Questions tagged [empirical-cumulative-distr-fn]

Empirical cumulative distribution function: a step function increasing by $1/n$ at each unique $X$-value that occurred in the sample.

Filter by
Sorted by
Tagged with
0 votes
0 answers
12 views

Distance between ecdf and cdf in R [closed]

I want to calculate the distance between ecdf and cdf with kolmogorov–Smirnov and plot the distance as function of the number of samples. This is my code so far: How I created "exp_v": ...
user avatar
  • 1
0 votes
0 answers
12 views

Measure for similarity of two distribution ECDF with sensitivity to the tails

Currently, I am looking for a measure to quantify the overall dissimilarity or similarity of two sample distributions (possibly of different size). I would like to compare observed data with model ...
user avatar
  • 11
0 votes
0 answers
11 views

Is the empirical distribution the only unbiased distribution estimator?

Given $n$ samples, if $\hat{p}$ is the empirical distribution of $p \in \Delta_{\mathcal{X}}$ where $\mathcal{X}$ is a finite domain, we know that $\mathbb{E} \hat{p} - p = 0$. Is the empirical ...
user avatar
1 vote
0 answers
13 views

Empirical distribution for feature binning

In paper "A simple yet effective baseline for non-attributed graph classification" (https://arxiv.org/pdf/1811.03508.pdf) authors use empirical distribution for feature binning. Precisely, ...
user avatar
  • 179
2 votes
1 answer
68 views

symmetrization in glivenko-cantelli proof

In this proof of the Glivenko-Cantelli theorem, page 2 of these notes, two types of symmetrization are used. The first transforms the sup of the centered empirical cdf $$P(\sup_{z\in\mathbb{R}}|(1/n)\...
user avatar
1 vote
1 answer
24 views

rank to quantile estimate?

R> x=c(92, 3, 1, 4, 15, 4) R> rank(x) [1] 6.0 2.0 1.0 3.5 5.0 3.5 Given the rank results of an input vector of sampled data, I can estimate the quantiles ...
user avatar
0 votes
0 answers
24 views

Does empirical cumulative distribution function (ECDF) has its Akaike information criterion (AIC)?

Working on multivariate distribution fitting, and right now I have marginal univariate transform models and a copula model. Was thinking if I pick ECDF for marginals, do I still have meaningful AIC? ...
user avatar
1 vote
1 answer
44 views

How to average several posteriors distributions from a Monte Carlo Simulation

Say you produce several posteriors distributions from different runs of the same model under different seeds. That is to say you have something like the following: ...
user avatar
  • 239
0 votes
0 answers
14 views

Doubt about distribution function of continuous distribution with (Generalized) Pareto tails

In this paper: https://www.sciencedirect.com/science/article/pii/S0167947315003163 They proposed an estimation method for the parameters of the Generalized Pareto Distribution. Defining: $$ F_n(x) \...
user avatar
  • 67
0 votes
0 answers
13 views

Expressions for entropy of an observed set of points (continuous variables) [duplicate]

The entropy of a discrete variable can be defined as $$H(x) = - \sum_{i=1}^n p(x) \log p(x) $$ or for continuous distributions and a density $f(x)$ we could compute $$h[f] = \int_{\mathbb{X}} f(x) \...
user avatar
1 vote
1 answer
66 views

Distance between two categorical distributions

I want to test whether two (empirical) categorical distributions taking on $K$ possible values (e.g. 5, with no innate underlying ordering) with associated (empirical) probabilities $p_k$ are the same....
user avatar
  • 57
0 votes
0 answers
30 views

Probabilities from ecdf and normalised data - is this acceptable difference? (using R)

I have a dataset of 500 observations, definitely not normally distributed: The minimum is around 50 000 in the data. If I use ecdf to predict e.g. 100 000, I get: ...
user avatar
1 vote
1 answer
94 views

What is a "bootstrap from the Empirical CDF"?

I am given the following set of questions. In all the questions the basic background is a sample X_1, ... , X_n. If n=3 and you observe the numbers 1, 2, and 4, what is the sample median. If you ...
user avatar
  • 531
0 votes
1 answer
61 views

Determine a product's rating given a known 3-sigma tolerance

Consider a 100Ω resistor with a 10% tolerance. We can assume this is the 3-sigma value since this is typical in manufacturing. Thus, we can expect ≈99.73% of such resistors to range from 90Ω to 110Ω. ...
user avatar
  • 103
1 vote
1 answer
45 views

Difference in means

For a df that looks something like the following ...
user avatar
0 votes
1 answer
105 views

