# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Distribution of $Y$ when, $Z = Y \times X$, $X \sim Poisson(\lambda_x)$ and $Z \sim Poisson(\lambda_z)$

Is there any know distribution such that when a random variable from it is multiplied with an IID random variable from a Poisson distribution, it results in a Poisson distributed random variable? ...
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### I am confused about the sum indices of these posterior distribution formulas

I am reading this notes and trying to understand how the posterior distribution formulas of the variational variables involved have been calculated. I am confused about the indices of the summation. ...
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### True mean of a truncated distribution?

I use C++ GSL library to generate random numbers now. The numbers obey a distribution, (e.g. normal or lognormal distribution). This library requires the input of expected value ${\mu}$ (i.e. mean) ...
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### Fitting distributions to censored and uncensored data in R

I need to fit lognormal, Pareto, and generalized Pareto distributions to some empirical data that is a combination of censored and uncensored data. I tried using the function ...
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### ISI PCB NC$9$ Limiting Distribution of Bernoulli to Poisson

Let $X_i\sim (i.i.d.)$, Bernoulli($\frac{\lambda}{n}$), $n\ge \lambda\ge 0$. $Y_i\sim (i.i.d.)$, Poisson($\frac{\lambda}{n}$). $\{X_i\}$ and $\{Y_i\}$ are independent. Define $T_n=\sum_{i=1}^{n^2}X_i$...
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### Can probability distribution predict the electricity consumption of the coming months? if no what do you recommend?

Can probability distribution predict the electricity consumption of the coming months based on a historical consumption data? can it give me a figure? If NO or not recommended for such case, what do ...
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### How to generate data from a generalized Dirichlet distribution?

I need to generate data from a generalized Dirichlet distribution in Python to test my model, but I have no idea how can I proceed with that, can anyone guide me?
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### What is the importance of non-informative prior in Bayesian Inference? [duplicate]

By the name, noninformative prior, the prior distribution doesn't contain any information about the parameter. Then why we use this thing to estimate the parameter by the Bayesian approach?
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### Deriving the Chi Square distribution [duplicate]

Let $X_1,...,X_n$ be IID random variable such that $X_i \sim N(0,1)$ for all $i=1,...,n$. Derive the distribution (i.e. give the pdf/cdf) of $\sum_{i=1}^{n} X_i^2$. I know that from the definition of ...
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### Distribution of sum of possibly non-independent Bernoulli random variables with known variance-covariance matrix

I wonder if there are any results concerning the distribution of sums of possibly non-IID Bernoulli random variables when covariances in all pairs of r.v.'s are known. To make this more concrete ...
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### How to sample from truncated distributions using scipy?

I have min and max values for certain variables such as: Expenses Loss Growth I'd like to add a distribution around them and plot a histogram in python. Distribution could be beta, gamma right type ...
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### Using convolution formula

I would like your help to solve the following exercise. I have also reported below my attempt, but I'm not sure I'm properly manipulating the various integrals involved (in particular the switching ...
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### How to know which set is most likely to have been generated by some probability distribution?

I have 3 sets of points in $R^n$: $X$, $A$ and $B$, how can I (preferably quickly) check which of the two sets $A$ and $B$ is most likely to have been generated by the same probability distribution as ...
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### Bayesian linear regression with given distributions X, y instead of pairs {(X1, y1),..(X100, y100)}

I'm wondering if is it possible to model data by knowing only distribution of features (X) and targets (y). Thus, instead of paired variables {(X1, y1), (X2, y2), .., (Xn, yn)} I know only mean value ...
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### Age-adjusted mortality rate given age distribution and total number of deaths

I am a bit confused as to how I can calculate age adjusted mortality rate given the two datasets that I have. My first dataset consists of covid deaths per city district and is a gross sum (...
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### How do you report error bars / uncertainties for a set of probabilities obtained from a hidden Markov state model?

I have a system I want to model with a hidden Markov state model. It has almost 30 different possible observations so I was doing some tests on a simpler system to get a handle of things. Preliminary ...