# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Memoryless Property of the Exponential Distribution

I was reading about the Memoryless Property of the Exponential Distribution: In simple terms, this means that : The probability of waiting more than "t + s" minutes given that you have ...
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### Why use KL divergence if the true distribution is never known?

The KL divergence for Bayesian is information gain or loss when you sample from some distribution rather than another, where one of them is the true distribution. The problem is you never know the ...
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### How to get the support of the inverse BoxCox's distribution?

I will take only the BoxCox's transformation for $\lambda \neq 0$ so it's: $Y_i=\displaystyle\frac{(X_i^{\lambda}-1)}{\lambda}$ and its inverse: $X_i=e^{ \displaystyle ln(Y_i \lambda+1)/\lambda}$ ...
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### Calculating total variation distance between multiple copies of the uniform distribution and a distribution slightly biased from uniform

Consider a distribution $D_1$ over two bits --- $0$ and $1$. \underset{X \in {D}_1}{\text{Pr}}[X = 1] = \frac{1}{2}, ~~~~~\underset{X \in {D}_1}{\text{Pr}}[X = 0] = \frac{1}{2}. \end{...
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### How to find plim of a variable?

Let $X_1,\ldots,X_n$ be a random sample of a population with uniform distribution in $(0, 1)$; and denote $Y_n = (X_1.X_2...X_n)^{1/n}$. How can I find $\operatorname{plim}$ of $Y_n$? The definition ...
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### Distribution of the product of a Gaussian random variable and a sum of constants [duplicate]

I want to get the distribution of the following quantity: $\sum_{i=1}^{N} M_i \cdot \overline e$ where: $M_i$ with $i=1,...,N$ are constant values $\overline e$ is a normally distributed random ...
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### Dunn tests across 2 different categories

I determined the medians of a biomarker across 2 categories: I.e based on 4 study groups (ie. non-pregnant, pregnant, PE1, PE2 and ranked as 0, 1, 2, 3), and also by categorising BMI (eg: normal, ...
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### Decide whether a discrete random variable is usual or unusual using Probability distribution?

We know that in frequency distribution we decide whether a value is usual or unusual depending on how many standard deviations it's away from mean. Moving forward to Probability distribution my ...
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### A problem in the derivation of distributed multiple model filtering

I have some problems with the derivation of multi-model filtering in a paper. The involved statements in this paper are as follows. My question is how did the above formula get from left to right? ...
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### How do you find the p-value for a uniform distribution?

If I am given a uniform distribution U ~ Uniform[-3, 2], how do I find P(2X+6>4)? I'm not sure where to begin other than noting that -3 is the mean and 2 is the variance.
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### Probability fruit basket problem

Suppose we have two healthy but curiously mixed boxes of fruit, with one box containing 8 apples and 4 grapefruit and the other containing 15 apples and 3 grapefruit. One of the boxes is selected at ...
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### Two equivalent ways of sampling with replacement

The original context of this problem is for a derivation of the lookdown model https://projecteuclid.org/journals/annals-of-probability/volume-24/issue-2/A-countable-representation-of-the-Fleming-Viot-...
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### Forecasting a skewed series

I am trying to forecast the following series. The grey line is the forecast and the black line is the actual. I want a similar pattern in the forecast as we se ein the actuals .. for this particular ...
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### What uncertainties to use when fitting a distribution model to binned sample data?

A common task is to fit to a sample of $N$ data $x_i$ (assumed 1D for the sake of argument) a model $p(x|a)$ (normalized to unit integral) for their distribution with some parameters $a$. One way is ...
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### Single-value alpha parameter for Dirichlet distribution

I'm trying to implement an event schema induction method from a paper from 2015. The authors use a generative approach to learn a language model. For this, they use a lot of probability distributions ...
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### Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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### How does the Bhattacharyya distance doesn't satisfy triangle inequality?

Googling doesn't seem to show many informative results. I don't know if the concept is too trivial that I should know immediately or it's an old topic. It's either article / blogs repeating the wiki ...
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### Multi-variate two-sample ANDERSON-DARLING TEST

Suppose we receive a reading of samples taken from a sensor system with multiple variables, which may be assumed as continuous real values. After few days, we receive another reading of samples from ...
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### Using the methods of moments in R for the dirichlet distribution

I'm trying to build a distribution of transition probabilities to randomly sample from in a Markov model where individuals can transition from one health state to another (assume that in the image ...
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### Joint distribution of data sampled iid from a bernoulli process, and the absence of binomial coefficient

Let's assume I have 4 observations with each observation is modelled as a bernoulli trial with probability $p$. Sucesses are labelled as 1, failure is 0. My observations $(x_1, x_2, x_3, x_4)$ are as ...
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### Interpretation of Chi square distribution with 1/2 degrees of freedom

How do I interpret the Chi square ditsribution with 1/2 degrees of freedom? I know that with for instance n degrees of freedom the interpretation is that this is the number of squared standard normal ...
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### Do stock price changes follow Pareto Distribution? [closed]

I calculated the distribution of the stock price daily ratios. The ratios are multiplicative, $d_t=p_{t} / p_{t-1}$. As far as I know the distribution should look like Power law distribution (Pareto ...
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### KL diveregence of subsequences

Let us have a random sequence $(X_1, Y_1,\ldots,X_n,Y_n)$, where $X_t$ takes value in some set $\mathcal{X}$ and $Y_i$ are scalars. The sequence is generated by the following process: $X_i$ is chosen ...
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### Right statistical test for frequency distribution

Say that after getting data from 5 different years on causes of teenage pregnancy you want to confirm that sexual assault is a common factor contributing to teenage pregnancy. Dividing the data into ...
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### Probability Distributions : "Mode" vs. "Expectation"

I have often heard the argument that in higher dimensions: the "mode" (most common value) of a probability distribution function does not correspond to the "expectation" (mean) of ...
This is a problem related with the classical $n$ bins and $m$ balls problem but has some modifications that makes it more tricky to solve: In this case, the probabilities of the bin´s system are not ...