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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CDFs for Right-Skewed Distributions

How does one determine the percentage of a sample less than or equal to some x value for a set of discrete data that appear to be right-skewed? For example, I have a number of data points, and if I ...
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What do I obtain if I subtract two CDFs?

Code: ...
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20 views

Percentage Beyond a Given Value for Empirically Defined Distribution

It is my understanding that standard deviation does not work well as a measurement for distributions that are heavily skewed. If I have a heavily right-skewed distribution, should I simply use the ...
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Difference between two vectors of unequal size

I have a predictive model function mPred and two different input variables matrices of the same size (nxm), iM1 and ...
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Dependent chi-squares vector: how to calculate cdf of $X_{(n)}$?

Consider a vector of central&1-degree Chi square distributed variable $(X_1, X_2,...,X_n)$, it is simple to calculate the cdf of $X_{(n)}$ (maximum of order statistics), when they are independent. ...
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21 views

convert lognormal Cumulative Density Function P90 and P10 values to mean and sigma [duplicate]

Practioners are used to defining lognormal distributions in terms of P90 and P10 cumulative density function values. To utilize these esperts' input I need to be able to convert these P90/P10 values ...
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44 views

Evaluate goodness-of-fit of estimation of Pareto-like distribution

I would like to evaluate the goodness-of-fit of the following (Pareto-like) distribution: $$ f(r) = \sigma \centerdot r^{-\rho} $$ The function estimates the population of cities given the rank $r$ in ...
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43 views

Estimating the area between two ecdfs

I wish to calculate the area between two ecdfs in R (see below): ...
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How to find pdf of a joint distribution in R?

$F(x,y) =\frac{1}{6}(x^2\, y+x\, y^2)\,,\quad 0\leq x\leq 2,\, 0\leq y\leq 1$ Above is the joint distribution given, how to find out cumulative distribution function of y? how to obtain joint ...
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Cumulative distribution function: what does $t$ in $\int\exp(-t^2)dt$ stand for?

I'm trying to teach myself how to quickly translate many different types of equations into VB, T-SQL and MDX code. Since I'm trying to build a skill, not just solve a single isolated problem, I'm try ...
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1answer
36 views

From joint cdf to joint pdf

We can get the joint pdf by differentiating the joint cdf, $\Pr(X\le x, Y\le y)$ with respect to x and y. However, sometimes it's easier to find $\Pr(X\ge x, Y\ge y)$. Notice that taking the ...
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1answer
26 views

Numerical approximation of percentiles from arbitrary pdf

Given an easily-computable probability density function $f(x)$, what algorithm can we use to numerically approximate percentiles? For instance, we might be looking for $x$ such that given $X \sim ...
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1answer
49 views

Convergence Issues for Bootstrap Distributions

the following is part of a proof from van der Vaarts book on asymptotic statistics: I want to show that if for a continuous distribution function F ...
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44 views

Probability of Achieving a Count Level in Time Series Data

I have some time-series data that displays a count value for every day: These count values begin at 1 or -1 and will continue to count up (or down) if conditions in the time series are met. If the ...
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1answer
30 views

Area below probabilities

Let $p$ be probabilities and $D$ is the real How can I proof that the areas $$\int p \; d F_{p}(p|D=1) = \int (1-p) \; d F_{1-p}(1-p|D=1)$$ are equal. Where $F_{p}$ is the empirical distribution ...
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How can I calculate a discrete Cumulative Distribution MultiDimensional Array from a discrete Probability Mass Array when dimensions > 2?

I would appreciate any help in trying to calculate the Cumulative Distribution Array of a Probability Mass Array when dimensions > 2, essentially a discrete joint cumulative distribution from a sample ...
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38 views

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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160 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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73 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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540 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
88 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
99 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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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
50 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 ...
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1answer
83 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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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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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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190 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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17 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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41 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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27 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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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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103 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
79 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
231 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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51 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
107 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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42 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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55 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
19 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
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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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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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28 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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35 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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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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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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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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50 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
83 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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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 ...