PDF stands for Probability Density Function. The PDF of a variable gives the relative probability for each value of a continuous variable. Use this tag when asking about probability functions in general, whether PDFs or discrete probability mass functions.

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Difference between joint density and density function of sum of two independent uniform random variables

I am not able to understand the difference between the joint density function and density function for a random variable $Z = X_1 + X_2$, where $X_1, X_2$ are uniform rvs in $[0,1]$. I think joint ...
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25 views

How can I approximate a pdf knowing the estimated CDF in R?

I have an estimate of a CDF in R (nonparametric) and I need to compare this distribution to another one by Kullback-Leibler. In order to do so, I need to find the pdf of this random variable. What is ...
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14 views

Separable Kernel Density Estimate

Thank you for reading my question. Before I begin, I am no mathematician and so any help/pointers are very welcome. I have been reading the following paper: ...
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11 views

PDF of hourly data

I have data for every hour of the past year for an insurance company making cold calls to sell. Each record indicates the hour and a Y or N if the salesperson was able to make the sell. If I wanted to ...
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1answer
30 views

Probabilistic Density

Variable $X$ has the following probability density: $f(x) =$\begin{cases} 0, & \text{x ∉ [0,2]} \\ kx(2-x), & \text{x ∈ [0,2]} \end{cases} How can I find the parameter $k$ so $f(x)$ is a ...
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28 views

What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables

$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs. ...
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35 views

Densities and Cumulative Distribution Functions

Has anyone seen this notation before? What does it mean? $\int_{0}^{\infty} f(x) G(x) dx$ $f(x)$ is a density and $G(x)$ is a cumulative distribution function
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21 views

how to measure similarity of two lists of continuous data with different length

I have two lists of continuous data with different length. a) How should I measure (dis)similarity of these two lists? or, as these lists can be formed into histogram, how can I quantify ...
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0answers
12 views

Copula density bounds

I was wondering if someone can help me with a problem I encountered in my work. I need a bivariate copula density that meets two constraints at the bounds, and I have difficulties in finding one that ...
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0answers
44 views

Generating random variables from a density function expression with R? [duplicate]

I am using R langage, and for my algorithm I should generate random variables knowing the expression of the density function. For exemple, the density function is : ...
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1answer
20 views

Constructing a random Experiment

Can someone help me as how to construct a random experiment which has the following density:$$\frac{1}{2\sqrt{2\pi}}\left(e^{\frac{-x^2}{2}}+e^{\frac{-(x-10)^2}{2}}\right)$$ Update: According to what ...
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1answer
51 views

Pdf of the square of a standard normal random variable [closed]

I have this problem where I must find the pdf of $Y = X^2$. All I know is that $X$ has the distribution $N(0,1)$. What kind of distribution is $Y = X^2$? Same as $X$? How do I find the pdf?
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1answer
98 views

Marginal density and conditional density from joint density [duplicate]

I am having trouble understanding how to solve this when the variables are not discrete. Let the simultaneous density of the non-discrete stochastic variables (X,Y) be I am then supposed to find ...
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2answers
77 views

Sample from distribution given by histogram

Given a histogram obtained using given data points, how do I randomly sample from the distribution predicted by the histogram? Any conceptual comment / R code would be welcome.
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1answer
18 views

Directly obtaining marginal cdf directly from joint cdf

I know how to obtain marginal PDF $f(x)$ from $f(x,y)$. Just integrate over $y$. But is there a way to directly obtain marginal CDF $F(x)$ from $F(x,y)$? Do I need to calculate marginal PDF $f(x)$ ...
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1answer
33 views

Uniquely determine the two parameters of a distribution given pre-determined probabilities for two disjoint subsets of its support

Let $F(x| \alpha, \beta)$ denote the cumulative density function of a probability distribution. Let $[a,b]$ and $[c,d]$ be two disjoint subsets of the support of $F$. Suppose that $F(b) - F(a) = p$ ...
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10 views

Detect bounding box of tables in PDF page

I am new to Machine Learning, doing courses and reading papers, and would like to solve the following problem as my learning journey: Given a PDF page I would like to detect the bounding boxes of all ...
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16 views

