# Questions tagged [cumulative-distribution-function]

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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### How to fit a function to a CDF in R?

Background: I've been given a dataframe that contains data for a CDF. The column X contains the 250 $X$ values, and the column P ...
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### Asymptotics of the survival function for Anderson Darling distribution?

I am using the ADinf procedure of Marsaglia & Marsaglia to compute the CDF of the Anderson Darling statistic. I am interested in the survival function, 1 minus ...
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### Cumulative distribution function for the product of two random variables

Given two random variables $x, y$, each with the probability distribution functions $p_x(x)$, $p_y(y)$, then if $z = xy$, then $p_z(z) = \int p_x(x)p_y(z/x)\frac{1}{|x|}dx$. Is there a similar proof ...
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### How can I convert kernel quantiles into sample quantiles?

I calculated the quantiles for an Epanechnikov kernel which I'm using to estimate the density of a sample. What I need is to find the sample quantiles knowing that it is composed of many Epanechnikov ...
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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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### Must the domain of a CDF be $\mathbb{R}$ or can it also be a strict subset?

So my question is whether the domain of a cumulative distribution function has to be $\mathbb{R}$ or whether it can also be a strict subset. The reason I'm asking is because I'm currently going ...
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### Under what conditions does the two-sided DKW inequality become a strict equality?

If the two-sided DKW inequality is tight, then there should be a choice of distribution and sample size where the equality holds. What is it?
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### What is the problem in my CDF derivation?

Let $Z = \frac{XY}{aX+bY+c}$ where the random variable $X$ and $Y$ follows gamma distribution such that $X\sim G(\lambda_x,\theta_x)$ and $Y\sim G(\lambda_y,\theta_y)$ The CDF of $Z$ can be ...
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### Finding probability of a point using bivariate copula density

I have a data in the form $\textbf{N} \times 2$. I am using bivariate copula to model the joint density of this distribution. Firstly, I fit 2 marginal distributions independently on each column of ...
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### Joint distribution of multivariate normal

Let $X$ and $Y$ be i.i.d. $N(0, 1)$, and let $S$ be a random sign (1 or -1, with equal probabilities) independent of $(X, Y)$. \begin{align*} P((SX,SY)∈B)&=P((X,Y)∈B,S=1)+P((−X,−Y)∈B,S=−1) \\ &...
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### How to add dependence between random vectors using a copula?

I understand that copulas can be used as a tool to add any conceivable dependence to a pair of random variables. However, I would like to add some dependence between two random vectors. Let us ...
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### It is true that $\mathbf X \sim F_X \Rightarrow F_X(\mathbf X) \sim U_{[0;1]}$; does the converse hold for multivariate $\mathbf X$?

For a univariate real-valued random variable I am pretty sure that the converse holds. Consider a multivariate $\mathbf X$ with values in $\mathbb R^n$ with measure $\mu(X)$ and its multivariate CDF ...
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### Equation for Inverse Poisson CDF

I am attempting to calculate quantile probabilities. I.e., the value above which there is only a 1% chance occurrence for an arrival process. The R code is pretty straight forward with say a lambda = ...
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### Conditional cdf

I want to know that how conditioning will affect the CDF of dependent random variables. More specifically, let's suppose, $\Gamma_R={g\over A}$ and $\Gamma_D={g\cdot h\over B}$, where $g$ and $h$ are ...
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### Joint CDF of random variables vis-a-vis that of their order statistics

Suppose $\{X_i\}_{i\in 1\ldots n}$ are $n$ independent, non-identically distributed RV's. Let $X_i \sim f_i(x) \mathbf{1}_{[0,1]}$, where $f_i$ is the $i$-th parent supported on $[0,1]$. I am ...
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### best visualization way to show a PDF+CDF to non-math people

EDIT: please ignore the actual formatting of the graph; it is meant as a demo and not "finalized". We are struggling to find the best way to present CDFs to our customers. They can read PDFs, but ...