# Questions tagged [density-function]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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### Power-law fitting with x-y relationship [closed]

I would like to fit a power-law distribution to data taking into account the x-y-relationship. I tried plfit & powerlaw package for python. But the problem with them is that if I shuffle the y-...
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### Interpreting y axis in density plot

200 people were tested, 20 of those were infected. I want to get a posterior distribution for the uncertainty associated with the probability that a person is infected. I do this like this: ...
133 views

### Calculating the cumulative distribution function and the probability density function of an interval with ratio of a shorter and longer segment

The interval $[0, 2]$ is divided into two parts by randomly marking a point in $[0, 1]$ according to the rectangular distribution. Let $X$ be the length ratio $L_1/L_2$ of the shorter segment $L_1$ to ...
60 views

### pdf vs probability vs likelihood [duplicate]

How to compute the log likelihood? Let's take a simple example using a normal distribution and scipy to do the work. Assuming X is the data, and the normal distribution as the model (...
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### Can a linear combination of two Normal densities be a Normal density? [duplicate]

Consider $f_i(x) = \frac{1}{\sqrt{2\pi}\sigma_{i}}e^{-\frac{1}{2}\left(\frac{x-\mu_{i}}{\sigma_{i}}\right)^{2}},$ $i=1,2$. Define another density by $$f(x) \equiv wf_1(x)+(1-w)f_2(x).$$ Is $f(x)$ also ...
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### accept reject function x 0<x<1 [duplicate]

hi everyone I'm trying to implement the code in r of accept and reject the function but I don't understand what I should do when my distribution function is not in 0 and 1 as in the case of fx(x)=x ...
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### Does the PDF $\exp\left(-\frac{x^2}{2}\right) \cosh(\gamma x)$ have a name?

Is there a name for the following probability density function: $$P(x) \propto \exp\left(-\frac{x^2}{2}\right) \cosh(\gamma x)$$ where $\gamma \ge 0$ and $x\in\mathbb{R}$? Eventually my goal is to ...
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### Beginner Probability Question: Find PDF and E(X) [closed]

From [1;2] continuous interval we choose 3 numbers randomly. Let $X$ be the minimum between those numbers. Find PDF and Expected value. I fail to understand the problem, since I believe that ...
1 vote
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### What is the cross product of two probability distributions $P \times Q$?

In many papers on machine learning and statistics, I encounter the following notation Let $P$ be a distribution, and let $Q$ be another distribution. Then the author creates an object $P \times Q$ ...
1 vote
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### Confidence interval for unsymmetrical Gaussian Mixure Model PDFs?

Let Y be a vector of observations. A Gaussian Mixure Model (GMM) is fit to the dataset. The distribution can appear unsymmetrical, with different thickness of tails in both sides. What is the best way ...
101 views

### Two dimensional random variable with uniform marginal probability density functions [duplicate]

I have access to some data for two variables - let's call them x and y. In particular, I have the distribution of data separately per each variable, something that allows me to estimate the marginal ...
1 vote
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### Is there a closed form for multi-step ARIMA/ARMA density forecasts conditioned on initial values?/alternatives to this?

I am attempting to create a benchmark for probabilistic forecasting of time series to test other models against and figured that a linear ARIMA/ARMA model would be a good starting point. I thought ...
458 views

### What is the resulting distribution if I merge two different distributions?

The title is not the best but I really do not know how to describe the scenario in a better way. The context Consider taking measurements of two different quantities: The time needed for a car to ...
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### PDF of the sine of a wrapped Normal distribution

I have a random variable which is an angle $\Theta$ that follows a wrapped Normal distribution. The angle $\Theta$ has a relatively small variance, so despite having a range from $(-\pi,\pi)$, ...
1 vote
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### Uniform Sampling From the Region Bounded by $\sqrt{x}$, $x=3$, and $y=0$

I want to sample uniformly from the area bounded by $y=0$, $x=3$, and $y=\sqrt{x}$: If I draw $x$ from $U[0, 3]$ and $y$ from $U[0, \sqrt{x}]$, the density will be higher in the bottom left corner: ...
1 vote
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### how to use the formula in picture for matlab? [closed]

[![the picture is pdf and realibility formula] 1how to use the formula in picture for matlab? 1
1 vote
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### Calculating PDF conditioned on event

I'm confused about problems where we calculate a PDF conditioned on an event. Consider this simple problem: We have two random variables, X and Y, X is uniformly distributed on [a,b], and Y is uniform ...
1 vote
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### Making use of relative density of genomic features between gene sets

I am looking at a particular genomic feature in two sets of genes: set A is a positive control set, where I know this feature is overall enriched in the genomic DNA of these genes, and set B is a (...
I think I have a misconception that I hope someone can help me clarify, I do not have a background in measure theory so that might be the problem. Say we have two random variables $X$ and $Y$ ...