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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128 views

How do you find a cutting point / strong slope within one-dimensional data

I have one-dimensional data. I want to find possible natural cutting points (strong slopes) within the data. For instance, if the data is ...
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1answer
15 views

R: MLE estimation of transition probability density (CIR)

I am trying to replicate the model Zhang and Zhu (http://onlinelibrary.wiley.com/doi/10.1002/fut.20209/epdf) used to get the parameters of a stochastic volatility model. Therefore, I determinded the ...
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1answer
21 views

Pattern Recognition - Visualizing Dense Data Points

I have a sample of around 5000 data (2D) points that are generated through a simulation of a cryptocurrency's mining events of following form. In column 2 one can see identical y-values with ...
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2answers
162 views

relation between probability and probability density function

According to this link: PDF To translate the probability density $ρ(x)$ into a probability, imagine that $I_x$ is some small interval around the point $x$. Then, assuming $ρ$ is continuous, the ...
2
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2answers
74 views

Why is the CDF of a sample uniformly distributed

I read here that given a sample $ X_1,X_2,...,X_n $ from a continuous distribution with cdf $ F_X $, the sample corresponding to $ U_i = F_X(X_i) $ follows a standard uniform distribution. I have ...
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0answers
17 views

Pmf of compound Poisson process

Can I obtain an analytic expression for pmf of compound Poisson process? $Y_t = \sum \limits_{i=1}^{Xt} D_i$ where $X_t$ ~ Poisson($\lambda$) and $D$ ~ Geometric($\rho$)
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1answer
38 views

why we use precision instead of variance in prior?

I am new comer in stat field. I am wondering about using precision instead of variance in prior.
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1answer
35 views

Probabilities of conditional expectation values in uniform distribution

Let's consider a continuous random variable $X$ as follows: $f_X(x)=\left\{ \begin{array}{ll}\frac{1}{2}, &\mbox{if} \ x\in[0,1] \\ \frac{1}{4}, &\mbox{if}\ x\in(1,3]\end{array}\right.$ ...
2
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1answer
38 views

Why does phase randomizing the Fourier transform of a data set render it Gaussian?

Let's say I have a data set $s_n$. I take the Fourier transform of this data set to obtain $\tilde{s}_n$. I randomize the complex phases of $\tilde{s}_n$ and I take an inverse transform to obtain ...
6
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1answer
148 views

Fastest way to solve Bayes estimator problem

The below problem is from an old PhD qualifying exam in our department. My own solution below is time-consuming and quite possibly wrong. It also relies on recognizing a less common distribution, so I ...
3
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1answer
28 views

sampling distribution of the mean for arbitrary 1-D pdf

I want to compute the sampling distribution of the mean for $k$ samples from an arbitrary, known probability density $f(x)$, with $x \in \mathbb{R}$. What is the most efficient way to do so ...
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0answers
12 views

Parameter estimation from unknown noise pdf

I have a noisy time series assumed to be the output of a linear process. My problem is that I do not know the pdf and hence I cannot estimate the parameters of the process model. I apply density ...
2
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1answer
64 views

Copula density function

In the equation $h_t(x,y|...) = ...$, can anyone explain me why the first derivatives of the marginal distributions are included? $H_t$ is a distribution function and $h_t$ its density function. ...
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3answers
92 views

Difference between density and probability [duplicate]

What is the difference between the density and probability? I have tried R in which I can use both pnorm and dnorm for the ...
0
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0answers
33 views

Why does my multivariate normal have a density greater than 1 (log-likelihood greater than 0)? [duplicate]

I am calculating the log-likelihood of multivariate Gaussian distribution. I am getting a positive log-likelihood. Density function ...
1
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0answers
42 views

Relationship between the Gamma and Beta distributions

I was looking at a proof of the following fact Let $X \sim \mbox{Gamma}(\alpha, 1)$ and $Y \sim \mbox{Gamma}(\beta, 1)$ where the paramaterization is such that $\alpha$ is the shape parameter. Then ...
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1answer
41 views

Proof for the p.d.f of minimum and maximum of a sample

The following is a question from a past paper for one of my university statistical inference modules, and I know how to use the formula for each the max/min, but Assume that the sample $X_1, X_2, ...
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0answers
35 views

2D Kernel density estimation with uncertainties

I would like to perform bivariate KDE with Gaussian kernels (preferably using Python, or R) of a dataset with heteroscedastic uncertainties. What would be the correct way to do this: to rescale a ...
2
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2answers
63 views

How to compute a marginal probability function from a joint probability function?

