Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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What is the shape of the Benini distribution?

The Benini distribution is a continuous univariate distribution that is used in actuarial applications. For all $x \geqslant \sigma$ it has density function: $$\text{Benini}(x| \alpha, \beta, \sigma)...
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What is the values of sample size when saying small or large sample?

A basic question in statistics. When it is said that: Fisher's exact test is employed when sample sizes are small. The normal distribution can be used as an approximation to the binomial ...
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How to compare two different coin flip distributions together?

There are two coins. With each of them we do the following steps: Flip the coins for n consecutive times Assign the number of all observed heads to H variable Replicate the experiment over t trails ...
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How to change (expand) the distribution of my data?

I have to train a regression model that can approximate the function used to map the inputs (3) onto a single output (1). The data is made of rows of the input-output pair ((X,Y,Z), SUM) where X,Y ...
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Central Tendency Examples?

Can someone give me separate cases of empirical distributions where: mean does not accurately describe the central tendency. median does not accurately describe the central tendency. mode does not ...
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Probability of not drawing a set of numbers from distribution

I'm running a simulation where random variates are drawn from a negative binomial distribution, with size s and mean mu. I need ...
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Seasonality affects samples on a heterogeneous system?

In a time window of a year, suppose that a social networks has a bimodal normal distribution that peaks at April and October approximately. Being a heterogenous social network, it has different types ...
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Permutation Tests: How to Interpret a Non-zero-centered Null Distribution

In a "textbook" experiment (e.g., a single treatment is randomly given to a subset of independent units, the SUTVA holds, etc.), my understanding is that a permutation test of the experiment should ...
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How to fit CDF on LogLog plot?

I build CDF of differences for Gold Pice. As series of day-diff multipliers. For both increase as green (>1) and decrease as red (<1) diffs. ...
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1answer
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+50

Probability distribution function expressed in terms of a divergent series

I'm interested in finding the CDF and PDF of $U_i$ defined as follows, $$U_i=\frac g{d^{\alpha}}$$ where $g$ is a gamma distributed random variable with shape $k$ and scale $\theta$, and $d$ is a ...
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21 views

How to best display the distribution of a large dataset with many outliers? [duplicate]

I have a very large data set (~300'000 data points) and a subset of it (6000 data points), which shows the difference of travel time [in seconds] of agents before and after a road closure. I want to ...
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9 views

What is the pdf of Bivariate Rayleigh and Rice Distribution? [closed]

I am looking for the PDF equation of bivariate Rayleigh and Rice distribution. I am also looking for a source where I can find the derivation of this bivariate distribution from the uni variate ...
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Probabililty of being first failure among different exponential distributions [closed]

Consider $n$ failure rates $\lambda_1,\lambda_2, \dots, \lambda_n >0$. If we assume that lifetime $X_i$ is exponentially distributed with failure rate $\lambda_i$, $X_i \sim \mathcal{E}(\lambda_i)...
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1answer
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Compute mean and variance of mixture of Gaussians given mean/variance of component gaussians [duplicate]

Given $N$ means and variances $\{\mu_1,\mu_2,....\mu_N\}$ , $\{\sigma_1^2,\sigma_2^2,....\sigma_N^2 \}$ ,and the fact that combined they make a gaussian mixture, how do I compute for that mixture $M$, ...
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1answer
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How to vectorize Multivariate Gaussian distribution?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows: $p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/...
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1answer
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Gaussian distribution in logistic regression

Suppose, we are doing logistic regression for datasets (X,y) and if we assume that x has gaussian distribution. What we try while finding y, is we try to maximize the log likelihood right? When we ...
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Expected frequency differences when sampling from a uniform?

Imagine I put people into different groups based on a uniformly distributed random variable $y = f(x)$ (e.g. microseconds of their arrival to a website). After a while, I observe how many people are ...
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2answers
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Moments of truncated Student's $t$-distribution

I performed random sampling on a Student's $t$-distribution. I used SciPy to calibrate my parameters and then truncated my allowable values to the maximum and minimum observation in the data for ...
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27 views

Determine modes in a histogram [closed]

If there are multiple distributions in a histogram(multimodal distribution), how can I find number of modes and cluster those modes? Current Approach Currently I'm using mean shift to find number of ...
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find the distribution of random variable (Wiener process)

$X_t=(t+3)W_{t+2}-2W_t$, $t>0$, $W_t$- Wiener process. I have to find the distribution of a random variable $X_t$ and answer the question whether it is a Wiener process. How to determine this ...
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Choosing between two normal distributions

I have two normal distributions with different means and variances: N(u1, s1) N(u2, s2) And I have some data points (X) that were sampled from each of them. For each data point, I want to calculate ...
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Likelihood of a single sample being in one of two populations

Consider the following analogy: I observe a man who is 175 cm tall. Independent of height, there is an equal chance that he could be from either Country A, or Country B. The height of men in Country ...
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Central Limit Theorem & Sample Mean

This is a question which was given to me in an exam, and I'm confused about the approach taken in the Answer Key. The question is summarised as follows: A bank has 500 customers The total annual loan ...
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Boolean negation of a continuous probability distribution

I'm trying to work out a small problem in the Bayesian framework. Imagine I have a prior knowledge that "A is of any color but not red". If the color space is discrete then this prior is easily ...
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different data distribution to limit over-fitting

I was wondering if, to limit over-fitting, it is useful to compute the accuracy of a model (for example, a classification one) on a test set with a completely different data distribution from the ...
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1answer
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How to choose and perform a goodness-of-fit test?

