Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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Joint densities does not exist, compute probability

I am taking a course in probability and in one of the PS I have got the following description: $Y_i ~ exp(\lambda_i)$ for $i=1,...,n+1$. Define $X_i = min(Y_i,Y_{n+1})$. In the first subsection of the ...
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Photo attractiveness rating experiment: significance and effect size

I'm a photographer working on a personal project where I experimentally test dating photo advice. I take photos of people under different conditions, changing one variable while keeping others ...
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Representative Sample of large dataset

If you wanted a representative sample to analyse interactions/posts, but couldn't pull the huge amount of data online has(billions/millions of records), how would you go about getting your sample for ...
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7answers
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How to calculate Zipf's law coefficient from a set of top frequencies?

I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies: ...
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0answers
16 views

implement gamma probability density and cumulative distribution function in Python [closed]

I try to implement a formula taken from here. I think I have implemented the left pdf from here: ...
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1answer
279 views

Regression Models when the Covariates have many Zeros

While researching this topic, I have come across different regression models which allow for the response variable to have many zeros. This includes: Negative Binomial Regression Zero Inflated ...
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20 views

How to model this queueing process

I need help with the following problem. In my eyes, the description of it is a bit sloppy/unclear, so hopefully someone can help me figure out how the related questions can be answered satisfactorily. ...
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1answer
29 views

Probability calculus on random bitstrings

If I randomly choose 2 bitstring on length (n) with n to be an even number, what is the probability, parametrized on n, that at least n/2 of the bits are equals? In my mind, since the random choice of ...
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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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Producing Random numbers with gamma in python [closed]

I have two pieces of code below. However I am not getting the desired results. The code below takes data and passes it to gamma.fit function. The idea is to get the scale and shape values for the data ...
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1answer
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Absorption Time of Continuous Markov Chains

I have the following question about the Absorption Times of Markov Chains in Continuous State-Space. I was reading the following article on Absorption Times of Markov Chains (https://en.wikipedia.org/...
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1answer
356 views

Interpolation between two distributions

I have a list of empirical measurements describing the rents of apartments grouped by the apartment's size. I.e there are five categories, apartments with 2.5, 3.5, 4.5, 5.5, 6.5 rooms. For each of ...
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1answer
79 views

Concise overview of prototypical distributions

[This question is mainly a reference request.] I'm searching for a somehow concise and complete table of prototypical distributions that would allow a test person to easily choose which typical ...
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Distribution of the exponential of an exponentially distributed random variable?

Let $X$ be an exponentially distributed random variable, that is, with density function $f(x)=\lambda e^{-\lambda x}$ for $x\ge 0$ ($\lambda>0$), and cdf $F_X(x)=1 - e^{-\lambda x}$. What is the ...
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Proof Maximum likelihood Hypergeometric model [closed]

Could somebody explain me how to infer in the hyper geometric model, and show the proof to obtain rigorously the maximum likelihood estimator in this model ?
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Distribution of Text data [closed]

How can I identify whether the training data and test data came from same distribution or not? I tried with TFIDF and cosine similarity ...
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1answer
42 views

MGF of the product of a exponential and a bernoulli random variable

Let $𝑍=π‘‹π‘Œ$ , where $X$ and $Y$ are independent, 𝑋 ~𝐸π‘₯π‘π‘œπ‘›π‘’π‘›π‘‘π‘–π‘Žπ‘™(0.01) and π‘ŒβˆΌπ΅π‘’π‘Ÿπ‘›π‘œπ‘’π‘™π‘™π‘–(0.3) Is there a way to find the m.g.f of 𝑍? I know that I can find the C.D.F by doing as ...
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474 views

machine learning to predict probability distributions

Is there a way that, given a sample set of random values, using machine learning techniques one can be able to predict its probability distribution. What I mean is that, if I generate different ...
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1answer
262 views

Fitting measured, real-world data to theoretical distribution: How to test goodness?

I have a large sets of real-world user data (30k, 80k, 90k measurements). To be precise those are simply session lengths for a specific system. I want to create a theoretical model of this, to ...
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1answer
201 views

Frailty Models: Gamma distributed frailty and Inverse Gaussian distributed frailty

In modelling of frailty using assumptions distributions of frailty are Gamma distributed frailty and Inverse Gaussian distributed frailty. Frailty is unobservable risk factor of mortality. How to ...
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1answer
37 views

Is there a name for this generalisation of the exponential distribution

Is there a name for the following: $$ f(x) = \lambda(x) e^{\int_0^x -\lambda(t) dt} $$ which is similar to an exponential distribution. If $f(x)$ is a polynomial, would this be classed as a gamma ...
4
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1answer
1k views

Weibull distribution with the negative shape parameter

Just wondering why in the literature Weibull distribution is always defined for positive shapes, whereas the extension in the negative direction is possible and has many useful properties. Suppose $X ...
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0answers
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Weibull Distribution v/s Beta Distribution

I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ...
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1answer
102 views

Expectation of the exponential function of Absolute Value of the Difference of Two Double parameter exponentially Distributed Random Variable

Suppose, $X_1,\ldots, X_n$ be iid having double parameter Exponential Distribution with common pdf $$f(x)= \dfrac{1}{\sigma} \exp\{ -(x-\mu)/\sigma \} I(x>\mu); \mu \in R, \sigma \in R^+ , n\ge5$$ ...
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2answers
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Is there bias when you estimate a truncated distribution in this way?

Let's say I have a process which generates non-negative integers based on some unknown probability distribution, however those numbers can not be more than some threshold $N$ (by the design of the ...
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4answers
127 views

What distribution is the most appropriate?

