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Questions tagged [cdf]

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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What is the analog of the PDF and CDF for the likelihood function?

In probability, we can find the cdf using the pdf and vise-versa. Integrating pdf yields the cdf. Does integrating the likelihood function yield any important thing? In statistics, $\mathcal{L} (M\...
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How to fit CDF on LogLog plot?

I build CDF of differences for Gold Pice. As series of day-diff multipliers. For both increase as green (>1) and decrease as red (<1) diffs. ...
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Gradient of multivariate normal distribution function?

Let $X\sim\mathcal{N}_J(\mu,\Sigma)$ be a multivariate normal with PDF $f_X$ and CDF $F_X$. Taking derivatives of $f_X$ wrt $X$, $\mu$ and $\Sigma$ is easy as shown here. However, I am interested in ...
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Find the CDF and use it to find all the medians

Show that for every $p$, $0\leq p\leq 1$, the function $f(x)$ = $p*sin(x) +(1-p)*cos(x)$, $0\leq x \leq \pi/2 $, and $f(x)=0$ otherwise, is a density function. Find its CDF and use it to find all the ...
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How to quantify distribution concentration in cdf?

For example, let's say I have a list of users, each user has its revenue. I can plot the cdf of both user and revenue, to see if there is some concentration, for example, may be 40% user contribute ...
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Do rank transformations induce dependence?

I am interested in an explanation of whether rank-transforming continuous variables induces dependence in model errors that violates the typical i.i.d assumption of generalized linear models. Suppose ...
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60 views

Obtaining the probability of exceedance corresponding a given return period

I have a time series of data (15 years). Following plots show the fitted PDF (generalized extreme value distribution) and corresponding CDF (i.e. 1 minus CDF). The data used here is not the total ...
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56 views

Inverse transform sampling and ambiguous Intervals

Let $F_i:\mathbb R\to[0,1]$ be a distribution function$^1$ and $$F_i^{-1}(t):=\inf\left\{x\in\mathbb R:F_i(x)\ge t\right\}\;\;\;\text{for }t\in[0,1].$$ I've got a computer program where only $F_i^{-...
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What is the expectation of the following joint CDF?

Yesterday, I asked the following question regarding copulas: "Let's say $X=(X_1,X_2)′$, where $X\in \mathbb R^2$. What is the expectation of the copula function $C(F_{X_1}(x_1),F_{X_2}(x_2))$ - i.e....
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What is the expectation of copula function? [duplicate]

Let's say $X=(X_1,X_2)'$, where $X\in \mathbb{R}^2$. What is the expectation of the copula function $C(F_{X_1}(x_1),F_{X_2}(x_2))$ - i.e. $\mathbb{E}_X\left[C(F_{X_1}(x_1),F_{X_2}(x_2))\right]$?
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How to graph distribution of Order statistics?

Is there a software that can graph the pdfs and Cds of an arbitrary number of order statistics or is there some code such software? How to do it? I'm trying to understand the distribution of order ...
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118 views

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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27 views

CDF of a random variable with different distributions in different range

I have a random variable $X$ that follows an exponential distribution $\exp(1)$ in the range $(0, t)$ ($t$ is a fixed point), but follows another exponential distribution $\exp(2)$ in the range $(t, \...
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How can I identify an unfamiliar cumulative distribution function?

I have 116 Bessel-corrected sample variances (average of squared distances from sample mean), each from a sample of three measurements. All measurements were done using the same method. I had ...
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Calculating the truncated version of the squared hyperbolic secant PDF

$ \newcommand{\sech}{\mathop{\rm sech}\nolimits} $ Hello, I have the following Probability Density Function (PDF): $f(x)=\frac{1}{2s}(\sech\frac{x}{s})^2$ This PDF has support for $x\in(-\...
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How to show CDF uniquely determined from equation

I have the following equation for a CDF that I would like to show is uniquely determined: $$\frac{h_1(x)}{f(x)}=\int_x^a h_2(z)(F(z)-F(x))^k\;dF(z)$$ Here $F$ is the CDF and $f$ is the PDF, which I ...
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Non-uniqueness of a CDF in N >= 2

Peacock in his paper on 'Two-dimensional goodness-of-fit testing in astronomy', http://adsabs.harvard.edu/full/1983MNRAS.202..615P, described the issue with the non-uniqueness of CDF in higer (N >= 2) ...
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If we know the cumulative distribution function (cdf) can we determinate the random variable?

