Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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42 views

Find distribution of the transformation $Y'(I-P_1)Y$ given distribution of $𝑌_{nx1}$ ~ 𝑁$(𝜇1, 𝜎^2𝐼)$

I am currently self learning econometrics from A Course in Econometrics of Goldberger and I'm attempting a problem sheet from the course given by my uni. The problem is the following: Let $𝑌_{nx1}$ ~�...
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1answer
19 views

Which probability result is greater? Using hypergeometric distribution or binomial distribution?

Suppose I have $N$ samples, and 1/4 of them are bad. I draw $n$ samples $(n<N)$, and I want to know what's the probability that less than 1/3 are bad. I know it should use hypergeometric ...
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1answer
19 views

Fitting a sample streamflow data to log-normal distribution

So I'm a beginner at python and I have a streamflow data for 132 months and I need to fit every months streamflow data to lognormal distribution and finally plot the original data and fitted data on ...
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52 views

The question about the exponential distribution?

It is very naive question, but I really get confused. As I saw in some plots the maximum of the exponential distribution function the maximum is at a non zero parameter, as in the formula we have the $...
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How to explain the difference between confidence and credible interval?

The key difference between Bayesian statistical inference and frequentist statistical methods concerns the nature of the unknown parameters that you are trying to estimate. In the frequentist ...
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1answer
34 views

Ancillary function of a random vector, which is independent of change of origin and scale

Let $(X_1,\ldots,X_n)$ be a random vector, whose distribution involves unknown: location parameter $\mu$ and a scale parameter $\sigma>0$. It follows, that any measurable function $f(X_1,\ldots,X_n)...
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3answers
149 views

How to do a statistical test for numeric data that is discretised and broken down by groups

Background I have a situation where I have data on bank balances available with various respondents, and a flag for whether they completed a desired action (i.e., whether they purchased a loan or not)....
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1answer
29 views

In which scenarios is the exponential power distribution better than the t-student distibution?

I know there are some differences between these two distributions (exponential power distribution does have a cusp at the origin and t-student doesn't), but there are also similarities (heavy tails). ...
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Probability density function for possible intersections/conjunctions

Imagine the following scenario: There are n senators voting on two bills to be passed. A fraction of n voted to pass each bill respectively. For simplicity, let's assume n/2 senators voted for bill 1 ...
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Existence of moments of random variables

I need to find an example of two random variables that share equal moments up to say 3 and no other moment exists. How should I go about approaching this problem? I tried to define two polynomial mgfs ...
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24 views

Identify the distribution/family of a variable

I have this distribution for my response variable that I want to use to build a model with a binary matrix as predictor variable. I think to use glm to do this, but I don't know which family to use, ...
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Poisson Distribution vs Poisson Process [duplicate]

I need to understand the relation between both these concepts with an example. I have an good understanding of Poisson distribution and it's applications. But I am having difficulties linking it to ...
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1answer
50 views

What distribution may electric vehicle battery capacity data follow?

I'm trying to find out the shape of the curve that reflects electro vehicles battery degradation data (depending on cumulative travelling distance). The red line on the plot doesn't seem a perfect fit....
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What is the difference between statistical distribution and probabilistic distribution?

What is the difference between statistical distribution and probabilistic distribution? Are these terms used interchangeably? Are they same or different?
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21 views

Confused by the latent variables in normalizing flow theory

I'm looking through the paper on variationl inference in normalizing flow and have difficulties with understanding some ideas. I know there are latent variables $\mathbf{z}_i$ and observed variables $\...
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Classification using Mann Whitney U test

Can the results of a Mann Whitney U test be used to classify future measurements into one of the two populations? If not, is there a better way to convert the measurements of two populations into the ...
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Bias in numerical estimation of Shannon Entropy

I am doing a numerical estimation of $H(X_1,X_2, \ldots, X_n)$, where $X_i$ are some discrete random variables. Using the definition of Shannon Entropy I know that $$ H(X_1,X_2, \ldots, X_n) = -\sum_{...
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How to fit distributions to data in R?

