# Questions tagged [pdf]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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### Bivariate Gamma distribution PDF

I'm analyzing a set of data, and I like to fit a gamma distribution. I know how to do it in one dimension, but the data that I'm analyzing now are two dimensional. Is there any way that I can have a ...
3answers
759 views

### How to formally test for a “break” in a normal (or other) distribution

It frequently comes up in social science that variables that should be distributed in some way, say normally, end up having a discontinuity in their distribution around certain points. For instance, ...
2answers
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### Histogram/distribution fitting for this dataset with unequal and open-ended intervals?

I have this income distribution data for various groups: https://docs.google.com/spreadsheet/ccc?key=0Akwg3n_e05cCdEdtT0VZYU5keW5DVkNoNmpBWmdzeUE As you can see, I have intervals/bins with varying ...
5answers
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### Does a univariate random variable's mean always equal the integral of its quantile function?

I just noticed that integrating a univariate random variable's quantile function (inverse cdf) from p=0 to p=1 produces the variable's mean. I haven't heard of this relationship before now, so I'm ...
4answers
82k views

### How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?

Given the random variable $$Y = \max(X_1, X_2, \ldots, X_n)$$ where $X_i$ are IID uniform variables, how do I calculate the PDF of $Y$?
3answers
300 views

### How to analyse data on metric space?

I just ran an experiment and I'm not sure how best to analyse the data. My data are distance values between objects in a metric space bounded by [0,1]. I have drawn up a probability density estimate ...
1answer
369 views

### Cumulative Distribution Function problems

Let $a$ and $b$ be two positive integers. Let also $X$ be a discrete random variable varying in $X(\Omega)=\{1, 2, \ldots, ab\}$ such that for every $x∈X(\Omega),P[X = x]=1/a - 1/b$. a) What ...
0answers
296 views

### Goodness-of-fit test without analytical PDF and CDF

I have closed form moment-generating function and characteristic function of a distribution, which describes waiting time of a continuous univariate random process. However, I cannot analytically ...
1answer
820 views

### What is the best way to visualize a single numeric variable as a heatmap?

I'm a hobbyist programmer whose friend recently took a business trip overseas. He's polled our mutual friends for bets on the size of his email inbox when he returns. I'd like to visualize this as a ...
1answer
1k views

### Problem printing greyscale or B&W ggplot2 images

I have an issue with printing/creating black and white and greyscale images with ggplot2. I have been trying to make some black and white, and greyscale graphics for publication, they look perfect on ...
1answer
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### What are density and intensity of point pattern?

A simplified explanation with the focus on the following questions is being inquired. Appreciation goes in advance to whom provides scientific--simple--practical explanation. Having an area A ...
1answer
196 views

0answers
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### Modeling membership function given some survey data or empirical distribution

For example, I have a set of numbers (say 0 to 10) that are presented to 100 subjects. Each subject is asked whether the number is a small or a large number. The results are that 100 people think ...
1answer
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### Marginal distribution of the diagonal of an inverse Wishart distributed matrix

Suppose $X\sim \operatorname{InvWishart}(\nu, \Sigma_0)$. I'm interested in the marginal distribution of the diagonal elements $\operatorname{diag}(X) = (x_{11}, \dots, x_{pp})$. There are a few ...
3answers
5k views

### Closed form formula for distribution function including skewness and kurtosis?

Is there such a formula? Given a set of data for which the mean, variance, skewness and kurtosis is known, or can be measured, is there a single formula which can be used to calculate the probability ...
1answer
103 views

### Given pdf of $I$ and $R$ (both $I$ and $R$ are independent RV's), how to find pdf of $W =I^2\cdot R$?

The title defines the question. May be the concept would do...like how to go about it? Thanks.
3answers
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### Best way to put two histograms on same scale?

Let's say I have two distributions I want to compare in detail, i.e. in a way that makes shape, scale and shift easily visible. One good way to do this is to plot a histogram for each distribution, ...
2answers
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### How can I display empirical pdf of my 100x1 vector data in Matlab?

I have a data which is 100x1 vector. How can I display its empirical pdf in Matlab? Also, if I want to compare the pdf of three vectors on the same graph, then how to do that? Right now I am using ...
4answers
46k views

### Difference between histogram and pdf?

If we want to visibly see the distribution of a continuous data, which one among histogram and pdf should be used? What are the differences, not formula wise, between histogram and pdf?
2answers
2k views

### Kernel bandwidth in Kernel density estimation

I am doing some Kernel density estimation, with a weighted points set (ie., each sample has a weight which is not necessary one), in N dimensions. Also, these samples are just in a metric space (ie., ...
3answers
909 views

### Series expansion of a density function

Here's something I've wondered about for a while, but haven't been able to discover the correct terminology. Say you have a relatively complicated density function that you suspect might have a close ...
2answers
67k views

### Finding the PDF given the CDF

How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?