All Questions
Tagged with density or density-function
448 questions with no upvoted or accepted answers
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Kernel Density Estimation - Comparison Between different sets of samples
Is there a way for compare the distribution of different set of samples?
For example, I have three sets, for example:
X1 = N(0, 1);
X2 = N(0.5, 1);
X3 = N(1, 1).
Each set is drown with a specific (...
- 101
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20
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Formalism to cope with probability density functions defined piecewise (in the second dimension)
I'm not sure how to pose this question, as I lack the correct terminology. Actually, my question tries to obtain insight on the terminology and notation to cope with the following problem:
I have a ...
- 365
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237
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How to choose sample size from probability density for computing mutual information based on continuous variables
I need to compute mutual information gain based two continuous variables $X$ and $Y$
$I(X|Y) = \int_X\int_Y p_{x.y}(x,y) \log(\frac{p_{x.y}(x,y)}{p_{x}(x)p_{y}(y)})$.
I have used Kernel Density ...
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56
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Conditional density under conditional indepencence?
Let $X,Y,Z$ three random variables such that the joint density can be factorized as
$$f(x,y,z) = f(x \mid z) f(y\mid z) f(z).$$
This is, I am assuming conditional independence of $X$ and $Y$ given $Z$....
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1
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107
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Roulette Wheel for sampling user defined pdf
Following is the pdf from which I want to sample so, I used roulette wheel sampling
Code to generate pdf
...
0
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1
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179
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Compute $E(X_1|X_1+X_2)$ $X_1, X_2$ both iid $Exponential(1)$
I recently stumbled across this question on CV:
Conditional expectation conditional on exponential random variable
And really liked the answer provided by @Rush, but I wanted to try to compute this ...
- 297
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29
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Group comparison for bivariate distributions
For two groups A and B that consist of n and m individual samples. Each individual sample has a unique 2-dimensional joint probability density functions (PDFs)of two variables. These PDFs are ...
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62
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Probability question in Mat
My teacher give me this question:
Using MATLAB, generate 10000 Random Vectors of size 500 with the PDF of Gamma distribution. Find the PDF of maximum and minimum of the generated Random vectors.
(Use ...
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117
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PDF transformation for y=|x|
Suppose I have the random variable X with a pdf:
$$f(x)=exp(-(x+1)) u(x+1)$$
where u is the unit step function; such that u = 0 for x<-1 and u=1 for x>-1
$$y= |x|$$
for $$-1<x<1$$
...
- 85
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159
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Viewing PMF as an instance of a PDF
I'm having difficulties in thinking about the probability mass function (PMF) as a special case of the probability density function (PDF).
I understand that PMF's are used in discrete examples, but ...
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53
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Best way to model the dependency of these two random variables (copula?)
I'm modelling the joint PDF of two variables that looks like this ,
where vt and vr are the random variables. The dashed line shows the joint pdf assuming they are independent (the product of its ...
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1
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59
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Applying assumptions about marginal and conditional PDFs
We are given $0 < x_2 < x_1 < 1$. What assumptions can you make about $f_1(x_1)$ and $f_{2|1}(x_2|x_1)$?
I know that $f(x_1) f_{2|1}(x_2|x_1) = \frac{1}{x_1}$. I know the expression can be ...
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Generating random correlation coefficients (Pearson $r$)
I'm trying generate some random correlation coefficients ($CC$) using the Fisher's $z$ transformation. An R implementation is shown below.
However, it looks like ...
- 4,056
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355
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Getting shape parameters from a beta probability density
Is there a way to calculate the shape parameters $a$ and $b$ of a beta distribution having only its probability density function? This small example might clear a bit what I want (I work on Python):
<...
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167
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Generating more samples of a random vector by convex combinations
I am not sure if my question is reasonable but I am wondering if there's someone who has seen a familiar idea elsewhere.
Consider a random vector $X$ and let $x_1,\dots,x_n$ be $n$ realizations of $X$...
- 491
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Left "tail" of one-tailed distributions
I think of the "tail" of a probability distribution as the behavior of its PDF $f(x)$ as $x\rightarrow +\infty$. For some PDFs with complicated expressions, it is sometimes easy to study their ...