I am given the following problem: A student S wants to take the tram to go home after his lectures are over. The tram line he’s used to take leaves every 7.5 minutes on average at the university. ...
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1answer
104 views

Name of a distribution similar to the exponential

for a simulation I'm using the continuous distribution $$F(x)=1-(1+x)e^{-cx} $$ for $x\geq 0$ with $c\geq 1$. Do you know if this distribution has a name?
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invariant distribution and invariant distribution under reparametrization

While studying MCMC or Markov chain, I always learn the concept of invariant distribution, ...
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0answers
24 views

Connection between the exponential distribution and extreme value distribution

I found here a justification that the connects the exponential distribution and standard extreme value distribution that goes as follows. Let $X\sim \text{Exp}(\lambda)$ and $Y=\log(X)$. Now $\lambda(...
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0answers
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Integrating functions [closed]

Attached is an integral containing a variable (u) and products of two exponential functions. Kindly assist to proffer solution
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2answers
51 views

Find marginal distribution of Y while knowing distribution of X and $Y|X$

Assume that X is uniformly distributed on (0, 1) and that the conditional distribution of Y given $X = x$ is a binomial distribution with parameters $(n, x)$. Then we say that Y has a binomial ...
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Metric to assess similarity of distributions

I am working on clinical synthetic data and I would like to learn more about metrics to compare synthetic vs measurements distributions. As there are methods to generate synthetic distributions with ...
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1answer
31 views

What would be the proper distribution to model the number of particles in a state in canonical ensemble

Suppose my system has $N$ particles, and I want to find a distribution for $n_i$, the number of particles in the $\epsilon_i$ energy state. What I do know is the boltzmann probability, which tells me ...
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1answer
31 views

Mixture of a realization of uniform variable and noise

Suppose that $X \sim U[0,1]$. After $X = x$ has realized, we don't observe $x$, but we instead observe a noisy signal of $x$, defined as $S = \tau x + (1 - \tau) U$, where $\tau \sim Ber(p)$ and $U \...
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Downsampling by sample, not by class, with lots of missing values

In R, I'm trying to downsample to the lowest number of samples, or a ratio would work as well, by class. All I see for downsampling is evening out class frequency, not sample frequency/sample rate. ...
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1answer
25 views

Scale and log transformation of a feature based on different measurements

I have a dependent variable (price) which has been measured in two different currencies (currencies are unknown) and the plot looks like this: Is it ok to log/scale them and handle them at once or ...
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33 views

Statistical Models that "Exploit" Distributional Knowledge of the Predictor Variables

I am trying to see if there any Statistical Models that (better) "Exploit" Distributional Knowledge of the Predictor Variables. For example, I feel that is a common misconception (e.g Where ...
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1answer
252 views

Distribution fitting to given loss data

I am into risk management and deal with Operational risk. As a part of BASEL II guidelines, we need to arrive at the capital charge the banks must set aside to counter any operational risk, if it ...
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The Elephant in The Room: How is Real-World Domain Knowledge Converted into Bayesian Priors?

I have been trying to look into the daunting problem within Bayesian Models: How is Real-World Domain Knowledge Converted into Bayesian Priors? Logically speaking, it seems that Bayesian Priors can be ...
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2answers
62 views

Difference between multinomial distribution with n trials and categorical distribution performed n times

I want to understand if there is any difference between performing multinomial distribution with 1 trial, 10000 times and performing multinomial distribution with 10000 trials, 1 time. Here is the ...
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Which two datasets have similar fit for a certain distribution?

I have one observed monthly precipitation dataset and 10 climate models datasets. And I found that all follow exponential distribution. But, I wanted to know which climate model is more similar to the ...
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1answer
135 views

Best way to check implementation of density, distribution function and random generation

What is the best way to check if implementation of density, distribution function, quantile function and random generation for some distribution are correct? For example, base R lacks Laplace ...
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1answer
19 views

Application of transformations of lognormal distributed random variables

I'm answering questions from a book and I have to do a simple transformation Y=g(X) of a lognormal distribution: $X \sim \mathcal{LN}(\mu,\,\sigma^{2})$ with $Y=ln(X)$ Then $Y \sim \mathcal{N}(\mu,\,\...
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1answer
233 views

How to determine if a distribution is Cauchy?

I am making a Cauchy random number generator and I want to make some tests to determine if my code is correct. What are some simple tests I can do to show that the distribution of the generated values ...
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0answers
68 views

Manually Deriving the Maximum Likelihood Estimates for Less Common Probability Distributions

I have a question relating to Manually Deriving the Maximum Likelihood Estimates for Less Common Probability Distributions. Suppose we generate 200 random numbers from a Normal Distribution ~ (1,2): <...
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0answers
10 views

Statistical Inference on Covariates (Instead of the Response Variable)

In statistical modelling, it seems as though we are always more interested in predicting the expected value of the response variable conditional on some observed vector of covariates. However, are ...
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1answer
20 views

Negative Infinity AIC and BIC

I was trying to compare best fit model for monthly precipitation data sets and negative and positive infinity (-inf and inf) as values have showed up for both AIC and BIC tests. Can anyone tell me ...
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1answer
27 views

Why is the expected value of any data point in the sample equal to population mean?

Suppose we have a distribution of heights of all males in a country. Let population size = N. Now, I take a sample of 100 males = {h1,h2,h3,....h100} How is the expected value of any data point, i.e., ...
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14 views

Negative KL divergence for train_test_split in sklearn for y_train and y_val

So, I am trying to understand if I have fair split of my train and val sets using train_test_split of sklearn, so I decided to run the KL divergence and JS div tests and I get the following results. ...
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1answer
224 views

How to fit a superimposed distribution (\eg a Gaussian distribution + a Uniform distribution)

Suppose we have a set of independent observations of a random variable X, which is a Superimposition of two mutual independent random variables (i.e. X = Y + Z), Y follows a uniform distribution, ...

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