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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2
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1answer
37 views

How to extend PDF of normalized sample to original sample?

To calculate the PDF function using Shannon entropy I have scaled my original sample by simply doing $x'=(x-a)/(b-a)$; where $b=\text{max}(x)$, and $a=\text{min}(x)$ and then I found the ...
2
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2answers
68 views

Identifying distribution of a variable

Consider a variable that can take both negative and positive values, and that has the following density plot: I am trying to identify the distribution of this variable. The density plot resembles ...
0
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0answers
11 views

What is the proper way to compare two estimated densities using sample data?

Say if have a dataset $X \subset \mathbb R^d$. I have two candidate probabilistic models M1 and M2 (e.g., M1 is a mixture of 2 gaussians and M2 is a mixture of 3 gaussians). I want to know which model ...
0
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1answer
26 views

How to bridge between seemingly unrelated but congruent PDF and PMF?

Let's assume a probability mass function $P$ on the discrete domain $\{0,...,N\}$ and a density function $f$ and the existence of two real factors $a$ and $b$ so that we have for all numbers $k$ in ...
0
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0answers
11 views

How to delete the noise when I try to calculate the inflection points from the density curve?

I need to get the inflections points from the density curve, and the get a method from the following link: Getting the inflection point(s) from a density plot But for my graph: When I try to use ...
0
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0answers
21 views

How to find the inflection point from my density plot curve? [duplicate]

I sampled the data qtl_500(50,000 points), and get the density curve of it as follow: plot(density(qtl_500k)) Now I hope to get the inflection point of this curve. Could anyone please give me ...
0
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1answer
47 views

Why does fitdistr does not work with gamma?

I am tring to find a probability density for some waiting time, but I am having a hard time. Fitdistr does not work with Gamma. Am I missing something? Is there ...
1
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0answers
30 views

Marginal distribution of a function of order statistics

From the joint distribution of any two order statistics, say $Y_j$ and $Y_k$, $j<k$ I would like to derive the distribution of $Z=F(Y_k)-F(Y_j)$. The initial pdf is: $$f_{Y_j,Y_k} (y_j,y_k) ...
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0answers
34 views

How to estimate distribution from DataBase?

I am currently working on a programme to compute the mutual information between a variable and a set of variables. Since I am working with discrete data, I am computing $\sum_{a\in A,b\in B,c\in ...
2
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1answer
42 views

showing a random variable has an exponential distribution

Let $X_{1},..,X_{n}$ be independent, each with a exp($\lambda$) distribution. Let $Z=min(X_{1},..X_n)$. Show that $n\lambda Z$ has an exp$(1)$ distribution. I calculate that $P(Z>z)=e^{-n\lambda ...
1
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0answers
13 views

Wilks's lambda distribution

Please help me, I don´t have any idea how to solve this problem. If $\textbf{A} \sim W_p(\mathbf{\Sigma}, m)$ and $\textbf{B} \sim W_p(\mathbf{\Sigma}, m)$ are independent Wishart matrices, show that ...
1
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0answers
12 views

Estimating distribution function for dependent observations

Let $X_1,\dots,X_n$ be identically but not necessary independent distributed with distribution function $F$. I'd like to estimate $F$ efficiently. In case, $X_1,\dots,X_n$ are i.i.d., we can estimate ...
0
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1answer
22 views

Derive the conditional pdf of data on prior parameters

In Bayesian statistics I see this derivation often. Given the likelihood function $f(X|\theta)$ and the prior $f( \theta |a, b)$, the author will derive $f(X|a,b)$. The steps in between are ...
3
votes
3answers
206 views

Determining the probability of $X_2 \ge X_1$ given they have different probability functions

Suppose that I have a random variable $X_1$ which is normally distributed, and a random variable $X_2$ having the density function shown in the figure below. How would I determine ${\rm P}(X_1 \le ...
1
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0answers
41 views

Need a working algorithm to find out optimal kernel bandwidth for density estimation

I am looking for a working algorithm for find out optimal kernel bandwidth for density estimation. I need to write my own program in pascal instead of using R or Matlab. So far all algorithms I ...
1
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0answers
18 views

Sampling from an arbitrary distribution with unknown CDF

I have a continuous distribution whose PDF I know the expression for but whose CDF is difficult to compute analytically. I understand that if I know the CDF value, then I can use inverse transform ...
0
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0answers
36 views

Conditional density plots with two continuous variables in R

I am very new to R. I have to create conditional density plots with two continuous variables. I have found a nice example with which to start, however this sample ...
1
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0answers
26 views

Is the multivariate Gauss the only pdf incorporating covariances?

