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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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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1answer
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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2answers
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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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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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
45 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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1answer
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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38 views

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) = ...
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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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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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1answer
25 views

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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2answers
254 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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2answers
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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1answer
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 ...
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39 views

Simulation of PDF of sum of correlated Gamma random variables (in R)

My question is very related to the general sum of Gamma RVs question found in the following link: [The sum of two independent gamma random variables There is some helpful R code there for generating ...