I got this question from my teacher yesterday. In my opinion the answer is no, but I can't prove it with a specific example (dice,dime or something). I was thinking also about a reductio ad absurdum ...
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getting a density function from a sample of 500

I'm pretty new to statistics so please excuse me if the answer is obvious. The scenario is the following: I am using mcmc to sample from a posterior distribution of a parameter. I then need to ...
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Given a pmf, how is it possible to calculate the cdf?

Given a pmf (probability mass function) for X (random variable): \begin{array}{|c|c|c|c|c|}\hline x&1&2&3&4\\ \hline p(x)&0.4&0.3&0.2&0.1\\ \hline \end{array} How ...
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Acceptance/rejection sampling and inverting CDF (R code illustration included)

I have the following example: Acceptance/rejection sampling In some cases the cumulative distribution function might not be (easily) invertible. For example if $X$ has the probability density ...
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What is the difference between Empirical and analytical PDF and CDF? More Precisely what would be the difference in their plotting?

I am relatively new to statistics with no statistical background whatsoever, I have an assignment in which i have to plot different distributions in these four manners, i have a gist of empirical PDF ...
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How to Average Percentiles

I'm currently writing my Master's Thesis which focuses on building software to do some things. I ran a few benchmarks for my program (Program A) and current alternatives (Program B) and want to ...
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Asymptotic Distribution of Minimum Uniform Random Variables

I've been working on this problem for a while, and I've made some progress, but I'm still stuck on some parts. I was hoping to get some assistance with this! Let $M_n = \min(X_1, ..., X_n)$ where $...
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72 views

CDF for a probit model

The cdf for a probit model is: $$ \Phi(\varepsilon)=\int_{-\infty}^\varepsilon \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{t^{2}}{2}\right) \, dt $$ My very simply question—that I should know the answer ...
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Fitting a normal CDF using proportion data

I have the following data (prop is like empirical CDF): ...
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Mix pdf and cdf in binary response model [duplicate]

Let's suppose that I have a model that tells me how likely is for an event to have come after a certain time lapsed, given by some kind an exponential distribution, i.e. $$ \mathbb{P}(T_E < t) = \...
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198 views

Inverse-normal CDF approximation in Excel, Python or R

I read that the implementations of Inverse-normal cumulative distribution function (CDF) /quantile / ppf in R, Python (scipy) and Excel give similar results. However, I can't find the very formulae ...
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Number of times an object gets sampled when sampling $N$ times with replacement from $M$ objects [closed]

Take $N$ draws with replacement from $M$ unique objects. As $N$ goes up, what is the distribution over the increment to the number of times I get each $M$? So say $M$ is 3 and $N$ is one. The ...
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R Multivariate Normal CDF

I am trying to estimate the CDF of a MVN distribution for some given ranges ([-Inf,mu], [mu,mu+3], [mu+3,Inf]). In R using package mvtnorm and function pmvnorm, with some dummy data: ...
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How to calculate the cumulative distribution function of a GEV distribution when $1+\xi(x-\mu)/\sigma\le0$?

I don't have a stats background let alone one in extreme value theory, and I have what I imagine is a simple question but one I that haven't been able to find the answer to. The cumulative ...
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CDF for f(x) = 0.5e^-|x|

This is the full question: "If a random variable has density f(x)= 0.5e^-|x|, for x∈R, find the cumulative distribution function". I know that to find cdf from the pdf you would have to integrate ...
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Basic CDF / CDF Notation Question

The following is copied from some old course notes: $F_{X-\theta}(x)=P(X-\theta < x) = P(X<x+\theta)=F_\theta(x+\theta)=F_0(x+\theta-\theta)=F_0(x)$ Is anyone able to explain the $P(X<x+\...
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What is the difference of $\Sigma$ esimation of Gaussian Copula based on known CDFs VS unknowns

Recently, I read this web page which explains the Copula package in R. A question occurred to me. Consider a data set $D_{n\times d}$ which $n$ is the number of samples and $d$ is the number of RVs. ...
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What information does a probability density function (PDF) graph provide?