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585
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Expectation of the inverse of $\textbf{z} \textbf{z}^{H}$ where $\textbf{z}$ is a complex Gaussian vector
Considering the vector $\textbf{z} \sim \mathcal{CN}(\textbf{0}_{M},\Theta_{M \times M})$, what would be the expectation of $\frac{1}{\textbf{z} \textbf{z}^{H}}$, i.e.,
$\mathbb{E} \left\lbrace \frac{...
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41
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Any trick to swap order of determinant and matrix inverse operation?
Been thinking through fitting a kind of Gaussian mixture model in more of a neural network style (kind of similar to RNADE or RMADE by Larochelle, without going into details) and see that this could ...
- 1,481
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Combination of probabilities for probability densities
Say, I have the following experiment: I have a large bucket of some material and I am trying to determine the melt temperature. So I take small samples and put them on a burner and note the ...
- 101
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Are there useful pmf/pdf factorizations if a subset of n random variables are mutually indepenent?
Example: Consider 3 discrete random variables X,Y,Z with pmf's denoted by P. If X and Y are mutually independent, then P(X,Y)=P(X)P(Y). Is there a useful way to factor P(X,Y,Z) using the info that X ...
- 101
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296
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Find PDF and CDF for bivariate distribution in R
I have a bivariate data with A=log-logistic B=weibull distribution;
...
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Test for multidimensional uniform density and representing lack thereof?
$Scientist_1$ seeks to maximize pumpkin size. They suspect that there are 6 key variables, that there are likely interactions between variables, and that there are kinks in the causal model. One ...
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89
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Empirical Density in R given posterior distribution
I am trying to solve the problem where I have calculated posterior distribution f(p|x) = Be(23,8) and prior f(p) = Be(1,1), given the n = 29 and x = 22.
representing the comparison by using
...
- 101
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1k
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Can the count data be used to calculate Kernel Density Estimate?
I have the number of amino acids in cytoplasmic domain for enzymes and non-enzymes for CD proteins.
I want to generate a probability density distribution for enzymes and non-enzymes using their ...
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37
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How to get the likelihood function of the following situation?
Consider a population with three kinds of individuals labeled, say, $1$,
$2$, and $3$ occurring in the following proportions: $p_1$ = $p^2$; $p_2 = 2p(1-
p)$; $p_3 = (1 - p)^2 \ ,(0 < p < 1)$. ...
- 213
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1
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99
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Need to know pdf of "x/z+sqrt(y^2-x^2)/z" , or any idea about its upper/lower bounds
I need to know the pdf of the following equation or any upper/lower bound would help. Let $X, Y, Z \sim N(0, \sigma^2)$. Then what is the distribution of:
$$A=\frac{x+ \sqrt{\mid y^2 - x^2 \mid}}{z}$$...
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553
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Composition of probability densities
There is a similarly worded question here but it doesn't quite answer my question.
I have three variables, $x, y, \text{and } z$, each with their own unique probability density functions. I want to ...
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How can I find the probability distribution function from the observed data to use in a Monte Carlo Simulation?
In exploring a data set, I think I've found an interesting instance where using a Monte Carlo method to plot a simulated group of points could yield somewhat accurate results.
The plotted data looks ...
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329
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Posterior Predictive Density of Linear Regression
I'm trying to derive the Posterior Predictive Density of a Linear Regression Model with a diffuse, uninformative prior such that we have:
$y_{i} = x_{i}'\beta + \varepsilon_{i}$ with $\varepsilon_{i}...
- 1,136
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2k
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Expected value with piecewise probability density function (PDF)
I am continuing the prepare for an exam by reviewing handouts from an old statistics course I took. The handout came with a set of solutions prepared by the instructor, but I suspect that one of the ...
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46
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Change of variables for a PDF of angles (circular/wrapped data)
I have a PDF with angle $\theta$ as the independent variable: $R(\theta)$. $\theta$ is defined up to mod $\pi$ -- accordingly, $R(\theta) = R(\theta + \pi)$. I need to express this PDF as a function ...
