Distribution Fitting with multiple changepoints

I have a time series of a random variable x, which randomly moves in and out of three broader states- "generally increasing", "generally decreasing", "more or less staying still". The distribution of ...
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11 views

compare means of variables with unequal N Sizes of a population

I am trying to compare means of 4 variables and the var have unequal N sizes with some missing values. According to the figure attached, can I compare mean of B with mean of C variable ? B has a lot ...
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1answer
27 views

How to implement MLE of Gumbel Distribution

I'm trying implement the Maximum Likelihood Estimation in R to Gumbel distribution, but the algorithm doesn't converge. I'm using this parametrization to gumbel: $${\frac {1}{\sigma}{{\rm e}^{{\...
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5 views

Confidence that a percent of population will be within bounds (parameter-less) [Tolerance Interval]]

Sometimes it's nice to be able to estimate the proportion of a population that will fall within certain bounds, given a set of sample data from that population. This is essentially a tolerance ...
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7 views

Objects and properties classification

I have a list of properties and objects: ...
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1answer
16 views

How to compute bounding coefficients for McDiarmid's inequality?

I am trying to understand the proof in Sec. A2 of Gretton et al.. To make the question self-contained, I summarize below the key ingredients. At the end of the post, I state my question. Given a ...
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14 views

Sampling from Hierarchical Distribution

Let's say I know $$ X \mid \mu, \sigma \sim \mathcal{N}(\mu, \sigma^2), \qquad \mu \sim Unif(a, b), \quad \sigma \sim Unif(c, d), $$ and I want to sample from $X \mid \mu, \sigma$. Is there a go-to ...
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1answer
17 views

Can I use information about the distribution of the dependent to improve prediction?

I'm trying to make predictions about a quantity on a per-subject basis. If I aggregate my complete sample I can get very good fit for distributions like gamma or Weibull, so I can make some ...
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25 views

How to find the Inverse CDF of a Skewed Normal Distribution

The Wikipedia article on the distribution also doesn't seem to specify any formulae on right hand side. Also wolframalpha says there is no closed form solution.
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39 views

Which distribution has an expected product equal to one?

Consider $n$ values $x_{1}$ to $x_{n}$ such that $x_{1}x_{2}\cdots x_{n} = 1$. Importantly, these values are non-independent, as their product must be equal to 1. The trivial case of $x_{i}=1 \quad \...
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60 views

Data distribution in GLM [on hold]

I want to do glm analysis for my data in r studio, my data are soil data (PH soil, percentage of clay and silt and loam, nitrogen soil), I have 5 plantation and 3 soil depth, plantation and soil depth ...
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1answer
48 views

Drawing sample size 1 from a uniform distribution - Difficulty in understanding Central Limit Theorem?

Let's say we have a uniform distribution and we are drawing samples of size 1 so that the mean is the drawn number itself. If we perform this activity sufficiently large number of times we would get ...
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19 views

Test for difference of spatial/temporal distribution

I have the data of the average hourly consumption of electric power in 50 districst of a city, for the days of 2 months: ...
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44 views

Tail probability for heavy tailed distributions

For some data (where I have the mean and standard deviation) I currently estimate the probability of getting samples greater than some x by using the Q function; i....
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Comparing 2 sets of distributions

I have a data set where I have 2 groups of samples, each with 5 samples within each group. Each sample has a distribution of particle sizes within it (500 or more items in each distribution). How do I ...
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1answer
33 views

Ratio of Gamma distributed variables with different parameters

I encounter a problem which I thought I can handle, however, I struggle a lot with finding a solution: The following setting applies: I want to compute the posterior probability of an event, which is ...
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1answer
32 views

The best family in GLM with R

I want to do GLM analysis for my data but i do not have information about my data distribution I do not know I should use of poisson, Gamma, qaussion or binomial, please guide me how i can identify ...
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Statistical test to determine the difference or similarity between two variables?

I want to know if there is a way to determine the probability of two variables are referring to the same thing, aka to know if there is an association between the two variables. Let’s say there is a ...
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Weibull distribution for lead time [closed]

I have monthly demand data for a certain product, it is following Weibull distribution (2 parameter,I calculated the 2 parameters). Now I want to know the 5 month distribution of demand based on the ...
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1answer
38 views

Data Transformation Needed for Logistic Regression?