Smoothed CDF to calculate asymptotic normality

If we have the following estimator: $\hat{F_Z}(z)=\frac{1}{N}\sum_{i=1}^N1\{Z_i\leq z\}$. The CDF of $Z$ is defined as $F_Z(z)=Pr(Z\leq z)$. $Z_1, ..., Z_N$ is i.i.d. data. What would be the steps to ...
user avatar
0 votes
0 answers
62 views

counts under unequally spaced intervals - stackoverflow points table

I am looking for a function similar to ecdf which help me to asses the quantile for certain number of stackoverflow points across all users. We have a table with ...
user avatar
  • 93
2 votes
0 answers
85 views

Plug-in principle with kernel density estimate

The plug-in principle says that to estimate a statistical functional of the form $$ T(\mu) = \int f(x)\ d\mu(x) $$ we can replace $\mu$ with the empirical distribution $\mu_n$ depending on data $X_1,\...
user avatar
  • 166
7 votes
1 answer
198 views

What are the simplest examples of nonlinear statistical functionals?

I am reading Wasserman's book "All of Statistics" in which he defines a statistical functional as any function $T(F)$ of the cumulative distribution function $F(x)$ that outputs a real ...
user avatar
  • 603
2 votes
1 answer
38 views

Picking a specific estimated CDF from a set of CDFs provided by an ECDF

Let $F_X$ be a CDF of an unknown random variable $X$. If we have independent samples $x_1, x_2, \ldots, x_n$ of $X$ then we can estimate $F_X$ non-parametrically using an ECDF $\hat{F}_n$. By Central ...
user avatar
  • 23
2 votes
2 answers
93 views

Notation for ECDF

I'm reviewing statistical functionals and U-statistics, trying to make notes, and I am tripping on notation. From my understanding, $X$ is used to denote a random variable and $x$ is used to denote an ...
user avatar
2 votes
1 answer
174 views

Density estimation from ECDF - numerical derivatives and scaled domains

Suppose we want to get a density estimate of some data X. One way is to compute the empirical CDF, ...
user avatar
  • 43
1 vote
0 answers
26 views

Nonparameteric Empirical Estimator For Stochastic Process

Motivation: If $X$ is a random-variable defined on some probability space $(\Omega,\Sigma,\mathbb{P})$ then Glivenko-Cantelli lemma guarantees that the empirical distribution $\frac1{N}\sum_{n=1}^N \...
user avatar
0 votes
0 answers
94 views

How to deal with a PDF that takes CDF data as input? (Metalog distributions)

I am trying to utilise the Metalog distribution in a Machine Learning project. For this project, I need to be able to obtain likelihoods using the PDF of the distribution. https://en.wikipedia.org/...
user avatar
1 vote
0 answers
59 views

Is it possible to convert a pdf obtained with density() to an ecdf?

Consider the following code that gives us (an estimate of) the pdf of a random variable $X$: X = rnorm(100,10,1) XDensity = density(X) I want to obtain the ecdf of ...
user avatar
  • 830
2 votes
0 answers
90 views

Fitting a function to ECDF [closed]

I have some ECDFs. I would like to summaries the ECDFs with functional approximations. I was thinking that a polynomial, spline, or other line fitting procedure would generate a nice parsimonious ...
user avatar
  • 943
0 votes
0 answers
24 views

Computing the most representative sample of a random variable

Let $X$ be a real-valued random variable and $n > 0$. Using numerical methods, how can we find the vector $\vec v$ of $n$ real numbers that is most characteristic of $X$, in the sense that the ...
user avatar
  • 19.1k
3 votes
1 answer
107 views

Median from two unmergable datasets

I am trying to calculate the "overall" median of a variable that is spread across two datasets. I have access to the raw data in each dataset but can't bring their raw data together. What ...
user avatar
2 votes
0 answers
427 views

Why are people using KS statistic to choose cutoff for binary predictions?

I've seen that people are sometimes using Kolmogorov-Smirnov statistic to determine a cutoff in a binary classification models, such as logistic regression. However, i do not fully understand why and ...
user avatar
  • 399
3 votes
1 answer
95 views

Obtaining an expression for empirical mean from empirical CDF definition

This is my first post so I will try to be as clear and concise as possible. I am doing a course in statistics and we define the true mean of a random gaussian variable to be as follows: $\mu$ = $\int_{...
user avatar
1 vote
1 answer
532 views

Confidence Interval of p-Quantile from Empirical CDF

I am trying to provide an interval estimate for the 0.8-quantile of some numeric data, which is assumed to be an IID sample from some unknown, continuous distribution. I constructed an Empirical CDF ...
user avatar
0 votes
0 answers
107 views

Empirical estimation of conditional distribution $Y|X$ at the boundaries of X

I want to estimate conditional distributions of Y | X. Where X contains several continuous covariates. I'm coding in R. I tried several methods so far, but none gives me entirely satisfactory results ...
user avatar
  • 157
1 vote
1 answer
70 views

Does the Glivenko-Cantelli theorem work back and forth?

