# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### What best describes the distribution of the histogram?

What best describes the distribution of the histogram below. I think it is a normal distribution but I am not sure. I am new to statistics so any help will be great.
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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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### Euclidean Norm normalized Normal Distribution

Let $X$ be a multivariate normal $\mathcal{N}(\mu, \Sigma^2)$ and let $X$ be anistropic, that is I am considering $\Sigma$ to be a diagonal matrix but the elements on the diagonal might be different. ...
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### Example distribution where 74% of probability is above the mean

Watching Why You Should Want Driverless Cars On Roads Now, at 8:14 Derek Muller claims: Surveys show 74 % of people believe they are above average drivers. This claim motivates my question, but some ...
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### Newbie: Difference between the meaning for the data analysis: proportion of correct responses and probability of correct responses

Very newbie, sorry if the question seems to be not very smart... If proportion of correct respones is defined as Number of hits + Number of correct rejections / Number of trials Is the probability of ...
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### Would Performing a T-Test between Nonequal Continuous Distributions Provide Valid Results?

I have two samples, and in performing a Kolmogorov–Smirnov test the sample distributions are shown to be significantly different from each other. In knowing that the two sample distributions are ...
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### Meaning of NOT having a distribution on data

In statistics and machine learning, a common starting point is to assume some unknown distribution $\mathbb{P}$ on the cartesian product $\mathcal{X} \times \mathcal{Y}$ of input space and output ...
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### What is area under cumulative distribution represent? [duplicate]

Exponential distribution has following probability density function which explains the curvature of a line (For simplicity I am just going to work with x>=0): f(x) = lambda e^{-lambda*x} to find ...
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### Using PDF values for Likelihood [duplicate]

Given that PDF value $𝑓_𝑋(𝑥)$ for a particular $𝑥=𝑥_1$ does not have any probabilistic meaning (by definition $𝑝(𝑥=𝑥_1)=0$). We still see the use of $𝑓_𝑋(𝑥_1)$ as its likelihood. My ...
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### Using Sigmoid in Maximum Likelihood Estimates [duplicate]

I have two questions regarding the use of Sigmoid in MLE: Clearly, the Sigmoid Function is not a PDF. But in the MLE of Logistic Regression, we see Sigmoid being used as if it is a PDF. Is my ...
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### Fitting distribution to literature-reported incidence rates or cumulative risks

I am building a simulation model in R. In this model, I would like to simulate a patient with a certain baseline age, and then simulate the time-to-event for breast cancer. I want to sample the time-...
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### Expectation and distribution of ratio of correlated Gamma/Chi-square random variables

This question is very similar to: Distribution of the ratio of dependent chi-square random variables But the big difference is what happens when we don't have standard normal variables. I want to ...
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### Confidence Interval using % changes (Trying to classify whether variation from SMA is significant)

0 So I'm attempting to figure out when a drop in the price of a security is "statistically significant". The distribution of the difference is log-normal (makes sense because it can only be ...
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### Finding a,b parameters if Highest Posterior Density is known

I know that a beta distribution with unknown parameters a,b has a 95% HPD of [0.25, 0.75]. What is the correct approach to solve for a,b?
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### Why aren't Normalizing Flows suitable for Discrete Distributions?

I am currently trying to understand why normalizing flows are not applicable to discrete distributions (a quick primer on NF can be found here). The assumptions on the transformation f between the ...
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### Trying to find a distribution for time dependent drought

I would like to seek your support on a modelling issue for which I could not find relevant past postings or published literature resolve it. I am running a cost benefit model to assess the impact of ...
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### Bayes theorem with multiple draws

Setting I have a question on the "Cookie Problem Revisited" exercise from Allen Downey's Think Bayes 2e. The Bayes theorem is defined as: $$P(H | E) = \frac{P(H) \ P(E | H)}{P(E)}$$ where ...
How can I calculate the $\alpha$ and $\beta$ parameters for a normal-inverse gamma distribution if I know the mean and variance?