# Tagged Questions

CDF is an acronym for 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.

26 views

62 views

### How to find the CDF of a random variable uniformly distributed around another random variable?

I'm working on some game theory models of incomplete information (which I've posted about a few times here). I think this question is pretty straightforward though, so the actual context is ...
94 views

### How to compute the CDF of this random variable?

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. Specifically, one player has the opportunity to choose any value $\eta$ from ...
20 views

### bivariate normal distribution & change of units

I need to find the bivariate normal CDF at the point (1 cm, 1 cm), i.e. the half-open interval $[-\infty,1] \times [-\infty,1]$ , where cm = centimeter, with mean = 0, covariance = Id. mvncdf( x = ...
39 views

### What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables

$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs. ...
49 views

### Densities and Cumulative Distribution Functions

Has anyone seen this notation before? What does it mean? $\int_{0}^{\infty} f(x) G(x) dx$ $f(x)$ is a density and $G(x)$ is a cumulative distribution function
49 views

### Finding the expected value of the cdf?

I have this question on a homework assignment, and I'm not sure how to solve it. Assume $X \sim \exp(\lambda=2)$, define $Y=F(x)$, where F(x) is the cdf function of $X$. Calculate the expected value ...
64 views

### P values and calculating residuals in chi-squared contingency tables

Given an n x m contingency table I calculate a chi-squared value and probability for that table telling me if there are cells that differ significantly from the mean. I go to calculate the adjusted ...
26 views

### Directly obtaining marginal cdf directly from joint cdf

I know how to obtain marginal PDF $f(x)$ from $f(x,y)$. Just integrate over $y$. But is there a way to directly obtain marginal CDF $F(x)$ from $F(x,y)$? Do I need to calculate marginal PDF $f(x)$ ...
38 views

### Uniquely determine the two parameters of a distribution given pre-determined probabilities for two disjoint subsets of its support

Let $F(x| \alpha, \beta)$ denote the cumulative density function of a probability distribution. Let $[a,b]$ and $[c,d]$ be two disjoint subsets of the support of $F$. Suppose that $F(b) - F(a) = p$ ...
56 views

### Conceptual question on random variables with the same cdf

Given a continuous random variable $X$ let $Z = F_X(X)$, where $F_X(s) = P(X \leq s)$. Then $P(Z \leq z) = z$ and we say that $Z$ is uniformly distributed. Say we have another continuous random ...
71 views

### 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 ...
72 views

### minimum cdf given mean and variance

Suppose I have some distribution with mean $\mu$ and variance $\sigma^2$. How to prove that for the distribution to have min $cdf$ over all the distributions with mean $\mu$ and variance $\sigma^2$, ...
78 views

### How do I determine parameters of normal & lognormal distribution given two points?

Assume I have two values which represent two quantiles for the same lognormal and/or normal distribution. How can I determine the parameters of the distribution? ...
156 views

### How are the Error Function and Standard Normal distribution function related?

If the Standard Normal PDF is $$f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$$ and the CDF is $$F(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-x^2/2}\mathrm{d}x\,,$$ how does this turn into an error ...
30 views

### Is it reasonable to estimate the CDF of a random variable with the help of kernel density estimation?

Given a set $S$ of samples from a random variable $X$ with pdf $f$ and cdf $F$, is it reasonable to estimate $F(x)$ by finding an estimation $\hat{f}$ of $f$ via kernel density estimation on $S$, and ...
39 views

### Numerically finding confidence interval bounds

I am asking an R question here on the basis that statistical expertise is needed, i.e., If the language is statistically oriented (such as R, SAS, Stata, SPSS, etc.), then decide based on the ...