I am wondering whether there is another probability density function known to literature which is similar to the multivariate normal distribution in the respect that the pdf incorporates the ...
0
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0answers
30 views

How to find out optimal KDE bandwidth via Bootstrap Aggregation

I am a programmer and trying to do some data analysis. Since I am very interested in statistics, and I have learned a lot of programming languages, learning how to use professional packages such as ...
0
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1answer
25 views

Joint expectation of normal distribution

I have a vector $v=(v_1,...,v_J)$, which is jointly normal. I then need to take the expectation of this vector. This should give me something like this: 1)$$E(v)=(E(v_1),...,E(v_J))$$ However, I ...
1
vote
1answer
45 views

Probability density function within [0,1] with specifiable mode

I needed a probability density function which worked on the interval $[0,1]$, had kind of a bell shape, and had an adjustable mode / peak $p$. I thought of a pdf $f(x|p)$, given by \begin{equation} ...
0
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0answers
25 views

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?
1
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2answers
65 views

If $X$~$Exp(1)$ and $Y$~$Exp(2)$, what is the pdf of $Z=X+Y$?

I am trying to find the following: If $X\sim\mathrm{Exp}(1)$ and $Y\sim\mathrm{Exp}(2)$, what is the pdf of $Z=X+Y$? I tried to use the convolution formula but am not sure what the limits of the ...
3
votes
1answer
37 views

Given $n$ different univariate non-normal sample sets calculate for a new sample, $x$, which it most likely belongs to [duplicate]

Say you have $n$ different, non-normal, potentially overlapping data sets of samples. Maybe their densities look something like: and you are given a new sample $x$, how would you decide to which of ...
1
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0answers
30 views

Why it is better to use the cumulative distribution to compute distances?

In the comments of this question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution ...
1
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1answer
36 views

Normalizing constant & rejection sampling

I think I understand what a normalizing constant is. Say for example you have a pdf $f(x)$ with support $0 \le x \le 5$. If you wanted to truncate the pdf and only look at $0 \le x \le 3$ you would ...
4
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4answers
206 views

What is the meaning of the density of a distribution at a point?

I know how to use PDFs to calculate probabilities, but I don't think I understand them. For example, at $X=0$ the PDF of the standard normal distribution is $\approx 0.4$. Does this have any useful ...
8
votes
1answer
113 views

Why is $E[Z|Z>c] = \int_c^\infty z_i \phi({z_i})\mathrm{d}z_i $ ($Z$ is censored)

In a problem set I proved this "lemma," whose result is not intuitive to me. $Z$ is a standard normal distribution in a censored model. Formally, $Z^* \sim Norm(0, \sigma^2)$, and $Z = max(Z^*, c)$. ...
3
votes
2answers
94 views

Why do a density plot and a rug plot seem to disagree?

The second peak of the density plot is large in this example. Why does the rug representation of the data--which seems to show few high values--not appear to match ...
5
votes
1answer
164 views

How to describe/explain the shape of a distribution which has two peaks?

How can I describe the shape of the following distribution, which has two peaks? What are the important things in describing the distribution shape? It is the output of the following ...
2
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0answers
47 views

Expectation of density ratio of two iid variables

Let $X \sim N(0,1)$ and $Y \sim N(0,1)$ be independent RVs and let $f$ be their density function. I'd like to compute the expectation of the density ratio \begin{align} ...
2
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2answers
199 views

Is it possible to convert a Rayleigh distribution into a Gaussian distribution?

...and how might we do this? If possible, I am curious if outliers in the Rayleigh distributed data would also remain outliers in the new Gaussian distributed data. Thanks.
1
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1answer
88 views

What is a density function?

I know about histograms and also know that if we connect the mid-points on the top of bars in a histogram we will get a frequency polygon. This polygon could then be 'smoothed' in a way that it ...
1
vote
1answer
58 views

What's a distribution with an abyss instead of a peak?

