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.

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CDF/ ECDF plot for data with two attributes

I have a data in the following format: $$ \begin{array}{rr} \textbf{colm_1} & \textbf{colm_2}\\ 3 & 1\\ 10 & 0\\ 3 & 0\\ 100 & 1\\ . & .\\ . & . \end{array} $$ colm_1 are ...
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1answer
143 views

What is the two-sample CDF of of $D^{+}$ and $D^{-}$ from the one-sided Kolmogorov-Smirnov Test?

I am trying to understand how to obtain $p$-values for the one-sided Kolmogorov-Smirnov test, and am struggling to find CDFs for $D^{+}_{n_{1},n_{2}}$ and $D^{-}_{n_{1},n_{2}}$ in the two-sample case. ...
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1answer
33 views

Discrete analog of CDF: “cumulative mass function”?

We call the integral of a probability density function (PDF) a cumulative distribution function (CDF). But what's the cumulative sum of a probability mass function (PMF) called? I've never heard the ...
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4answers
397 views

Calculating PDF given CDF

I know that the PDF is the first derivative of the CDF for a continuous random variable, and the difference for a discrete random variable. However, I would like to know why this is, why are there ...
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2answers
73 views

Approximation of logarithm of standard normal CDF for x<0

Does anyone know of an approximation for the logarithm of the standard normal CDF for x<0? I need to implement an algorithm that very quickly calculates it. The straightforward way, of course, is ...
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1answer
88 views

Integrating an empirical CDF

I have an empirical distribution $G(x)$. I calculate it as follows x <- seq(0, 1000, 0.1) g <- ecdf(var1) G <- g(x) I denote $h(x) = dG/dx$, ...
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34 views

How to calculate CDF of g(X)

Let $X$ a random variable with distribution $F_X(x)$ $$Y=g(X) = \left\{ \begin{array}{lr} X-c & : X > c\\ 0 & : -c < X \le c \\ X+c & : X \le -c \end{array} \right\}$$ ...
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1answer
49 views

Rectifier function of random variable

Let $X$ be a random variable with distribution $F_X$ and density $f_X$. Define $$g(x) = \left\{ \begin{array}{lr} x & : x \ge 0\\ 0 & : x < 0 \end{array} \right\}$$ and let ...
2
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1answer
67 views

Non-central scaled Student's t cumulative density function required (alternatively the pdf)

I need to cite the pdf(density) or cdf(distribution function) of a non-central scaled Student's t distribution. There is an article about the non-central Student's t distribution ...
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20 views

Kolmogorov–Smirnov “with perturbation”

Let $F$ be known continuous CDF of a continuous R.V. and $F_n$ represent the empirical CDF for sample of size $n$, hypothesized to be drawn from $F$. The Kolmogorov–Smirnov statistic is $D_n :=sup ...
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23 views

Distribution of number of values less than cutoff within symmetric Dirichlet

Assume have a symmetric Dirichlet distribution with $a_1= \dots =a_k = a$ $ (X_1, \ldots, X_K)\sim\operatorname{Dir}(a) $ I am trying to determine the distribution of the number of values less than ...
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1answer
172 views

Why can't one generalize the Kolmogorov-Smirnov test to 2 or more dimensions?

The question says it all. I've read both that one can't generalize KS to a dimension equal or larger than two, and that famous implementations like that in Numerical Recipes are simply wrong. Could ...
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0answers
15 views

Tail probabilities and the GHK simulator

I am trying to use the GHK simulator to estimate the probabilities $F(\mathbf{x} > k\mathbf{a})$ that the values of a high dimensional ($n>1000$), correlated random vector $\mathbf{x}$ will ...
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35 views

Estimation of percentiles in multivariate posterior distribution

Background: I am using Bayesian inference to find a posterior density. The parameters are change points in a piecewise Wiener process, and I wish to calculate the hitting time of some threshold $a$. ...
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26 views

Is $Max${$F(X),G(Y)$} necessarily a distribution function?