I have 6 sets of Volume(v) & Duration(d) data. I have fitted a quite few distributions to the data such as Weibull, Gamma, Log-Normal, Exponential, GEV, Pareto, Log Logistic, Poisson, and GP. This ...
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Mixed random variables [closed]

Given X ~ N(0,1) , Y ~ Ber(1/4) Z = X if Y = 0 -X if Y = 1 How to approach this question if i want to prove that Z and X are dependent .
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Finding PDF of max of sum of truncated sinusoids

Suppose I am adding N sinusoids. The frequencies, phases, and amplitudes are chosen to be iid in the range f1 to f2, 0 to 2pi, and A1 to A2 respectively. Now, if I am observing the sum from time t1 to ...
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69 views

Probability or likelihood under normal distribution(s)?

I've modeled my data with a mixture model of two gaussians centered at approximately 0.33 and 0.5, respectively. Now I want to "assign" a probability to each data point that it belongs to ...
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2answers
31 views

function for normalized change in probabilities

I need a function that takes in a vector of probabilities, a value and an index. the value is can be negative, 0 or positive, and can be of any absolute value. it then adds the value to the ...
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1answer
22 views

Definition indepedence and identically distributed (iid)

Bruce Hansen's book "Econometrics" defines a random sample as follows: "The observations $(y_i,x_i, z_i)$ are a random sample if they are mutually independent and identically ...
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What is the method to combine multiple distributions?

Let's say that we have one distribution, and sample x data. We have another distribution and sample y data. I want to put these two distributions together and generate a new distribution. So after ...
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23 views

Survival Analysis weibull AFT model and gumbel distribution

I am trying to find the link between the gumbel distribution and the weibull distribution. If I understand this post by pymc3, if I was to model log time instead of time directly with a gumbel ...
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26 views

How to Compare Variances?

I have a dataset which contains height and weight variables. The mean and variance for height are 165 cm and 25 cm. The mean and variance for weight are 70 kg and 16 kg. How to compare variances of ...
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442 views

Central Limit Theorem - Rule of thumb for repeated sampling

My question was inspired by this post which concerns some of the myths and misunderstandings surrounding the Central Limit Theorem. I was asked a question by a colleague once and I couldn't offer an ...
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Test for statistical distribution

I'm new to statistical analysis and I'm trying to identify which distribution fits my BD better. My BD has length of stay (LOS) data in two different hospitals: ...
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Conditional Gaussian from Joint Distribution

I have the random variables $X$ and $Y$ related through the following: \begin{align} X &= N_X \\ Y &= 4X + N_Y \end{align} where $N_X, N_Y \overset{\text{iid}}{\sim} \mathcal N(0,1)$. Is ...
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1answer
39 views

Does $(X,X)'$ follow a bivariate normal distribution?

I'm fairly new to multivariate distributions. I'm trying to figure out if $(X,X)^{'}$ follow a bivariate normal distribution (the prime = transposed). If $X\sim N(\mu, \sigma^{2})$ where $\mu \in \...
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2answers
83 views

Maximum likelihood estimator of $\theta$ for uniform distribution [closed]

For Uniformly Distributed random variables $X_1,X_2,\dots,X_n$ $\in \mathcal{R}$, the p.d.f is given by: $f(x_i) = 1/θ$ ; if $0≤x_i≤θ$ $f(x) = 0$ ; otherwise If the uniformly distributed random ...
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Is it possible to fit Non-Stationary GEV to a series of data in R fixing one of the distribution parameters?

Good morning, I have a series of annual maxima data (say "AMdata") I'd like to model through a non-stationary GEV distribution. In particular, I want the location to vary linearly in time, i....
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1answer
75 views

What is a Dirac distribution on a hyperplane?

