File:Edgeworth expansion of the density of the sample mean of three Chi2 variables.png
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Edgeworth_expansion_of_the_density_of_the_sample_mean_of_three_Chi2_variables.png (480 × 480 pixels, file size: 31 KB, MIME type: image/png)
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[edit]DescriptionEdgeworth expansion of the density of the sample mean of three Chi2 variables.png |
English: This is a statistical chart that shows the density of the sample mean of three chi2 variables. The chart compares the true density, the normal approximation, and two edgeworth expansions |
Date | |
Source | Own work |
Author | EtudiantEco |
Source Code
[edit]This chart was created with the software R, version 3.02, using the package EQL [1]
library(EQL) n <- 3 df <- 2 ### Set grid: x_eval_chi <- seq(0,10, by=0.05) ## true distribution: true <- dgamma(x=x_eval_chi, shape=df*n/2, scale=2/n) ##Plot true plot(x_eval_chi, true, col=1, lty=1, type="l", xlab="x", ylab="density", lwd=2) title(expression(paste("Density of the sample mean of three ", chi^2, "(2) variables"))) ## add normal approximation: lines(x_eval_chi, dnorm(x_eval_chi,mean=df, sd=sqrt(2*df/n)), col=3, lwd=2) ## compute edgeworth approximations: edge_2 <- edgeworth(x_eval_chi, n=n, mu=df, sigma2=2*df, rho3=sqrt(8/df), rho4=12/df, type="mean", deg=2)$approx edge_3 <- edgeworth(x_eval_chi, n=n, mu=df, sigma2=2*df, rho3=sqrt(8/df), rho4=12/df, type="mean", deg=3)$approx]] ## add edgeworth on graph: lines(x_eval_chi, edge_2, col=4) lines(x_eval_chi, edge_3, col=4, lty=2) ## add legend: legend("topright", leg=c("True", "Edgeworth, degree 2", "Edgeworth, degree 3", "Normal"), col=c(1,4,4,3), lty=c(1,1,2,1))
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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- to share – to copy, distribute and transmit the work
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 16:44, 3 November 2013 | 480 × 480 (31 KB) | EtudiantEco (talk | contribs) | User created page with UploadWizard |
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