I am looking at part a) and I have found the marginal p.f for $Y$ to be $e^{-2}2^{y}/y!$. I have set up for the equation for the marginal p.f for $X$ but I have no idea how to start it. Help would ...
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1answer
66 views

Is every cumulative probability density function Borel measurable?

I have seemingly simple question, which does not need to have a simple answer :) Is every cumulative probability density function Borel measurable?
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0answers
40 views

Imposing a model on a pdf

(This question is an attempt to zoom in on the key issue in this question using as little information as possible.) Lets say I want to derive the likelihood function of $\beta$ given $x$ and $y$ for ...
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0answers
41 views

Derivation of likelihood function for latent variable model made explicit

I am trying to make the steps deriving the likelihood function for the following latent variable model as explicit as possible: $$Y^0=X\beta + u$$ where $$u \sim NID(0,\sigma^2).$$ The observed data ...
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0answers
14 views

Estimate density before or after separating into pre-defined bins?

I want to estimate the density of positive real item price data so that I can predict expected revenue per transaction given a known service fee schedule. Suppose also that the fee schedule is defined ...
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1answer
50 views

Probability Density Functions of a Worker and his Waking up routine

The Problem: A worker wakes at 6 am and lies in bed for up to 2 hours. Upon rising it takes him an hour to shower and prepare which is preceded by him doing whatever he pleases. He never leaves for ...
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0answers
36 views

How to extrapolate future probability density functions if you have a time series of them as input?

I'm sorry for lack of technical vocabulary, I'm not a mathematician but an undergraduate student in business informatics. This is my current situation: I am given an observations vector ...
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1answer
53 views

Understanding “the kernel has zero mean”

I am trying to understand kernel density estimation and found the graphic below illustrating different kernel functions on Wikipedia. I have no trouble reconciling it with the two statements "the ...
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0answers
18 views

Multivariate extension of Welch-Satterthwaite approximation

The Welch-Satterthwaite approximation can be used to approximate the distribution of sums of gamma random variables. See section 4.1 here, for example. Can we use a corresponding approximation for ...
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0answers
11 views

Additive best-fit parametric kernel estimation?

I'm thinking of a process similar to kernel density estimation, but using fitted kernels. The process would be something like this: Create a histogram $H_1(x)$ with infinitesimal bins (such that the ...
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0answers
35 views

How does the stats.gaussian_kde method calcute the pdf?

I am using the scipy.stats.gaussian_kde method from scipy to generate random samples from the data. It works fine! What I have ...
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0answers
19 views

Interpreting Poisson regression: Deriving results from the CDF

I am trying to interpret a Poisson regression without being very interested in the mean. As a complication, I also have an exposure variable. Let $y_i$ be a count variable, and $p$ the offset, for ...
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0answers
30 views

Estimate density dependent on another variable

I have an (unknown) random function $y=f(x)$, i.e. for each value of $x \in [0,1]$ it is a random variable with some distribution. Also I can sample this function, and got values of $y$ for many ...
2
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2answers
64 views

How is $p_{i}$ for a set of continuous data points related to the probability function $f(x)$?

I have the following set of continuous measurements: 155.08 178 264.81 238 378 140.38 130.5 140.69 155.5 To average this data, I sum the values and divide by the ...
2
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1answer
91 views

Overlap between two normal pdfs [duplicate]

I have two normally distributed random variables (estimated from two different sets of samples), and I'd like to know how "similar" those variables are (in order to compare the sets). I had the idea ...
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1answer
57 views

How to interpret height of density plot

How should I interpret the height of density plots: For example in the above plot, peak is at about 0.07 at x=18. Can I infer that about 7% of values are around 18? Can I be more specific than ...
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11 views

How can I write a skew-normal distribution function given these 3 points?