If $F(X)$ and $G(Y)$ denote two distribution functions, then is $Max${$F(X),G(Y)$} necessarily a distribution function as well?
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24 views

Inconsistency in output from my implementation of noncentral t CDF and R's pt()

I am trying to implement a noncentral t CDF as expressed by Guenther (1978), Lenth (1989), and the Wikipedia article on the non-central t in R. I have got my algorithm half working: when the signs of ...
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0answers
92 views

How to guess a curve distribution from count data

I have a sample composed by 2500 count data values. I've plotted in R the corresponding histogram and ecdf. I've run the One-Sample Kolmogorov-Smirnov test to check if the distribution is either ...
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1answer
67 views

What inferential method produces the empirical CDF?

The empirical cdf is an estimate of the cdf. What kind of estimation method (such as method of moments, MLE, ...) constructs the empirical cdf? Is the empirical cdf a nonparametric estimate? Do ...
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3answers
172 views

CDF and logistic regression

Is the probability calculated by a logistic regression model (the one that is logit transformed) the fit of cumulative distribution function of successes of original data (ordered by the X variable)? ...
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1answer
50 views

Using GLM with transformed data

I have a dataset with outcomes from a Vasicek distribution (see this pdf) and some covariates. Re-expressing the Vasicek's pdf into the exponential family form requires me to transform my data, i.e. ...
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1answer
97 views

Obtaining a Probability Distribution From a Survival Function

Edit: I basically want to have a probability curve where a X value of 0.002 would be associated with a Probability of 1 and would also have data points of (0.005,0.1), (0.008,0) which is seen in the ...
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34 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 ...
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54 views

CDF of distribution $A+B$

I have two independent continuous random variables, $A$ and $B$. I want to find the cumulative distribution function of $A+B$. $A$ is log-logistically distributed, and $B$ is normally distributed. ...
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1answer
18 views

Distribution function of an indicated random variable

A random variable $X$ has a distribution function $F$. Let $Y\triangleq XI_{(a,b)}(X)$ with $1<a<b$. Find $G$, the c. d. f. of $Y$. $$\begin{align} G(y) &\triangleq \mathbb P(Y\le y) =\\ ...
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1answer
40 views

Help understanding uniform marginal distribution in Farlie-Morgenstern family.

http://imgur.com/FeFf3e9 The imgur link is to a screenshot of the relevant section in my text. I have trouble understanding how if $H(x, \infty)=F(x)$ is the marginal distribution of $x$, how $F(x) = ...
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33 views

Asymptotic convergence involving EDF

Please help me proving this: Suppose that $Y_1,\ldots,Y_n$ are i.i.d. nonnegative RV's with CDF $F$ and $E(Y_i)=\mu<\infty$. Let $y_1,\ldots,y_n$ be a realization from which an EDF $\hat{F}$ is ...
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20 views

Change of distribution for a variable in R [closed]

I'm combining several variables with different distributions that I'd ultimately like to curve back to something that looks like the empirical distribution of one of them in particular. So, ...
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34 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 ...
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3answers
85 views

CDF of a random vector

I am reading a book that in one page it talks about cdf of a random vector. This is from the book: Given $X=(X_1,...,X_n)$, each of the random variables $X_1, ... ,X_n$ can be characterized from a ...
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1answer
124 views

Inverse CDF of normal variable

The following paragraph was an excerpt from R PerformanceAnalytics documentation on VaR. The most common estimate is a normal (or Gaussian) distribution $R\sim \mathcal{N}(\mu,\sigma)$ for the ...
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3answers
911 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 ...
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2answers
48 views

cumulative distribution function , cdf problem

I cannot understand how step 2 transformed to step 3, anybody help me please ???
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1answer
81 views

Likelihood of censored data

Let $X_1,X_2,\ldots, X_{n_1}$ be IID with PDF $f(x-\theta) $, for $-\infty<x<\infty$ and $-\infty<\theta<\infty$. Denote the CDF of $X_i$ by $F(x-\theta)$. Let $Z_1,Z_2, \ldots, Z_{n_2}$ ...
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1answer
40 views

Relationship between Bernoulli and Normal CDF

Is there any relationship between the draw from a Bernoulli with parameter $p$ and the Normal CDF. Specifically is the condition $p>\Phi(x)$, where $x$ is drawn from the standard normal ...
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2answers
147 views

Difference of two random variable distributions

I have two sets of random variables. I have generated two CDFs for them. Two of the CDFs are plotted graphically. I need to find the difference in distribution of the two CDFs. I have learned about ...
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2answers
108 views

Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person?

