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Results tagged with empirical-cumulative-distr-fn
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user 919
Empirical cumulative distribution function: a step function increasing by $1/n$ at each unique $X$-value that occurred in the sample.
3
votes
Can some one give a step-by-step computation for an empirical distribution with this concret...
Although that post didn't say so, it was using "$\delta$" in the sense of an abstract mathematical object that one can integrate. Its rules are especially simple: for any function $f,$ the integral o …
- 334k
14
votes
Accepted
Integrating an empirical CDF
Let the sorted data be $x_1 \le x_2 \le \cdots \le x_n$. To understand the empirical CDF $G$, consider one of the values of the $x_i$--let's call it $\gamma$--and suppose that some number $k$ of the …
- 334k
11
votes
How to Compute Bivariate Empirical Distribution?
By definition, the ECDF $F$ at any location $(x,y)$ counts the data points that lie to the left and beneath $(x,y)$. Specifically, writing $(x_i,y_i), i=1, 2, \ldots, n$ for the data points (which ma …
- 334k
13
votes
What inferential method produces the empirical CDF?
In An Introduction to the Bootstrap, Efron and Tibshirani find it useful to characterize the empirical cumulative distribution function (ecdf) as the nonparametric maximum likelihood estimate of the " …
- 334k
4
votes
Accepted
Median from two unmergable datasets
By adapting the (simple, recursive) method for approximating QQ plots I described at https://stats.stackexchange.com/a/35268/919, you can efficiently find a precise (piecewise linear) approximation of …
- 334k
2
votes
Accepted
Covariance between two binomial random variables or expectation of product of binomial rando...
The basis of this result is the observation that
$$F(x) = \Pr(X_i\le x) = E[I(X_i\le x)]$$
for all $i.$
For $i\ne j,$ the variables $X_i$ and $X_j$ are independent, whence so are their indicators, giv …
- 334k
52
votes
Accepted
Intuitive explanation of Kolmogorov Smirnov Test
The Kolmogorov-Smirnov test assesses the hypothesis that a random sample (of numerical data) came from a continuous distribution that was completely specified without referring to the data.
Here is th …
- 334k