Compound Distributions — Basic Techniques and Key General Results from First Principles

Could someone please point me to a source with notation, terminology, key results and basic techniques to approach compound distributions? Definition Compound probability distribution is the ...
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25 views

Kernel density estimator for sum of marginals

Imagine that there are two random variables $X$ and $Y$ with corresponding density functions and a joint density given by $f(x,y)$. The expected value of the kernel density estimator of the joint is ...
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15 views

Probability densities and perturbation of marginals

I came across the following problem in a project recently. Suppose you have two random variables X and Y which are not independent, i.e. $f(x,y)\neq f(x)f(y)$ for all $x$ and $y$. I would like to find ...
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1answer
46 views

PDF and CDF of sum of two independent $\Gamma$-distributed random variables [duplicate]

Let $X \sim \Gamma(m, p)$ with a shape parameter $m$ and a scale parameter $p$ and $Y \sim \Gamma(m, q)$ with a shape parameter $m$ and a scale parameter $q$, and let $X$ and $Y$ be independent. ...
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1answer
34 views

Probability Density function and mean

I have a problem where I am working out the failure time of a system before time $t$. I have the probability of this happening: $$ 1 − R(t) + R(t)(1 − R(t))^2(1 − R(t)^2) . $$ How can I work out the ...
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1answer
27 views

Random Variable Transformation

Consider a Probability density function f(x) which is uniformly distributed between say (-5,5).Now if i define a random variable "y" which is related to the random variable "x" as follows: y = 1 ; ...
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51 views

Finding what happened between two PDFs from the parameters of a resulting PDF

Assuming $X$ and $Y$ are Gaussian random variables with PDFs of $f(X)$ and $g(Y)$ with parameters of $(\mu_x, \Sigma_x)$ and $(\mu_y, \Sigma_y)$, we know that: for the operation of sum ($+$), if ...
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18 views

What is the relationship between generative models and density estimation?

If aren't they synonymous, what distinguishes the one from the other? Is probability density estimation a certain kind of generative model? Can any generative model be regarded as density estimation?
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32 views

Relationship between the probability and likelihood functions

I've read a number of different explanations trying to understand the likelihood function, and I understand the purpose of it, but some statements sound contradictory. Consider observed data X, model ...
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1answer
22 views

Trouble plotting probability

I have a density function that can be written as follows: $$ f(r) = \frac{(1-r^2)^{\frac{n-4}{2}}}{\mathbf{B}\left(\frac{1}{2}, \frac{n-2}{2}\right)}$$ Where $\mathbf{B}$ is the beta function. I got ...
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1answer
12 views

Basic question regarding construction of likelihood function from a Cox PH model

I have a simple question (which I sense may have a complicated answer) regarding the fundamental logic concerning how the likelihood function from a Cox PH model is derived. Assuming the $i^{th}$ ...
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19 views

Bias of an estimated Gaussian density

I have an iid sample, $X_1,\dots,X_N \in R^d$, from a multivariate normal density with mean $\mu$ and covariance matrix $\Sigma$. I am estimating the density $p(y) = N(y| \mu, \Sigma)$, using ...
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4answers
274 views

Distribution of Y from distribution of X

If the PDF of distribution of $x$ is $PDF_X$ and there is a mathematical relationship between $y$ and $x$: $$y=f(x)$$ is it possible to find $PDF_Y$ ? If yes, how to calculate it?
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32 views

Joint Probability Density Function

I'm trying to find the Joint Probability Density Function of three variables, they are random continuous variables. I was thinking about using a copula function since I saw them recommended here ...
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1answer
23 views

Two dimensional PDF candidate for barbell like distribution

I have this empirical sample, which I drew on the scatter plot. It's got to be unimodal according to theory, and it surely does look like one. A simple way to model it is with bivariate normal. ...
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13 views

Setting up forecasting (time-series) with multiple kernel densities

I am hoping that someone here can guide me a little as to what kind of method to use for my forecasting model which I am writing in R. I am forecasting energy useage in KWH over time. I have numerous ...
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1answer
39 views

