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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test for differences in empirical cumulative distribution functions between groups
What test could I use to test for differences in empirical cumulative distribution functions between two or more groups? Note that I am not looking for a test two compare two ecdf (Kolmogorov–Smirnov ...
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Computing the CECDF (Complementary Empirical Cumulative Distribution Function) in R
The ECDF can be calculated using the function ecdf() in R.
I have the following expression I'd like to define in terms of the CECDF, but for some odd reason things ...
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Random sample and its underlying sample space [duplicate]
A random sample of size $n$ is a random vector $X=(X_1, ..., X_n)$, where all $X_i$ are i.i.d., and are measurable functions on some sample space $\Omega$.
Let's say, $\Omega = \{H,T\}$, i.e., heads ...
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Almost sure convergence using exponential tail bound
I have a question about a theorem in the following set of lecture notes 'A Gentle Introduction to Empirical Process theory' (http://www.stat.columbia.edu/~bodhi/Talks/Emp-Proc-Lecture-Notes.pdf). In ...
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How do you determine an appropriate block length for calculating "block maxima" for GEV distribution?
I have some time series data spanning 30+ years and I am trying to do some extreme value analysis. Major disclaimer: I am not a statistician so I feel that I am wading into waters beyond my area of ...
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Finding Cumulative Distribution Function of weighted data
I have census tract data where each row holds the population size and a variable value (e.g., income). I want to plot the cumulative distribution function (CDF) of the TRUE population, i.e., ...
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Why not use eCDF to choose the model of survivability?
I have been reading a little bit about survivability and I am a little confused about choosing models. Let me set an experiment:
You run 50 toasters until all of them fail, noting down their lifespan $...
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How do you test if two discrete ECDFs are drawn from the same population?
Background
I have two Empirical Cumulative Distribution Functions (ECDFs) based on two samples of very different sizes.
Sample 1:
1020 data points, Power-Law-like distribution, discrete data in the ...
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Resample random variable to fit different variance
Suppose I have samples drawn from a random variable, and I want to multiply that random variable with a scalar constant. How should I transform the samples such that they would have been drawn from ...
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Proof of empirical expression of Cramer-Von Mises Statistics
I would like to know how to derive the empirical expression of the test statistics below:
$$
\omega^2 = \sum_{i=1}^{n}(U_{(i)}-\frac{2i-1}{2n})^2 + \frac{1}{12n}
$$
from
$$
\omega^2 = n \int_\Omega(...
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Confidence interval for sum of product of scaled binomial random variables
I have discrete, independent, but not necessarily identically distributed random variables $X_1,\dots,X_n$ that take on non-negative integer values. Each random variable has unknown distribution ...
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Comparing the output distribution of two ML models
Consider a regression task (e.g. predicting house prices) with a given train and test sets.
We start with constructing a linear regression model, in which we assume $y_i=X^T\beta+\epsilon$ with $E[\...
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Transforming data with a fitted distribution function
I have a bivariate dataset on $[0,1]^2$ in which I am interested in fitting a joint distribution. I fit a Gaussian copula but am unsure how to judge if it's a good fit. I tried transforming my data ...
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Adjustment needed for multivariate Dvoretzky–Kiefer–Wolfowitz inequality on MCMC samples?
I was thinking about studying bounds on the multivariate empirical cumulative distribution function for samples from an MCMC chains. The multivariate Dvoretzky–Kiefer–Wolfowitz inequality would seem ...
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Covariance between two binomial random variables or expectation of product of binomial random variables
I have an empirical distribution $S_n(x)$ (= proportion of samples less than equal to x) from a random sample $X_1, X_2, ..., X_n$ for a random variable $X \sim F_X$. Consider the random variable $T_n(...
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