I'm planning to do logistic regression with my dependent variable as either with injury or no injury with one of my independent variables as average computer use. I have attached a sample ...
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Insight Sampling Distribution

I have the following problem. When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 92.0 and a standard deviation of 3.6 A ...
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1answer
15 views

Distance Metrics for Comparing Theoretical Sampling Distributions

I have a sampling probability density function (denoted $f(x|M,N)$ that becomes hard to calculate for large degrees of freedom (i.e. as $M$ and $N$ get big). If I have another pdf (say $f^{*}(x|M,N)$ ...
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1answer
25 views

Conditional distribution (on N) of arrival times in a nonhomogenous poisson process

Conditional on $N(t)$, given some $\lambda(t)$ characterizing some Nonhomogenous poisson point process, the distribution of an arrival time $t_i$ is $\lambda(t_i)/\int_{A}\lambda\left(t\right)dt$ ...
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94 views

How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
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Binary Stochastic Programming with Independent or Positively Correlated Co-efficients

A manufacturer can select a maximum of $N$ stores to fulfill orders from a total of $M$ stores who are looking for inventory, $N\le M$. The case when $N\geq M$ is trivially solved when all stores ...
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How can I determine if a weighed random function is working as expected?

I am writing a series of program utilities which heavily utilize weighted random functions, where the user defines a probability density function as a piecewise curve with a series of ...
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1answer
60 views

How do distribution functions (e.g. Gaussian, Bernoulli, Poisson, etc.) relate to deep learning?

I know that neural nets use activation functions, but where do distribution functions play into deep neural networks? For example, the h2o.deeplearning() function ...
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How to forecast number of participants in a study?

Assume I have a set of people who live at location A, B and C (let's say 3 at every location). Further assume I want to conduct a study for what I need at least 1 person per location. My Question: ...
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Python Scipy - How to test the goodness of fit only for a part of an exponential probability density function?

I have a dataset that contains the distance (in cm) between the emission point and the interaction point of about 50 000 fluorescence X-rays. When I plot its histogram, I should expect an exponential ...
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30 views

Probability Distribution for Inter-arrival Time

I'm trying to build a simulation for a quality control process, where quality analysts inspect the product and report faults if they found any. I have a dataset of this bug reports, so I'm trying to ...
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81 views

What does it mean for a probability density function to have this property?

What does it mean for a probability density function $f(x)$ to have the following property? $$I= 1+\int_{x=0}^{\infty}x^2 \left(\frac{f'(x)^2}{f(x)}-f''(x)\right)dx>0$$ This comes from ...
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50 views

Finding probability assuming null hypothesis is true

Candidates 1,2 and 3 are running for a position in a company. Candidate 1 claims 38% favourability among all the voters. Assuming this is true, what is the probability that in a random sample of 500 ...
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Is there a specific name for this heavily skewed distribution?

I have a column chart that looks like this: The chart is not well labeled because of data privacy and security issues. However, I can give you some information about the data behind this chart. Let'...
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1answer
19 views

Given a value, and a dataset with two classes, what is the probability that it belongs to each class?

I have a dataset of continuous values from 0.0-1.0 with two possible class labels (say 30% are 'red' and 70% are 'blue'). Given a random value between 0.0-1.0, I want to give the probability that it ...
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Probability distribution of accessing server with uniformly shared, non-uniformly accessed files

Assume I have a large number of files, and I know that the probability of accessing each one of them follows a Zipf distribution. Then I uniformly share the files in a number of servers, so that I ...
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20 views

weighted stdev or quantiles to show variation

I have data in the "dat" vector and I am looking to report the weighted mean and also some information on the variation of that mean. As a toy example you can see the data in the "value" vector and ...
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2answers
74 views

What distribution could simulate “realistic” human survival times?

I want to simulate more or less realistic survival times for humans. I want to use a basic distribution$^*$ to do so. What distribution and what parameters would, to some extent, resemble the survival ...
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Aggregate distribution of claims

I'm working on claims data, and I have to estimate the distribution of the aggregate claim distribution. I founded the severity distribution and the frequency, now i have to combine them to find the ...
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Fitting GLMM (lme4 in r) to uneven data and excluding strong effect

I'm stucked with my analysis and kindly ask for hints. I have to say that i'm not really a "mathematical mind" and new in mixed models. I'm dealing with strongly unevenly distributed data along the ...
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27 views

How to calculate probability of winning best of 7 series

A) many sports use a best of 7 series to decide championships( i.e first team to win 4 games , e.g world series, nba finals, stanl cup finals. If a team has a probability p of winning any one game, ...