# 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.

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### 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": ...
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### 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 ...
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### 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 ...
1 vote
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### 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, ...
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### 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/...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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 ...
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### Fit cdf and pdf from points on empirical cdf

I have cumulative counts with respect to a variable x, which looks like: ...
1 vote
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### 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 ...
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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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 ...