# 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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### 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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### 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: ...
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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### 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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### 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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### 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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### 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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### 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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### 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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### MGF of the product of a exponential and a bernoulli random variable

Let $𝑍=𝑋𝑌$ , where $X$ and $Y$ are independent, 𝑋 ~𝐸𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑖𝑎𝑙(0.01) and 𝑌∼𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(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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### 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 ...
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 ...
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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### 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 ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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., ...