Suppose I have a set of normally distributed data with mean µ, such that 34% of the data lie between µ–σ and µ, and 34% more of the data lie between µ and µ+σ. Then we know I can write a distribution ...
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1answer
88 views

How to find the normalizing constant for a distribution of unbounded support?

The probability density of a random variable is $$f(x) = ax^2 e^{-kx} ;k\gt0,0\le x\le \infty$$ What is the value of $a$? I understand that first we'll have to take the integral of the function ...
2
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1answer
160 views

Deriving Density Function (pdf) from Distribution Function (cdf)

A random variable $V$ has the distribution function: $$ F(v) = \begin{cases} 0, & \text{for $v<0$ } \\ 1-(1-v)^A, & \text{for $0\le v\le1$ } \\ 1,& \text{for $v>1$ } \\ \end{cases} ...
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0answers
29 views

Why small values produce undulating densities when ploting logarithm of a loguniform prior (in R)?

I am using a program that draws random values in a log-uniform distribution let say between 1 and 100. When I plot the density of the produced values with R it looks like a log-uniform distribution ...
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0answers
53 views

What is the name of this distribution family?

I am trying to identify this probability density function so I can read up on it to find confidence intervals for $\theta$: $$f(x;\theta,v)=\frac{\theta v^\theta}{x^{\theta+1}}I_{[v,\infty)]}(x);\ ...
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26 views

Is there any general formulation procedure of probability density functions?

There are so many probability density functions for continuous variables around the world. Unlike the probability mass functions of discrete variables, these PDFs do not directly give you the ...
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0answers
20 views

Distribution with fixed mean and closest to a given distribution

I was wondering if this problem has been tackled in some way in the probability/functional analysis literature: Given a pdf $f$ such that the expectation is zero and $\mu\in\mathbb R$, find the ...
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0answers
17 views

Find the mean of lognormal rv's with available variance and the sum of rv's

I have the sum of a bunch of random variables $S$, v = [1 1 2 2 3 3 4 ...]; S = sum(v); I know that vector $v$ is lognormally distributed, BUT I DON'T KNOW IT. ...
2
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1answer
207 views

PDF of dependent variables

In my recent question an answer was given, and I am able to compute it myself. Still, I'd like to understand where does that answer come from. Hence, what's the approach to handle dependent variables ...
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0answers
46 views

Compute a PDF in Mathematica/mathStatica [closed]

Let $X,Y$ be iid uniform in $[0,1]$ RVs, and $U$ has a PDF $f_U(u)=\frac{1}{4}\ln\left(\frac{4}{u}\right)$, $u\in(0,4]$. Mathematica itself is able to compute the PDF of $X+Y+\sqrt{(X-Y)^2+U}$ (see my ...
2
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0answers
24 views

Multivariate distribution for products of random variables

Suppose I have an $n$-dimensional complex, zero mean normal distribution with covariance matrix $\Sigma$, which is not diagonal. Denoting each of the random variables as $x_1, \dots ,x_n$ I would ...
6
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0answers
100 views

What is the name of the density estimation method where all possible pairs are used to create a Normal mixture distribution?

I just thought of a neat (not necessarily good) way of creating one dimensional density estimates and my question is: Does this density estimation method have a name? If not, is it a special case of ...
6
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2answers
105 views

PDF of a sum of dependent variables

This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
3
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1answer
52 views

Moments and density tails

Assume that the first $n$ moments $m_1,\dots\,m_n$ of a random variable $X\in\mathbb{R}$ are known, but not its probability density function $p(x)$. Does there exist a methodology to characterize ...
13
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2answers
234 views

What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?

I have four independent uniformly distributed variables $a,b,c,d$, each in $[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be ...
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0answers
13 views

Student t distribution: standardization [duplicate]

I got a question concerning the standardization of a student t distribution. I see that the "plain vanilla" t distribution has density $f(x|\nu)=\frac{\Gamma(\frac{\nu+1}{2}) ...