Questions tagged [distributions]
A distribution is a mathematical description of probabilities or frequencies.
8,239
questions
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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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0answers
14 views
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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0answers
13 views
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 ...
0
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0answers
12 views
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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11 views
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 ...
0
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1answer
33 views
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 ...
1
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1answer
18 views
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 ...
1
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1answer
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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0answers
23 views
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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0answers
18 views
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 ...
-1
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0answers
36 views
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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0answers
48 views
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 ...
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0answers
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 ...
0
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1answer
38 views
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 ...
0
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0answers
11 views
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 ...
0
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1answer
47 views
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 ...
1
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1answer
56 views
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 ...
0
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0answers
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 ...
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0answers
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 ...
0
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1answer
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 ...
0
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0answers
28 views
Is there a PDF for a linear combination of Levy alpha-stable and normal distributions?
For independent random variables $X\sim\mathcal{S}(\alpha,0,1,0)$ and $Y\sim\mathcal{N}(0,1)$, what is the distribution of $Y\sigma_Y-X\sigma_X$ where $\sigma_X,\sigma_Y\in\mathbb{R}^+$ (such that $\...
0
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1answer
20 views
Sufficient Statistic for Absolutely Continuous Distribution [duplicate]
The following is a homework problem. Please tell me if my solution is correct and if not please point out my mistakes.
Let $x_{1}, x_{2},...,x_{M}$ be i.i.d. samples from the absolute continuous ...
2
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1answer
36 views
The Shape of Probability Distribution Functions [closed]
https://youtu.be/v-j0UmWf3Us
@37:48
Here, the presenter indicates that that the "negative log" of a single dimensional Gaussian distribution makes a "parabola bowl shape". This &...
3
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2answers
125 views
Can probability distributions be used as an alternative for regression models?
Suppose you have 3 variables: height, weight and salary. Can you first attempt to fit a 3 dimensional probability distribution to this data - then, if someone gives you a height and weight measurement,...
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0answers
15 views
Can stochastic gradient descent for Bayesian Inference? [duplicate]
I was looking at the Bayesian MAP estimate formula which is the "argmax(likelihood * prior)".
Can this be calculated using stochastic gradient descent? Gradient descent requires knowing the ...
1
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1answer
49 views
Understanding how to find the $1$ in $100$ chance on the $t$-table
Background
In my university class, we've been discussing the following experiment:
Consider an experiment on artificially raised salmon, with two treat-ments (one a control) and $20$ fish per ...
0
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1answer
44 views
Conjugate Prior for Alpha Power Inverse Weibull Distribution
Let $X$ has Alpha Power Inverse Weibull (APIW) distribution with pdf
$f(x) = \frac{\log \alpha}{\alpha - 1} \lambda \beta x^{-(\beta+1)} e^{-\lambda x^{-\beta}} \alpha^{e^{-\lambda x^{-\beta}}}, \; x&...
1
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1answer
35 views
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 ...
1
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1answer
36 views
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 ...
0
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0answers
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 $[0,1]$ ...
0
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0answers
38 views
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)
...
4
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1answer
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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0answers
20 views
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),...
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0answers
41 views
Meaning of more likely or less likely in probability [duplicate]
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, ...
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0answers
55 views
+50
Show that the support restriction is not a binding constraint for the existence of a distribution
Let $\mathcal{P}$ be the family of continuous distribution functions in $\mathbb{R}^3$ whose marginals are symmetric around zero and identical.
Fix a vector of reals $\theta\equiv (\theta_1, \theta_2)\...
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0answers
25 views
How can I solve this probelm? [closed]
A king gives a convict a second chance to escape his prosecution with a gamble. He
prepares two identical boxes and 10 white and 10 black marbles. The convict is allowed to
distribute the 20 marbles ...
1
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1answer
34 views
Is there any way or function in R to find the derivatives of incomplete gamma function or is it possible to obtain its derivative manually?
I am working with a probability distribution and I have to find the derivative of incomplete gamma function as
\begin{equation*}
\Gamma(\frac{\theta}{\beta}x^{2},\theta) = \int_{0}^{\frac{\theta}{\...
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0answers
10 views
Compare two sets of data that are time series
I have two treatments, $A$ and $B$, and I'd like compare their results to simply see if they are significantly different. I have a limited statistical tool set and might naively use a t-test for this.
...
1
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1answer
34 views
probability density function of forecast's percent error
Imagine that I am trying to estimate the "number of sales (dollars)" that a client will have when they host a booth at a music festival. The "low forecast" and "high forecast&...
1
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0answers
30 views
Comparing 2 sample means
I'm trying to quantify the difference between two sample means. I'm not sure if I can use the standard two sample t-test.
The first sample comes from the difference of two time series (inflation rate ...
0
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0answers
59 views
Confusion with different interpretations of lognormal distribution questions
My textbook is making me a bit confused on what method to use when solving lognormal distribution questions.
The first question says, "Calculate P(7.5<X<12.5) if X is a random variable that ...
1
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1answer
61 views
Why person-years follow a Poisson ditribution?
While studing poisson distributions, this simple question came to my mind:
Poisson distribution are made of variables which only have integer numbers and are always >0 (as an example: number of ...
6
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3answers
839 views
Flipping Coins : Probability of Sequences vs Probability of Individuals
Here is a problem I thought of:
Suppose I am watching someone flip a fair coin. Each flip is
completely independent from the previous flip.
I watch this person flip 3 consecutive heads.
I interrupt ...
0
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0answers
22 views
Analysis of intermittent time series/demand patterns (spare parts)
I am currently familiarizing myself with the world of demand forecasting. More specifically, I'm looking at spare parts forecasting, which means intermittent time series and demand patterns are ...
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0answers
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Can a time dependent lagged function be used as a rate parameter?
Question: Can the rate parameter in a mm1 queue or a poisson process be a lagged function of itself?
https://en.m.wikipedia.org/wiki/Poisson_point_process
https://en.m.wikipedia.org/wiki/M/M/1_queue
...
3
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0answers
111 views
When will $\mathbb{E}[g(S_n/n)]$ exist given $\mathbb{E}[g(X_1)]$ exists?
Suppose $X_1, X_2,..., X_n$ are i.i.d. random variables with distribution $\pi$ on some probability space. Let $g$ be a measurable function such that $\mathbb E_\pi[g(X_1)]<\infty$. I am curious ...
0
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0answers
18 views
How to calculate Lévy random number
The calculation process of the Lévy distribution is:
Among them, l is a Lévy random number, which obeys Lévy distribution; u, v obey the standard normal distribution; β is a constant, the value is 0&...
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0answers
23 views
Statistical differences between proportion percentages of multiple groups
I have data about 3 categories of people and the frequency distribution percentages of how many times some people belonging to these categories have visited one of three restaurants over a certain ...
2
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2answers
39 views
Distribute a fixed number of events to the days of a year following a specific distribution
I am trying to distribute a given (fixed) number of events of a year over the respective year. The empirical distribution can be modelled with a Poisson distribution because there are usually only ...
2
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0answers
29 views
On average what is the norm of a sample from a multivariate normal distribution? [duplicate]
Problem
Suppose I sample a multivariate standard normal sample $x \sim N(0, I_d)$ where $d \geq 1$ is the dimension. What is the expected value of the norm of $x$
$$
\mathbb{E}[\|x\|] = ?
$$
Using ...
