# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Probability fruit basket problem [closed]

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 ...
24 views

### 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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### Find two dimensional sufficient statistics? [closed]

Suppose that x is equal to X1,... Xn is an I.i.d sample with density Find two-dimensional sufficient statistics for theta and phi Hence or otherwise show that the sufficient statistics in part (a) is ...
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### Select the best random variable [closed]

Let's assume I am offered to keep one of three slot machines, each with unknown and unique reward distributions. Each machine can output a -1, 0 or a 1 after each try. Given the following collected ...
39 views

### 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 changes (diffs). The diffs 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 ...
25 views

### mixture of exponential and gamma distribution

I'm not particularly good at statistics and whatever elementary statistics I have had exposure to are now rusty. However, I am working on a problem that I am hoping to gain some insights into: My goal ...
34 views

### classical m balls and n bins problem but more tricky

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 ...
30 views

### How to compare 2 ordinal distributions?

A sample answered a dichotomous question and were rated twice on an ordinal scale (high, medium, low), using 2 different rating methods (the question did not influence the ratings). The results can be ...
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### Will MSE-based estimator generate symmetric residuals if the error has got symmetric support (not distribution)?

This question is more specific than :my old question Take follow regression model: $y=f(x)+e$ Where $e\sim D$ with a such symmetric support $A=(-a,a)$, not symmetric distribution. Now given a data set ...
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### Will quadratic-based estimation (not necessarily MSE) always generate a symmetric residuals after training it?

These are error's empirical distribution for XGB, RF and kNN, the last one have taken on another dataset. Neither of them is normally distribuited but they all are symmetric. None of used algorithms ...
64 views

### What distribution has the following likelihood function?

I'm working with a model that uses the Beta-Binomial natural conjugate family. In other words, the prior over the variable of interest $\theta \sim Beta(\alpha_0,\beta_0)$ distribution over $[0,1]$ ...
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### is this a safe assumption of normality and linearity? Anova/Linear Model (with code and example)

I fitted a linear model (estimated using OLS) to predict T1_var with two factors : Phenotype (Control and PD), Condition (Treated, Not treated) ...
102 views

### Mean finger volume: Is a GLM with log link function appropriate?

I have a model where the volume ($V$) of a finger is normally distributed, with mean $\mu = \beta_0 L^{\beta_1}D^{\beta_2}$ (where $L=$ length, $D=$ diameter and $\beta_i \in \Bbb R$ for $i=0,1,2$) ...
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### What statistics describe a distribution uniquely and completely? [closed]

I have a very weird and possibly amateurish question. I have a situation where I need to keep track of some activity until some event occurs. I want to store that activity (say, a series of 0s and 1s),...
Suppose, I'm performing a certain experiment with many outcomes corresponding to $4$ events: $A,B,C,D$. We have been given the following data: $$p(A)>p(B),p(C),p(D)$$ $$p(A)<p(A^c)$$ This means, ...