When people talk about the 80-20 rule in the context of wealth, it is usually expressed, verbally, by stating that the 20 percent of the people with the highest wealth get 80 percent of the wealth, ...
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168 views

Interpretation of regression data, RMSE, and model predictions

I am doing an analysis where I am using one data set of 12 rows (Mold), and running a linear regression analysis on this data set to generate two different linear regression equations. From there I ...
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1answer
2k views

How to find/estimate probability density function from density function in R

Suppose that I have a variable like X with unknown distribution. In Mathematica, by using SmoothKernelDensity function we can ...
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1answer
131 views

Inverse function for a non-decreasing CDF

For a CDF that is not strictly increasing, i.e. its inverse is not defined, define the quantile function $$F^{-1} (u) =\inf \{x: F(x) \geq u \},\quad 0<u<1. $$ Where U has a uniform $(0,1)$ ...
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0answers
88 views

What is the dimension (or units) of a CDF and PDF?

Given a continuous random variable $X$, what are the units of the PDF and CDF of $X$?
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2answers
76 views

Joint cdf of extreme values

A die is rolled twice, $X_1$ : the minimum value to appear in the two rolls $X_2$ : the maximum I would like to derive $\ F_{X_1,X_2}(x_1,x_2)$. I know that that the CDF of $\ X_1 $ = $\ 1- ...
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2answers
213 views

Variance of sample mean of bootstrap sample

Let $X_{1},...,X_{n}$be distinct observations (no ties). Let $X_{1}^{*},...,X_{n}^{*}$denote a bootstrap sample (a sample from the empirical CDF) and let ...
3
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0answers
174 views

Can we make the Irwin-Hall distribution more general?

I need to find a symmetric low-kurtosis distribution class, which includes the uniform, the triangular and the normal Gaussian distribution. The Irwin-Hall distribution (sum of standard uniform) ...
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1answer
90 views

Combining discrete and continuous variables

I need to find the pdf of a random variable which is a mixture of discrete and continuous random variables. I have seen on this website but it does not exist in the general case, but maybe in this one ...
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0answers
50 views

Computing the pdf for product of rv

$X_1$, $X_2$...$X_i$ are independently and identically distributed rvs with distribution of $X_i \sim beta(\alpha,\beta=1)$. Compute the pdf of $Y=\Pi_{i=1}^nX_i$ Is the following solution correct: ...
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2answers
75 views

Probability of having real roots

Let $U,V,W$ are independent random variables with $\mathrm{Uniform}(0,1)$ distribution. I am trying to find the probability that $Ux^{2}+Vx+W$ has real roots, that is, $P(V^{2}-4UW> 0)$ I have ...
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1answer
67 views

Different answers for probability density function and cumulative density function

I have a function $f(x)=2ae^{-ax}(1-e^{-ax})$, for $x>0, a>0$. This is a pdf. I need to find $P(X>1)$. I have done all my work in such a way that I should get the same answer whether I use ...
2
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1answer
85 views

Calculating probability

If $f(x,y)=2x , 0\leq x\leq 1 ,0\leq y\leq 1 $, find $ P(Y < e^{-X} \cap X > Y)$ Given X and Y have joint distribution. Here is my approach: $$ P(Y < e^{-X} \cap X > Y) = 1- P(Y > ...
3
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1answer
202 views

Expected value of a random variable differing from arithmetic mean

I am a student who is taking a random processes class. I have seen that expected value of a discrete random variable is equal to the arithmetic mean of the distribution provided the values it takes. ...
0
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1answer
111 views

Solving for a pdf of a function of a continuous random variable. Justification and reason for the procedure [duplicate]

Short version: When solving for the pdf of a function of a continuous random variable(say, $Y=X^2$), why can't you just plug in inverse of that($\pm\sqrt{x}$) into the pdf of the RV? Why do you have ...