# 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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### 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: ...
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### 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 ...
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### 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. ...
36 views

### Difference in means

For a df that looks something like the following ...
87 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 ...
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### 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 ...
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### Reverse Cumulative Frequency explanation

I've been seeing a lot of Reverse Cumulative Frequency (RCMF) plots lately and trying to figure out how to understand the way reverse cumulative frequencies are calculated, and the interpretation of ...
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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 ...
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### 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 ...
171 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 ...
196 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 ...
295 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 ...
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### 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 ...
38 views

### Fit cdf and pdf from points on empirical cdf

I have cumulative counts with respect to a variable x, which looks like: ...
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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 ...
42 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 ...
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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 ...
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### 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 ...
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### 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 ...
359 views

### Maximum likelihood as minimizing the dissimilarity between the empirical distriution and the model distribution

I am reading Ian Goodfellow "Deep Learning" book. At page 128 it says One way to interpret maximum likelihood estimation is to view it as minimizing the dissimilarity between the empirical ...