# 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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### Random variables implicit in Glivenko-Cantelli theorem

Theorem 1 here states $\lim_{n\to\infty} \sup_x |\mathbb{F}_n(x) - F(x)| = 0$ with probability $1$, where $\mathbb{F}_n$ is the empirical distribution function of the first $n$ $X$s, which are i.i.d. ...
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### Compare CCDF of datasets with different sample size

I have 3 dataframes with the same structure (each dataframe includes a different type of tweet). Here are the columns of dataframes: id, ...
25 views

### Estimation of Distribution using multiple ECDFs

Every day, I keep track of the processing times for each input to my CPU and create empirical cumulative distribution functions (ECDFs) based on this data. Let's assume I have 100 observations per day ...
1 vote
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### Quantize a continuous random variable

Suppose we have a continuous random variable $X$. We do not know its distribution function, but have $n$ i.i.d. samples. I am looking for methods that quantize (discretize) $X$ into a categorical ...
1 vote
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### How to apply a seasonal index into an eCDF?

I am doing a Before/After analysis, which is aiming at evaluating the effect of a change. Assume I have made a change at the beginning of June-2022, and I want to evaluate the effect of the change ...
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### How to simulate critical values for a two sample KS test?

I believe I managed to simulate critical values for a single sample with the following code in R. ...
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### Averaging ECDF vertically : Proof of convergence

Suppose we have a set A , we split into multiple disjoint subsets ai We only have access to the ai sets , is there a way to compute the ECDF for the set A without looking at it ? If for example we ...
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### Doubt in empirical distribution, sample and random variable

I have a basic doubt in sample and random variables. I have read related posts on this site but still some doubt is still left. Suppose we have a population and we are drawing some entries from it ...
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### How to compare two empirical CDFs obtained from current status data

I have failure time information of a product in the form of current status data, which looks something like this. Observed Time($t_i$) failed ? ($y_i$) 5 hrs 1 6 hrs 0 5 hrs 0 7 hrs 1 ...
55 views

### How to plot a confidence band around the ecdf in the form (ecdf-b, ecdf+b) for a certain b in R?

I need to plot a confidence band around my ecdf. I calculated a value b and I basically just need to plot ecdf+b and ecdf-b but R doesnt let me do that. Does anyone know how this can be done?
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### Empirical distribution function by sampling from a m.v. distribution

I have mathematically rewritten my problem as a function of multiple iid variables: $$f(X_1, X_2, ..., X_n),$$ where $$X_i \in \mathcal{N}(0,1)$$ I now want to determine the empirical distribution ...
451 views

### When was the earliest appearance of Empirical Cumulative Distribution Plots?

I would be surprised if we actually had a date here. I am curious who, if anyone, created the ecdf plot. When did the ecdf make its first appearance? If we do not know when the first ecdf plot was ...
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### Does this statistic comparing two samples using EDFs have a name?

So, I wanted to cook up a statistic that was similar to the Wasserstein metric for finite sized samples from distributions on a continuous support that is also invariant to reparameterization of the 1-...
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### Substitution principle - Sample mean estimator

We can read in Keith Knight - Mathematical Statistics Example 4.22 the following. EXAMPLE 4.22: Suppose that $\theta(F)=\int_{-\infty}^{\infty} h(x) d F(x)$. Substituting $\widehat{F}$ for $F$, we get ...
1 vote
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### How to estimate correlations between the standard errors on empirical quantile estimates from two correlated series?

I have two very long series of samples from a pair of correlated random variables, $x$ and $y$. (they are fat tailed distributions, roughly Pareto, if that helps). (if you're curious...$x$ and $y$ are ...
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### Reference request: Almost sure weak convergence

(Reposting from Math StackExchange) I've encountered the term "almost sure weak convergence" of empirical measures in several places but haven't been able to find a textbook reference. Could ...
275 views

1 vote
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### rank to quantile estimate?

R> x=c(92, 3, 1, 4, 15, 4) R> rank(x)  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 ...
1 vote
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### 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: ...
688 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....
81 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: ...
410 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 ...
320 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. ...
1 vote
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### Difference in means

For a df that looks something like the following ...
132 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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### 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 ...
29 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 ...
367 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 ...
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### 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 ...
209 views