If we have a sample $X_1, X_2, \ldots, X_n \sim F$ then $\hspace{1mm}sup_x|F_n(x) -F(x)|\xrightarrow{a.s./p}0$. Now, if I can come up with a theoretical cdf $F$ such that $\hspace{1mm}sup_x|F_n(x) -F(...
user avatar
  • 43
0 votes
0 answers
268 views

Is it accurate to take the maximum distance between CDF and ECDF only at the edges? (Kolmogorov-Smirnov Test)

I have two samples, one obtained empirically and the other is the result of a simulation. I want to tune the simulation so that the result resembles the reality, for that I will minimize the KS ...
user avatar
0 votes
1 answer
629 views

Example of cumulative distribution function and the empirical distribution function [closed]

A random of 100 rolls of the die. The outcomes 1, 2, 3, 4, 5, 6, occurred 13, 19, 10, 17, 14, 27 times, respectively. Calculate the cumulative distribution function and the empirical distribution ...
user avatar
0 votes
1 answer
609 views

How can i find empirical survival function using survival function in R?

The survival function is given by: S(y; α, λ) = (α/α−1)* (1 − α^(−e^(−λy ))), if α is not equal 1 = e^(−λy) if α =1 y = 1 4 4 7 11 13 15 15 17 18 19 19 20 20 ...
user avatar
  • 25
37 votes
4 answers
4k views

Intuitive explanation of Kolmogorov Smirnov Test

What is the cleanest, easiest way to explain someone the concept of Kolmogorov Smirnov Test? What does it intuitively mean? It's a concept that I have difficulty in articulating - especially when ...
user avatar
  • 2,391
3 votes
0 answers
154 views

Comparing empirical distributions with an interaction effect

My experiment includes two subject groups: group1 and group2. Both groups undergo a behavioral test, the result of which is called “movement celerity” (this is my dependent variable). Both groups are ...
user avatar
0 votes
1 answer
92 views

Fit cdf and pdf from points on empirical cdf

I have cumulative counts with respect to a variable x, which looks like: ...
user avatar
  • 1,052
1 vote
1 answer
108 views

Can we apply the Probability Integral Transform to Dependent Random Variables?

Let's suppose we deal with a non-homogeneous Poisson process having intensity function λ(t), t ≥ 0. The event times X1, X2, … of ...
user avatar
  • 163
0 votes
1 answer
50 views

How to perform van Zyl's (2018) ecf-based normality test in R [closed]

I have been reading quite a bit on empirical characteristic function (ecf) based normality tests, but cannot find any functions to perform such a test in R and lack the mathematical ability to figure ...
user avatar
  • 45
2 votes
0 answers
43 views

What are “absolute ECDFs” called (if anybody uses them)?

By absolute ECDF, I am referring to an ECDF that shows the absolute number of samples above some value as opposed to the fraction of such samples. For example, the bottom plot below displays such an ...
user avatar
  • 2,297
1 vote
0 answers
23 views

Quantile-calculation example: Why the term $c$?

I need help to interpret a solution to the following example: Based on historical claim amounts $x_1,...,x_{47}$, which are assumed to be outcomes from an unknown claim distribution, you are ...
user avatar
0 votes
2 answers
767 views

Simulate data from ECDF in R [closed]

Consider the following 11 continuous non-negative observations: 0, 0.3, 0.31, 0.33, 0.37, 0.49, 0.51, 0.53, 0.59, 0.6 Obtain the empirical cumulative distribution function for these observations. ...
user avatar
2 votes
1 answer
141 views

How to quantify distribution concentration in cdf? [closed]

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 ...
user avatar
  • 1,145
2 votes
0 answers
106 views

Measuring distance between cumulative distribution and empirical distribution

What is an easy to understand step by step procedure on how to compute a distance between a cumulative distribution function and an empirical distribution function given a random sample using ...
user avatar
8 votes
3 answers
2k views

Confidence Interval of CDF

I am trying to determine if there is a statistically meaningful distinction between the cumulative probability density curves shown in the figure below. It's simple enough to do a $t$-test on the ...
user avatar
0 votes
0 answers
30 views

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 ...
user avatar
  • 67
2 votes
0 answers
59 views

What linear transformation minimizes the Kolmogorov–Smirnov distance between two sets of points?

Suppose we have two sets of real-valued points $X_1, \dots, X_m$ and $Y_1, \dots, Y_n$. We want to find the linear transformation that makes the distributions look alike. If we want them to have the ...
user avatar
4 votes
1 answer
752 views

MLE as an expectation over the empirical distribution

I am reading Ian Goodfellow "Deep Learning" book. At page 128, it writes the maximum log-likelihood estimator and then says it is equivalent to the expectation over the empirical distribution To ...
user avatar