# Questions tagged [pdf]

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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### modelling Cumulative Distribution of a variable with many zeros and few large values [closed]

I have a data set with many zero values and a few large values, making the dataset highly skewed. I wonder, any probable distribution function, that can be fitted to the data, probably any mixture ...
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### Why when I increase the standard deviation in the pdf function the graph looks squeezed instead of more dispersed?

So what I am doing is this: ...
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### Which pdf to choose for the prior of an angle?

I have a system in which one uncertain variable is a direction in two dimensions. If I want to define a prior for this, is there an elegant way to reflect the fact that the parameter space dimension ...
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### What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
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### How do I convert a standard normal RV to a generalised error RV?

The generalised error distribution (sometimes called the generalised normal distribution) is a generalisation of the normal distribution allowing variation of the kurtosis away from mesokurtosis. ...
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### Find the CDF and use it to find all the medians

Show that for every $p$, $0\leq p\leq 1$, the function $f(x)$ = $p*sin(x) +(1-p)*cos(x)$, $0\leq x \leq \pi/2$, and $f(x)=0$ otherwise, is a density function. Find its CDF and use it to find all the ...
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### Can we sample from the wrapped normal distribution and evaluate the density of the sample simultaneously?

In a computer program (written in C++), given $x\in[0,1)$ and $\sigma>0$, I need to sample $y$ from the wrapped normal distribution $\mathcal W_{x,\:\sigma^2}$ with mean $x$ and variance $\sigma^2$ ...
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### Density function of a stationary processus [duplicate]

I have a question: Let X be a wide-sense stationary processes. is a density function of X is almost periodic? why? A continuous function $F:R \rightarrow L_2$ is said to be almost periodic, if for ...
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### Predictive density via LOOCV

I am looking for a way to generate a density prediction (in contrast to a point prediction or a prediction interval) in a multiple regression setting without relying on stringent parametric ...
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### Request for Explanation: Deriving Probability Density Function of a Maximum Likelihood Estimator of a Uniform Distribution [duplicate]

I am reviewing some practice problems and have both a question and its solution but am struggling to understand them and am hoping someone can help me. I am struggling to follow the logic for ...
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### Questions about pmf of multinomial distribution with indicator variables

I was reading through the textbook of Introduction to Machine Learning, it introduces $z^{t} = (z_{1}^{t},...,z_{k}^{t})$, where $z_{i}$ is an indicator variable, each with probability $\pi_{i}$, then ...
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### Simplifying modified Bessel function of the first kind

The modified Bessel function of the first kind shows up in the normalizing constant of a lot of random variables (e.g. the normal product distribution, the noncentral chi-square distribution, the ...
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### Does the below Plot refer to a Valid PDF?

I have tried to creat a valid PDF according to some special function I have got the below Plot , I got it for n=6 Integrand Range[n/n], Now My question here Is : Is that below Plot refer to a valid ...
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### GANs: What does the pdf of the sample data p(x) mean? [closed]

In the context of GANs, the concept of a probability distribution comes up as the generator tries to emulate the "distribution" of the data: $p_{data}(x)$. For me, the use of "distribution" here ...
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### A Multinomial Geometric distribution? What is this distribution called?

In a problem I am dealing with I repeatedly interact with a distribution of the following form, $$p(n_1, n_2, \ldots n_M)=\binom{\sum_{i=1}^Mn_i}{n_1\cdots n_m} w_0\prod_{i=1}^Mw_i^{n_i}$$ where $p$ ...
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### problem in understand exponential PDF [duplicate]

I'm studying a paper called "Optimization based on bacterial chemotaxis". As it can be understood from its name, it has proposed an optimization algorithm based on the reaction of a bacterium toward ...
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### Finding distribution of $\frac{X^2}{Y}$ given joint pdf of $X$ and $Y$

So I have the joint distribution of $X$ and $Y$: \begin{align} f(x,y) = cx, \ 0 < x^2 < y < \sqrt{x} < 1 \end{align} and I want to find the distribution of $X^2/Y$. So I set $U = X^2/Y$ ...
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### Why density plot tails are beyond maximum and minimum values?

I am trying to interpret the tails of a density curve, which go beyond xlims(0 in this case). I understand that area under the curve between any two points represents the probability of that event. ...
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### How can I calculate this PDF

I'm trying to reproduce the results of a ray tracing paper which uses reinforcement learning. I asked my question in the computer graphics community of this site, but I think my problem can easily be ...
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### Example: Writing the joint PDF $f(x, y)$ as the product of a marginal and a conditional probability function
I am presented with the following notes on Bivariate distribtions: If we can write the joint probability density function $f(x, y)$ of a pair of random variables $(X, Y)$ as the product of a ...
Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...