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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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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72 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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65 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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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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44 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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86 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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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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49 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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16 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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30 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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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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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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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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1answer
99 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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720 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
44 views

cumulative distribution function , cdf problem

I cannot understand how step 2 transformed to step 3, anybody help me please ???
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80 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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37 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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129 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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101 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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145 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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804 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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114 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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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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74 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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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 ...
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152 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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81 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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48 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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74 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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65 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 ...
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84 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 > ...
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158 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. ...
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93 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 ...
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Is it true that $F_U(U(\bar\omega)) = F_X(z)$ implies $z=X(\bar\omega)$?

For a statistics class, I have to prove a result which leads me to the following question. If I can show that it is true, my proof is done. So here is the question. Suppose that $U: \Omega ...
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1answer
110 views

Find the pdf of Y when pdf of X is given

$$ f_{X}(x) = \frac{3}{8}(x+1)^{2} ,\ -1 < x < 1 $$ $$Y = \begin{cases} 1 - X^{2} & X \leq 0,\\ 1- X, & X > 0.\end{cases}$$ I started with : $$ F_{Y}(y) = 1 - P(Y \leq y) $$ $$ ...
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142 views

Show that the random variable $V=X-a$ and $U=a-X$ have same distribution?

Given $X$ is a continuous random variable whose density is symmetric about a point $a$. Show that $V=X-a$ and $U=a-X$ have same distribution. $$F_U(u) = P(U \leq u) = P(X-a \leq u) = F_X(a+u)$$ ...
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88 views

Problems in scale Bayesian network mode using R

The problem that we have is as follows. We have close to 60 discrete random variables each of which shall take on an average of 5 categorical values. We have developed a Bayesian network ...
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1answer
60 views

What is the official name of the simple stepwise CDF estimation

I have a set of observed one-dimensional independent data set: X[1...N]. What is the official name of the simple estimation of CDF function with stepwise function P(x[i]) == i / N
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102 views

How to calculate simple CDF like Wolfram Alpha, but locally?

I received this great answer, Statistical significance of conditional probabilties, to my question about how to calculate the significance of conditional probability equations. They explained HDI was ...
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195 views

Calculate CDF of Binomial Distribution

I need to solve the following problem: Given $n$ yes/no experiments, and a success probability $p$, at least how many successes $k$ can I expect (say, with a 'confidence' of $c=95\%$ or more)? ...
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54 views

Sample variance robustness

I am trying to understand the robustness of the sample variance. I want to calculate its influence function and in order to do so a previous step is to obtain the functional for the contaminated ...
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88 views

Is there any PDF which satisfies the following criteria?

For an applied economics paper, I am looking for a 2-parameter probability distribution function that has the following properties: Simple, closed-form PDF $f(x)$ and CDF $F(x)$, defined on the ...
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344 views

Kernel density estimation (CDF) with Epanechnikov kernel in Matlab

The code for Kernel density estimation was given in a recent CrossValidated question by Julio Miguel Galvez entitled "Kernel density estimation with Epanechnikov kernel in Matlab", as follows. How ...
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262 views

Are there techniques to merge two cumulative distribution functions?

I'm trying to estimate quantiles from cumulative distribution functions. Given N CDFs are there techniques that can be used to merge them to form another CDF from which a quantile can be estimated ? ...
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129 views

Find and plot cumulative distribution function

We toss a fair coin. If a head appears then $X\sim N(0,1)$. If a tail appears then $X=1$ with probability $1$. Find the unconditional CDF of $X$ and plot it.
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71 views

Finding conditions on unspecified CDF that permit a solution to an equation

[A duplicate thread can also be found at http://mathoverflow.net/questions/131142/finding-conditions-on-unspecified-cdf-that-permit-a-solution-to-an-equation ] Let $F(\alpha) := ...
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115 views

Estimation of conditional CDF vs PDF, practical differences

I'm trying to figure out where and when one would opt to work with the conditional cdf $F(y|X=x)$ rather than the pdf $f(y|X=x)$. I am thinking of $y$ as being a real valued response, and $x$ as being ...
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157 views

Fast way to calculate difference in normal CDFs

I'm running a computationally intensive method where I have to calculate the difference in Normal CDF's millions of times, such as pnorm(y)-pnorm(x) I have not ...