# 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 $1$. \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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### 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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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 $f(\vec{... 0answers 38 views ### Is possible to compare two density distributions 'trends'? I have responses from two groups (A and B) on a confidence rating about a distance judgment task. The participants saw pairs of stimuli and after they were asked to rate their confidence about the ... 3answers 309 views ### Why are confidence intervals of hazard ratios not symmetric? My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean ... 3answers 81 views ### How to combine state-level COVID-19 vaccination rates with national demographic data at the individual level? I’m investigating possible correlations between the COVID-19 vaccination rate in the United States and the results of a long-running survey of scientific personality traits like "Agreeableness&... 0answers 29 views ### Probability density function scalar-valued non-linear function of continuous random variables Is it possible to numerically calculate the probability density function for a scalar-valued function where each variable is independent and has a known distribution? For example in the simple case of ... 0answers 21 views ### How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want? Let there be 500 units of stock$s$of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood$m$of 5% that it is precisely the item that the customer ... 3answers 505 views ### Are discrete random variables, with same domain and uniform probability, always independent? If$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)$and ... 1answer 45 views ### Distance between two categorical distributions I want to test whether two (empirical) categorical distributions taking on$K$possible values (e.g. 5, with no innate underlying ordering) with associated (empirical) probabilities$p_k$are the same.... 1answer 22 views ### Correct way to sample I have two independent random variables with known distributions. I want to sample a point from the space formed by these two. Example, x1~N(0,1) and x2~N(0,1). This will create a space with circular ... 1answer 43 views ### Marginal distribution from joint distribution Let X be a random variable$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 ... 0answers 23 views ### 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 ... 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 ... 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://... 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 ... 0answers 20 views ### 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 ... 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 ... 0answers 59 views ### 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 ... 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 ... 2answers 56 views ### 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 ... 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 ... 1answer 93 views ### 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 ... 0answers 28 views ### 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 ... 0answers 20 views ### 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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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 ...