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Questions tagged [empirical-cdf]

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cumulative distribution function for non-normal distribution

From this article, I read that the author drew four versions of CDFs each plotted in different distributions (all four plots come from the same sample data) From these four plots, the author chooses ...
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8 views

Plotting groups of sample distributions as CDF with dispersion

Context I repeatedly run an experiment each repetition of which results in a sample of observations that I assume follow some distribution. (It is not important here what the distribution represents.)...
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Confidence on the median for a weighted empirical distribution

I have observation data $x_1, \dots, x_n$ with associated positive weights $w_1, \dots, w_n$ such that $\sum_i w_i = 1$, representing a "weighted" empirical distribution with CDF $$ \hat{F}(x) = \sum_{...
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1answer
51 views

Difference between empirical distribution and the data-generating distribution? [closed]

I understand that an empirical distribution is basically sampling from the sample set with replacement. However I am not quite sure how $ \hat{p}_{data} $ and $ p_{data}$ in Maximum likelihood ...
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Weighted Empirical Cumulative Distribution Function (CFD): order values before or after weighting? [before]

My input data are some observations of a continuous variable, let's say the number of kilometers of motorbikes. I did a survey and I collected some observations. Somehow, I computed weights for all ...
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25 views

Bounds for the expected value of the Kolmogorov-Smirnoff loss function

Let $$ \mathcal{F}=\{F:\mathbb{R}\longrightarrow\mathbb{R}: \text{$F$ is the CDF of some probability measure on $\mathbb{R}$}\}. $$ Consider the loss function, $L:\mathcal F\times\mathcal F\to\mathbb ...
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1answer
73 views

Covariance of An Empirical Distribution Function Evaluated at Different Points

The problem is extracted from All of Statistics (Exercise 7.5), Larry Wasserman. I don't have a solution manual to the book so I post here the problem together with my attempted answer: Let $x$ and $...
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1answer
264 views

Sampling from empirical distribution

I have a vector of y (min is > 0, max could be 1), for which, i have no idea what distribution is. But based on the data we have, vector y, we can get the empirical cumulative probability distribution,...
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1answer
56 views

Confidence interval for samples from an empirical distribution

I have data where a number of respondents are asked to rate the characteristic of a set of subjects on a scale of 1 to 100. A different number of respondents were asked to rate every subject, so we ...
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1answer
32 views

Comparison of empirical distributions in ciruclar/polar coordinates

I have 4 sets of 24 measurements of a polar variable (univariate). I want to use a statistical test, like the Kolmogorov-Smirnov test, to test whether said sets differ significantly from each other. ...
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80 views

What is the differences between estimating the margins and transforming them using cumulative distribution function

In copula models, the estimation of copula parameters is based on the pseudo-observations of the original data. As I understand, we can transform the margins using the cumulative distribution function ...
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46 views

Empirical distribution function for sample

I have a short question regarding empirical distribution function. We have a sample of $(1, 2.1, 1.5, 3)$. What's the value of the empirical distribution function for this sample $F_{4}$ at $x=2$? ...
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30 views

PDF for the ith ORDERED uniformly random sample compared to an evenly spaced sample

Let $r_1 ≤ r_2 ≤ ... ≤ r_N$ denote an ORDERED set of N realizations of real numbers that are uniformly random on the number line from 0 to 1. Let $R_1 < R_2 < ... < R_N$ denote a set of ...
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Can you get the probability of an event happening before n days using its empirical cumulative distribution?

I have data of the number of days it takes an object to change from state A to state B, and I am interested in knowing what is the probability that this change of states happens before n days. Can I ...