I am looking for a (commonly used) probability density function, which would look like a normal distribution flipped upside down. It would look like a uniform distribution with a dent in the middle. ...
4
votes
1answer
44 views

Relationship between tail behavior of a density function and the radius of convergence of its Taylor expansion

Given a continuous probability density function $f(x)$, whose Taylor expansion is $f(x) = \sum\limits_{n=0}^\infty a_n x^n$ with radius of convergence $r$. Can we say something about the relationship ...
3
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0answers
33 views

Shouldn't a function of data from a PDF repeated over and over on new data eventually yield a Gaussian PDF?

I got into an interesting discussion with a co-worker today and we are not sure what the answer is: We have $N=1000$ samples from a Rayleigh PDF. We take those $N$ samples, and compute their ...
4
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1answer
49 views

Estimate probability of event using moments of a distribution or a Taylor expansion involving the moments

Let's say we have four moments $(\mu_1, \mu_2, \mu_3, \mu_4)$ of a probabilty distribution of a random variable $X$ and the goal is to get the probability $\rm{P}(X \leq t)$ for a certain value of ...
1
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0answers
50 views

Probability density estimation with Dirichlet process

I'm trying to estimate a joint probability density function in a quite high dimensional space (around 15 or even more). I've heard about Dirichlet process methods to do this kind of things. Do you ...
1
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1answer
71 views

Delta function in monte carlo sampling

I am confused by the dirac delta function in the formulation of monte carlo sampling. http://www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf, for instance, defines in section 3.1 page 8 the ...
1
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2answers
71 views

Ordered gamma variables led to an ugly integral

Suppose $X_1,X_2,...X_n$ are i. i. d. random variables with p. d. f. $$f(x)=xe^{-x}I_{(0,\infty)}\!(x)$$ and let $Y_1,...,Y_n$ be the order statistics for these variables. a) Find the conditional p. ...
2
votes
0answers
39 views

Sum of random vectors with fixed amplitudes

Is there a simple way to evaluate the pdf of the amplitude of a sum of vectors with fixed amplitudes and random phases? Explicitly, let $Ae^{i\phi}=\sum_{n=1}^NA_ne^{i\phi_n}$, where $N$ is a fixed ...
2
votes
1answer
76 views

Fitting a probability distribution to non i.i.d. data? [closed]

I have temperature time series data that I have determined is not independently and identically distributed (from looking at the autocorrelation plots and Ljung-Box tests). However, I am still able ...
2
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0answers
43 views

Excepted conditional density and conditional expectation

Apparently one can obtain a regression analysis as $$g(x)=\frac{\int yf(y,x)dy}{f(x)}$$ where $$f(x)=\int f(y,x)dy$$ is the marginal density of $X_i$. In effect, I believe, the above expression ...
8
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3answers
197 views

Where is density estimation useful?

After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three ...
9
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3answers
705 views

Which to believe: Kolmogorov-Smirnov test or Q-Q plot?

I'm trying to determine if my dataset of continuous data follows a gamma distribution with parameters shape $=$ 1.7 and rate $=$ 0.000063. The problem is when I use R to create a Q-Q plot of my ...
2
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1answer
38 views

Probability distribution satisfying constraints?

Reposted from Math.SE: Continuing from this question. Given two random variables $X$ and $Y$ where $X \sim \operatorname{Beta}(a, b)$ and $Y \sim \operatorname{Beta}(c, d)$, I'm looking for a random ...
0
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1answer
29 views

A random variable that is invariant under null & alternative hypotheses

Suppose a random variable $X$ has probability density function $f_0$ and $f_1$ under null and alternative hypothesis, respectively. Is it possible to find another random variable, $g(X)$, which has ...
2
votes
1answer
73 views

Discovering a distribution and plotting a trendline in excel

My wife is a server at a restaurant and I've been tracking her tips over the last 9-10 months. The domain of her set is $[\$75,\$702]$ with a mean of \$236.7 and a standard deviation of \$106.64. ...
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2answers
49 views

What is the expected partial value function really called?

If f is a pdf, the integral of x*f(x) over the entire range where f(x) > 0 gives, of course, the expected value. Suppose that integrate the same function, x*f(x) from negative infinity up to t, ...
0
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2answers
86 views

Struggling with copula theory

I'm really struggling with bivariate copula's. Long story short, I can only use Gaussian copulas. I'm therefore interested in the joint PDF for which the Gaussian copula can be applied. So for ...