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# Questions tagged [cdf]

Cumulative distribution function. While the PDF gives the probability density of each value of a random variable, the CDF (often denoted $F(x)$) gives the probability that the random variable will be less than or equal to a specified value.

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### What is the expectation of the following joint CDF?

Yesterday, I asked the following question regarding copulas: "Let's say $X=(X_1,X_2)′$, where $X\in \mathbb R^2$. What is the expectation of the copula function $C(F_{X_1}(x_1),F_{X_2}(x_2))$ - i.e....
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### What is the expectation of copula function? [duplicate]

Let's say $X=(X_1,X_2)'$, where $X\in \mathbb{R}^2$. What is the expectation of the copula function $C(F_{X_1}(x_1),F_{X_2}(x_2))$ - i.e. $\mathbb{E}_X\left[C(F_{X_1}(x_1),F_{X_2}(x_2))\right]$?
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### How to graph distribution of Order statistics?

Is there a software that can graph the pdfs and Cds of an arbitrary number of order statistics or is there some code such software? How to do it? I'm trying to understand the distribution of order ...
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### Efficient sampling from a multivariate Gaussian Mixture distribution for a given CDF level

I have a multivariate Gaussian Mixture (GM) distribution. I am wondering if there is any more efficient way of drawing samples (i.e., identify the iso-surface) from a multivariate Gaussian Mixture ...
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### How to show CDF uniquely determined from equation

I have the following equation for a CDF that I would like to show is uniquely determined: $$\frac{h_1(x)}{f(x)}=\int_x^a h_2(z)(F(z)-F(x))^k\;dF(z)$$ Here $F$ is the CDF and $f$ is the PDF, which I ...
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### Non-uniqueness of a CDF in N >= 2

Peacock in his paper on 'Two-dimensional goodness-of-fit testing in astronomy', http://adsabs.harvard.edu/full/1983MNRAS.202..615P, described the issue with the non-uniqueness of CDF in higer (N >= 2) ...
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### If we know the cumulative distribution function (cdf) can we determinate the random variable?

I got this question from my teacher yesterday. In my opinion the answer is no, but I can't prove it with a specific example (dice,dime or something). I was thinking also about a reductio ad absurdum ...
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### getting a density function from a sample of 500

I'm pretty new to statistics so please excuse me if the answer is obvious. The scenario is the following: I am using mcmc to sample from a posterior distribution of a parameter. I then need to ...
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### Given a pmf, how is it possible to calculate the cdf?

Given a pmf (probability mass function) for X (random variable): \begin{array}{|c|c|c|c|c|}\hline x&1&2&3&4\\ \hline p(x)&0.4&0.3&0.2&0.1\\ \hline \end{array} How ...
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### Acceptance/rejection sampling and inverting CDF (R code illustration included)

I have the following example: Acceptance/rejection sampling In some cases the cumulative distribution function might not be (easily) invertible. For example if $X$ has the probability density ...
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### What is the difference between Empirical and analytical PDF and CDF? More Precisely what would be the difference in their plotting?

I am relatively new to statistics with no statistical background whatsoever, I have an assignment in which i have to plot different distributions in these four manners, i have a gist of empirical PDF ...