Help to understand this. Expected value of $S^\alpha$ in Gaussian distribution

Lets $X_1,\cdots,X_n$ be simple random sample from $\mathcal{N}(\mu,\sigma)$. $\overline{x}$ is sample mean. Let $$S^2=\begin{cases}\sum_{i=1}^n (x_i-\mu)^2, \mathrm{ where\ } \mu \mathrm{\ is\ ...
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Is this a mistake in my exercise? A density for a transformed variable

Let $(X,Y)$ be invariant under transformations by orthogonal matrices, and let their joint density be $g(x,y) = f(x)f(y)$, where $f$ are the marginal densities. Show that $$g(x,y) = f(x)f(y) = ...
4
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1answer
61 views

How to change variable of distribution from vector to angle from fixed point?

I have a distribution of vector $\textbf{x}=\langle \sin{\phi_x}\cos{\theta_x}, \sin{\phi_x}\sin{\theta_x}, \cos{\phi_x} \rangle$ on the unit sphere (von Mises-Fisher): ...
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0answers
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Is it reasonable to estimate the CDF of a random variable with the help of kernel density estimation?

Given a set $S$ of samples from a random variable $X$ with pdf $f$ and cdf $F$, is it reasonable to estimate $F(x)$ by finding an estimation $\hat{f}$ of $f$ via kernel density estimation on $S$, and ...
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IID random variable problem

Given N IID random variables X1,X2,X3....each with uniform distribution in [0 1]. How can i find the probability that one of the them is maximum? say, what is P(X1 is largest) = ? i think all have ...
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26 views

Is the following integral of a pdf an identity, i.e. always true?

I am reading a paper and the author starts a proof with this $$ p(\hat{R}|R) = \int p(\hat{R},\theta|R)d\theta $$ p is the density function. Is this something that is always true? Can you help me ...
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34 views

Effect Size PDF (and Confidence Intervals)

I've already read this, which isn't very helpful. Consider Cohen's $d$ for two independent random samples $\{X_{1j}\}_{j=1}^{n_1=N}, \{X_{2j}\}_{j=1}^{n_2 = N}$, given by $$d = \dfrac{\bar{X}_1 - ...
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10 views

How classify output of a composite indicator using fuzzy concepts?

Suppose that we created a composite indicator to compare a company branches performance in a country. This company has 5 current levels for performance. This is histogram of composite indicator output ...
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29 views

Joint PDF (or MGF) of random sums

I am interested in finding the joint PDF of two sums of random variables. Let: $\textbf{Z} = \left[ {\begin{array}{*{20}{c}} {{z_1}} \\ {{z_2}} \end{array}} \right] = \textbf{D}\textbf{X}$ ...
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8 views

Classifying the F7 (First 7 days Activity) Metric

In social networks we have a commonly used metric called F7. It is the number of days a user logged in during their fist week since sign up. This means it has a range of [1,7] since you must at least ...
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255 views

Probability of failure

A structure will fail if subjected to a load greater then its own resistance: failure := load > resistance We can assume that the load and the resistance are ...
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108 views

how to fit pdf of known form to data

I have a set $X$ of 1000 data points. I know the PDF has a certain form, but there are two constant parameters for which I need to derive values in order to bet fit the data. Is there an established ...
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71 views

What type of distribution is this?

What kind of distribution is the one reported here below?
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24 views

Calculate the PDF given a list of values and a list of correlated

The question itself is simple; I have a list of event/values and another list of values correlated with the first one. Let's say something like that: ...
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1answer
36 views

Find the p.d.f of Z = X+Y given a joint pdf

Let $X$ and $Y$ be random variables for which the joint p.d.f. is as follows: $f (x, y)=\left\{\begin{matrix} 2(x+y) && &0\le x\le y \le 1\\ 0&& &elsewhere ...
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2answers
51 views

What does “PDF overlap” mean? “To see whether a probability density function overlaps”

I ran across the following sentence in a journal: "To see whether a probability density function overlaps" What does this word mean in the statistics literature, "overlaps"?
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52 views

Normal Distribution with P(x|y) [closed]

Hi I am solving one problem based Bayes' formula. I need to calculate the normal distribution of P(x|y). The following data is given. P(x | y = 0) = N(x1,0,1) and P(x | y = 1) = N(x2,0,16) where N ...