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466
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Calculating the PDF of the monotonic function of a Random Variable results in error
I am given the PDF of a random variable X and I am asked to calculate the PDF of the random variable Y = g(X) = 1/X (Y's domain is the interval [0,1]). By observing that g is monotonic I apply the ...
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How to show that a particular density is not a normal density
Let $\phi_{1}(x_{1},x_{2})$ and $\phi_{2}(x_{1},x_{2})$ be two different normal density functions with zero means, unit variances and different correlation coefficients $\rho_{1}$ and $\rho_{2}$ ...
- 213
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81
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Sufficient condition on variance of RV for solution to equation
Let $\tilde{\theta}$ be a non-negative random variable drawn from a twice continuously differentiable CDF $F(\theta) := \Pr\{\tilde{\theta} \leq \theta\}$ over the support $[0, \overline{\theta}]$, ...
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41
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Differences between these representations of classification problems in probability terms
Say that $\mathcal{X}$ is the set of observations, and $\mathcal{Y}$ is the set of classification labels.
Also say that $X$ is a continuous random variable that takes values in $\mathcal{X}$, and $Y$ ...
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201
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probability density function of a cumulative density function
I was reading that the probability density function (pdf say $f(x)$) of a cumulative distribution function (cdf say denoted as $F(x)$) is uniformly distributed from 0 to 1.
Basically this is what I ...
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1
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40
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formulating pdf from supports
for a pdf which is triangular, with support over (b, 2b) and a peak when x = 5b/3, what would the pdf be?
How do you determine a pdf from supports and a given shape?
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Density estimation for points regularly spaced on a grid? Infer spacing between pdf peaks?
Due to a fundamental characteristic of the data, points are clustered together on a 1-D grid-like structure with equal spacing.
Plotting these points in a histogram shows a pdf with several ...
- 703
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Find the density of a function of a random variable with known distribution
For example, if $X$ is a normal r.v than the distribution of $Z=X^{2}$ is (F is the CDF):
$$F_{Z}(z)=P(Z<z)=P(X^{2}<z)=P(-\sqrt{z}<X<\sqrt{z})=F_{X}(\sqrt{z})-F_{X}(-\sqrt{z}) −P(X=\sqrt{z}...
- 902
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833
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Joint Density and Covariance between Two Random Variables with the same Mean and Variance
This seems like a deceptively simple question, (and it perhaps is and I am missing something) but I could not find anything on this.
Q1)
Are there any general results / relationships to get the Joint ...
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36
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Is the following integral of a pdf an identity, i.e. always true?
I am reading a paper and the author starts a proof with this
$$
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 ...
- 1,275
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Calculating risk for a density estimator
I am trying to solve a textbook problem in Wasserman's "All of Nonparametric Statistics." I have run into a lot of messy integration and am confident that the crowdsource can show me what I am missing....
- 101
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145
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What are these "hyper-distributions" called?
This may be an elementary question. Say we have a univariate continuous random variable $X$ with unknown pdf $p(x)$, $ \forall x \in X$.
Presumably we can assign a second probability measure $Q(p)$ ...
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92
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Likelihood of a Poisson-described event to occur in the next second
Consider a recurring event for which the time periods between consecutive events is exponentially distributed. For argument's sake, I'm waiting for a taxi on a busy street. How might one calculate the ...
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1k
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Absolutely continuous probability distribution and its probability density
A Wikipedia article states:
A random variable $X$ has density $f_X$,
where $f_X$ is a non-negative Lebesgue-integrable function...
$F_X$ is the cumulative distribution function of $X$...
$...
- 177
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98
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beanplots: plus sign?
I would like to draw bean plots using the statsmodel package for Python.
In the example provided on the documentation, I see a red plus sign in each beanplot:
What does it represent?
- 489
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1
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8k
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Multiplication of two random distribution
I am trying to find the resulting PDF , when two random functions are multiplied.
First function obeys normal distribution and second function obeys cauchy distribution.
Can anybody tell me how to ...
-1
votes
1
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339
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Plot pdf of Random Variables
"Let x and y be independent random variables, which are both uniform in (-2,6) If z=x+y find and plot its pdf."
How can I draw this pdf?
My working:
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