I'm trying to understand message passing for compressed sensing. I came acrross this distribution: As the title suggests, how does this distribution look like? I know the first products term in the ...
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1answer
41 views

Integral of distribution followed by Bernoulli

I am new to learning probability theory. Here I got confused but I had a sense of feeling it's correct. This is what I saw from the lecture notes. Let $P\sim Bern(p), Q\sim Bern(q)$. Then is the ...
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23 views

Conditional distribution of Ornstein-Uhlenbeck on two fixed points

The conditional distribution of a Ornstein-Uhlenbeck $X(t)$ conditional on $X(0)$ is given by $$ X(t)|X(0) = X(0)e^{-t} + \mu(1 - e^{-t}) $$ This process is usually only defined for $t>0$ (future ...
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27 views

Distribution of sum of Indicator Variables

Let $X1 $, $X2 $, $X3 $...$Xn $ be n observations with distribution function $F $. Let $F^{*} $ be the empirical distribution of the random sample. $F^{*} = \frac{1}{n} \sum I(X_{i} \le x)$ where I = ...
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Kolmogorov-Smirov two sample test, ties — will adding random noise fix the problem?

There are a lot of questions on this site about warning for "ties" in the Kolmogorov-Smirnov test. Here are a few of those questions. Is there an alternative to the Kolmogorov-Smirnov test ...
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How to estimate parameters and pdf of a random variable transformed from a lognormal random variable?

I have a continuous random variable Y that follows lognormal distribution with known parameters (mu and sigma). Let Y be transformed to X=Y-20000. So it is basically shifted to left. How do I find the ...
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How to fit a Log-Pearson Type 3 distribution in PearsonDS

I am using the pearsonFitML function in the PearsonDS package to do a maximum likelihood estimation of parameters in R. I am specifically interested in fitting a Log Pearson Type 3 distribution to my ...
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100 views

Distribution of X+U when X is a discrete and U is a continous random variable

Suppose $X$ and $U$ are independent random variables. $X$ is a discrete uniform variable and $U$ is a continuous uniform $[0,1]$ variable. What is the value of $\mathbb P(X+U\leq y)$, where $y$ is a ...
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1answer
46 views

Conditional + Marginal Probabilities

If $X \sim Gamma (\alpha, \beta)$ and $Y|X \sim Gamma(c, X)$, how can I derive the marginal probability density function of $Y$ and the conditional probability density function of $X|Y$? I know that ...
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1answer
42 views

What is the chance that the flips of a coin tossed 2n times will be 50/50?

The distribution of heads in coin tosses is 50%, but in reality, what is the chance that 2n tosses (keeping the number of tosses even) will turn up EXACTLY 50% heads and 50% tails? More generally, how ...
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1answer
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3-part question on joint PDFs

a.) Let U, V be uniformly distributed over the set $\{(u,v): $$0<u<v<1$}. Let $X$ = $-$$log(U)$, $Y$ = $-$$log(V)$, $Z$ = $max$($X$,$Y$). a.) Draw the support of the joint distribution ($U$, $...
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1answer
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Question relating to joint PDFs

Here are my questions: Let $X$ ~ Unif$(0, 1)$, and $0<a<b<1$. Also, let \begin{cases} Y = 1 & \text{if $0<X<b$} \\ ...
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What is the distribution of gap lengths in a Poisson process?

In a Poisson process with a finite period (and a known long-term-average event rate), what is the distribution of gap lengths between events? The number of events within a fixed period will be given ...
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Example of random variable with a unique moment sequence but mgf DNE in a neighborhood of 0

Do you have an example of a random variable $X$ with a unique moment sequence but whose mgf does not exist in a neighborhood of 0? In other words, I'm looking for a counterexample to the converse of ...
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Fitting a distribution to my timeseries: two R-packages, two contrary results

typical R-User here, applying a bunch of packages to my data, hoping for a convincing result although I understand only half of what I do at most (and then getting rejected by the reviewers, surprise)....
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2answers
69 views

Expectation of Mixed Random Variable (Contradiction with Manual Solution)

$X \sim \mathcal{N}(1,\text{negligible variance})$ and $Y \sim \mathcal{N}(2,\text{negligible variance})$ \begin{equation*} Z= \begin{cases} X, & \ \text{w/pr}\quad p\\ Y, &...
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104 views

Does this distribution have a name? $p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \right)$

Quick question. Anyone able to attribute the following kernel to a known probability distribution (univariate, continous on the real line)? $$ p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \...
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18 views

How can an algorithm identify variables distribution given a dataset?

Using Python, I would like to write an algorithm that generates correlated variables given a dataset (i.e given the marginal distributions of the variables and the correlation matrix). To do so, I was ...