I notice there are a lot of questions on the topic (most are along the lines of: how to do a Chi-squared goodness-of-fit test), but mine is perhaps more general. Using an example I recently ...
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1answer
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How do I convert a standard normal RV to a generalised error RV?

The generalised error distribution (sometimes called the generalised normal distribution) is a generalisation of the normal distribution allowing variation of the kurtosis away from mesokurtosis. ...
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2answers
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Distribution Fitting: does every continuous distribution have a discrete distribution equivalent? [closed]

Sometimes you find a good fit in a continuous distribution function, but the data is discrete. Normal and Binomial are automatic pairs. Both symmetrical, non-skewed. Does this exist for others?
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Is square-normal distribution another name for Chi-squared distribution?

This wiki page mentions square-normal distribution: https://en.wikipedia.org/wiki/Probability_distribution_fitting I google "square-normal distribution", it gives me Chi Square Distribution, but I ...
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Computation of out-of-sample error

I have a question on how one would theoretically compute the out of sample error of a given hypothesis in a data learning problem. I've been working through Learning From Data: A Short Course (http://...
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1answer
54 views

Notation and meaning of a general probability distribution

I had two questions regarding the meaning and notation of a probability distribution when it is not specifically specified. For example, some papers jump right into their approach with notation like (...
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1answer
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Do I need to standardize my data?

I have the results of mass spectrometry, there are 2500 peaks and in each peak there is the recorded intensity for the samples. My data looks like this: ...
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1answer
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Transformation of Uniform(0,1) random variable [closed]

Let $X \sim U[0,1]$. Find the pdf of $Y=4\sqrt{X}(1-\sqrt{X})$. I have been studying transformation of random variables and came across this exercise. Can anyone provide me a hint on how to ...
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Confused with the concept with random variable in a sequence of coin tosses

While I am studying probability and random variable, I am kind of mixed up with the following questions in my mind, so I am struggling with getting clear understands about those two questions below: ...
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Are all rate parameter the same? [closed]

Is the following definition correct? $\lambda = $ rate parameter $=$ average amount of y-value per x-axis unit. $Poisson(\lambda), Gamma(\alpha, \lambda), Exponential(\lambda)$ have the same ...
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1answer
27 views

elementary statistics: compare binomial to normal distributions

Thank you for your help. I want to compare binomial and normal distributions to prove to myself (numerically) how binomial distributions approach normal distributions as n increases. I know books say ...
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Detecting the dependency of a probability distribution

I have this joint probability distribution between the two binary values $A$ and $B$ $$ \begin{array}{|c|c|c|c|} \hline A& B& P(A,B)\\ \hline 0& 0 &.40\\ 0& 1 &.30\\ 1&...
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Average/Aggregation of 10 Discrete Probabilty Distributions

I have 2 experiments, where I have repeated each 10 times (20 experiments in total). I want to compare experiment A with experiment B. I create a probability distribution from each exp (20 prob ...
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explanation of Hidden markov model and its values

So i'm trying to learn about the Hidden Markov Model (HMM) and are solving some problems. Im run into a question that I dont quite understand and are hopeing that someone on here can help me ...
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Degree of freedom of different distributions: Chi-Square Goodness of Fit Test

I try to understand why the number of constraints differ for the distributions in the table below, for the Chi-square goodness of fit test. I found the content in the following link. https://www....
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A question about hypothesis testing on non normal distributions

I have a set of 20 distributions (4 sets of 5) none of them are normally distributed but all are qualitatively similar and all have ~700k data points. The images below are a typical example. First ...
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1answer
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log sampling distribution?

I am using a python parameter optimization library https://keras-team.github.io/keras-tuner/documentation/hyperparameters/ And here were have the option to define a sampling distribution for various ...
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What distribution has exactly three parameters for mean, variance, and skewness?

Common distributions usually fix their skewness. Beta distribution has two parameters to determine all of the mean, variance, and skewness. Student-T's skewness can change by some definitions but it ...
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Can I assume data points follow Logistic Distribution with distances from the decision boundary in Logistic Regression?

While I was doing some researches on Logistic Regression, I read a post saying that distances from the decision boundary in Logistic Regression follow Logistic Distribution. I am not sure if the ...
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Non-stochastic vs Stochastic regressors and sampling distributions and causation?

I was wondering if I understand these correctly. Would an example of a stochastic regressor be weather? so when thinking about the sampling distribtuion and causality, I would think of repeated ...
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Proper metric for the distance between two Wishart distributions

Let $A$ and $B$ be samples acquired from two distinct Wishart distributions $X$ and $Y$, respectively. The sampling units in $A$ and $B$ are two distinct sets of $p \times p$ random matrices. I want ...
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Does Entropy values enough creterion to determine the nature of any probability distribution?

Entropy is the measure of randomness of a process or variable and it can be defined as follows. for a random variable $X \in$ set $A$ :- $H(X)= \sum_{x_i \in A} -p(x_i) \log (p(x_i)) $, Now there are ...
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2answers
81 views

Distribution of $\hat{y}=Hy$

I wish to find the distribution of $\hat{y}=Hy$ where $H$ is the hat matrix $X(X'X)^{-1}X'$ in which a dash represents the transpose. Also, $\epsilon$ is $N(0, \sigma^2)$ distributed. Thanks
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1answer
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Distribution of gradients across dimensions for neural networks

Does the distribution of gradients for neural networks known to follow a particular distribution? That is, suppose I've a model with $N$ parameters. Then, the (stochastic) gradient at some point is a ...
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6answers
3k views

How to generate random integers between 1 and 4 that have a specific mean?

I need to generate 100 random integers in R, where each integer is between 1 and 4 (hence 1,2,3,4) and the mean is equal to a specific value. If I draw random ...