Questions tagged [distributions]
A distribution is a mathematical description of probabilities or frequencies.
8,418
questions
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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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1answer
33 views
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 $1$.
\begin{equation}
\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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1answer
56 views
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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12 views
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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0answers
5 views
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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1answer
31 views
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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Is sampling from a transformed pdf the same as transforming samples in the same way from the original pdf?
Suppose I have a pdf $f(\vec{v})$ over $\vec{v}$ and define $\vec{u}=T(\vec{v})$, i.e. a transformation of $\vec{v}$. Would sampling $f(\vec{u})$ be the same as taking samples $\vec{v}_i$ from $f(\vec{...
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38 views
Is possible to compare two density distributions 'trends'?
I have responses from two groups (A and B) on a confidence rating about a distance judgment task. The participants saw pairs of stimuli and after they were asked to rate their confidence about the ...
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3answers
309 views
Why are confidence intervals of hazard ratios not symmetric?
My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean ...
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3answers
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How to combine state-level COVID-19 vaccination rates with national demographic data at the individual level?
I’m investigating possible correlations between the COVID-19 vaccination rate in the United States and the results of a long-running survey of scientific personality traits like "Agreeableness&...
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Probability density function scalar-valued non-linear function of continuous random variables
Is it possible to numerically calculate the probability density function for a scalar-valued function where each variable is independent and has a known distribution? For example in the simple case of ...
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0answers
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How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want?
Let there be 500 units of stock $s$ of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood $m$ of 5% that it is precisely the item that the customer ...
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3answers
505 views
Are discrete random variables, with same domain and uniform probability, always independent?
If $X$ and $Y$ are discrete random variables, both with domain $\{-1,0,1\}$, with uniform probability, does this imply they are independent? What would be the expected value $\mathbb{E}(XY)$ and ...
1
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1answer
45 views
Distance between two categorical distributions
I want to test whether two (empirical) categorical distributions taking on $K$ possible values (e.g. 5, with no innate underlying ordering) with associated (empirical) probabilities $p_k$ are the same....
0
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1answer
22 views
Correct way to sample
I have two independent random variables with known distributions. I want to sample a point from the space formed by these two. Example, x1~N(0,1) and x2~N(0,1). This will create a space with circular ...
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1answer
43 views
Marginal distribution from joint distribution
Let X be a random variable $X$ with distribution
$$f_X(x) = \begin{cases} 2x & x \in [0, 1] \\ 0 & \text{else} \end{cases}$$. Given $X = x$, suppose the conditional distribution of $Y$ is ...
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Function in `R` for inferring if two distributions are similar / not dissimilar?
Background
According to this site by Laerd Statistics one can use a Wilcoxon Rank-Sum / Mann-Whitney U test for determining if there is a statistically significant difference between the mean ranks of ...
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1answer
37 views
How to tune `wilcox.test` in `R` to compare means instead of medians
My question is: how does one tune wilcox.test in R to compare means instead of medians?
Background
According to this site by ...
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1answer
71 views
Distributions fitting, a comparison
I tried to make a comparison among various candidate distributions fitting for my data. These data are daily returns of S&P500 US equity Index. Among others I tried with t-location-scale (https://...
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1answer
48 views
Determine what range represents 95% of a skewed data set
I have a set of reference wetlands and experimentally manipulated wetlands and I am comparing many water quality variables between them. My thought was to first identify which of the manipulated ...
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How to test stock price predicted probability distribution?
I made an algorithm that calculates the probability distribution for the stock price. How can I measure how good it is?
I have stock price for Microsoft for last 20 years. And for every day ...
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1answer
200 views
Is it possible for a distribution to have infinite variance but finite covariance or vice versa?
Is it possible to have distributions s.t. one/both have infinite variance, but finite covariance? What about finite variance but infinite covariance?
If so, what are example distributions/what is the ...
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0answers
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What can we infer from the sample size and mean?
I came across this interesting question today and haven't been able to understand how the statistician was able to arrive at the estimate:
A sample of 300 customers were asked to participate in a ...
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1answer
43 views
Computing probability distributions over bootstrap samples for two statistics
I have a data set $x= c(0.9575,0.4950,0.1080,0.9359,0.6326)$ and I'm trying to compute the probability distributions for the statistics $\bar X^* - \bar X$ and $\sqrt n(\bar X^* - \bar X)/s^*$, over ...
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2answers
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Why I get high observation when I generate data from t-distribution in R
I want to generate 200 samples from t-distribution with the degree of freedom=1 and sample size is 10 and in R
I use this code
...
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1answer
80 views
What type of variable is file size?
Variables can be discrete or continuous. Discrete variables are variables obtained by counting. Continuous variables are generated by measuring something.
My variable is "file size" and I ...
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1answer
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Prove that a distribution is continuous at a point if and only if it has zero probability at that point
Let $X$ be a random variable with distribution function $F$.
Prove that $F$ is continuous at $x = a$ if and only if $\mathbb{P}(X = a) = 0$.
Could anyone give some hints? I am wondering where I ...
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fitting GAM to longitudinal heavy-tailed count data
I am trying to fit a generalized additive model to the sum of events occurring over a fixed interval (count data >= 1). I would like to model these data as a function of day-of-year and include ...
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0answers
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Maximum entropy distribution of a positive continuous variable with known mean and vanishing probability at 0
I am working on a problem where I know that the variable of concern $x$ is positive, and has no upper bound on its value and whose probability would vanish as we approach 0, $\lim_{x \rightarrow 0^+} ...
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87 views
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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0answers
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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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1answer
40 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 ...
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1answer
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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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1answer
31 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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42 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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1answer
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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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1answer
48 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 ...
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1answer
68 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 ...
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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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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 ...