This sounds like a simple question and I know PDF graphs are used a lot in presentations and financial publications. Yet, what information does it actually provide? The CDF actually gives you ...
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Calculating CDF for Dry Days (0mm/day)?

I am working on daily precipitation data and need to calculate cumulative Distribution Function (CDF) of daily precipitation data, however, I don’t understand how to transform 0 mm/day (dry days) to ...
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Convergence in law of the remedian

I try to understand the theroem 2 of this article about the remedian (https://pdfs.semanticscholar.org/3d64/5e60691838bf4699e79458d96930ba7bf24e.pdf) I will try to phrase it more general so that you ...
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How do I get the CDF of a gamma distribution with mean and sd?

I have the mean and standard deviation of my data, which I determined follows a gamma distribution. I don't understand the function I found online for the CDF of a gamma distribution because of the ...
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Analytical solution to the multivariate CDF given multivariate pdf

Is there any way of approximating or analytically solving the below CDF (let's say even for $n\to\infty$)? I am trying to find the below probability: \begin{align} &P\left[X_{2}-X_{1} \leq 0,...
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How to prove KL(q(z)|p(z)) = E_q(z) [ log f(z) ] where f is the CDF of p?

As title. It was used in https://arxiv.org/abs/1905.10549 without proving.
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If $X$ follows standard normal distribution, find the correlation coefficient between $X$ and $\Phi(X)$

If $X$ follows standard normal distribution, find the correlation coefficient between $X$ and $\Phi(X)$, where $\Phi(X)$ is the cdf of $X$. My attempt is: First we have to calculate $Cov(X, \Phi(X))$...
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Derivation of CDF of a function that results in an exponential distribution

I was looking through wiki's treatment on the title topic in https://en.wikipedia.org/wiki/Random_variable and am completely stumped on this particular section: There are several specifics that ...
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Can I increase the sample size by generating random numbers to apply the Chi-Square Goodness of Fit Test?

Does increasing the sample size by random number generation change the distribution? I have a sample of size 8. Each sample value represents the number of bus arrivals at a bus stop every 15 minutes. ...
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How to find quantiles and likelihoods of mixture distributions?

My PDF: M was estimated and found to be 5. I need to work out the quartiles for the PDF above. In addition, I need to use different methods of estimation to estimate the parameters. So far I've ...
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Tcdf and invT with incomplete beta [duplicate]

I am working in python. I have a function for incomplete beta. Iow would I calculate tCDF and invT using this? the incomplete beta function that I have is this: ...
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Joint CDF of M(t) and B(t), where B(t) is the standard BM and M(t) is maximum value of standard BM on [0,t]

We have to find - $F_{M(t),B(t)}(m,x) = P(M(t) \leq m, B(t) \leq x)$. $T_{m} = inf\{t\geq 0: B(t) = m\}$. We know that, $$ P(M(t) \geq m, B(t) \leq x) = P(T_{m} \leq t, B(t) \leq x)$$, $$ = P(T_{m}...
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Strategies for predicting values of a time-dependent CDF, given covariates

I've got data that looks like this: ...
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Consistent estimator and distribution function

a general question: If the distribution function $F_n$ of some estimator $T_n$ suffices \lim_{n \rightarrow \infty} F_n(x) = 1 \text{ or } 0 \forall x}. Does that imply that $T_n$ is consistent? I ...
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Calculate the derivative of the CDF with respect to the mean value [duplicate]

I want to derive the cumulative density function (cdf) for variables following normal distribution with respect to the parameters of the cdf (such as the mean or the standard deviation)
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Conditional transformation of variables

I've seen a trick for finding the p.d.f of $r(X,Y)$ where $X$ and $Y$ are r.v's by first calculating the cdf i.e $P(r(X,Y) \leq l)$ and then differentiating to find the pdf. So if $\Omega = \{(x,y) | ...