- #1
Usjes
- 9
- 0
Hi,
It has been a long time since I have worked with pdfs so perhaps someone can help. According to Wikipedia (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Additivity) the pdf of the addition of n independend Chi_squared distributed R.V.s is also Chi_squared distributed but with n*k degrees of freedom where the original R.V.s each had k DofF. It goes on though to say that the mean of n such Chi_squared R.V.s has a Gamma Distribution (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Sample_mean)
But the mean is just the sum scaled by 1/n, does this imply that the Gamma distribution is essentially the same as the Chi_squared distribution (just compressed along the x-axis) ? Or is the Wikipedia entry wrong ? I just find it odd that there would be two 'standard' distributions that are just transforms of one-another, can anyone anyone confirm this ?
Thanks,
Usjes.
It has been a long time since I have worked with pdfs so perhaps someone can help. According to Wikipedia (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Additivity) the pdf of the addition of n independend Chi_squared distributed R.V.s is also Chi_squared distributed but with n*k degrees of freedom where the original R.V.s each had k DofF. It goes on though to say that the mean of n such Chi_squared R.V.s has a Gamma Distribution (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Sample_mean)
But the mean is just the sum scaled by 1/n, does this imply that the Gamma distribution is essentially the same as the Chi_squared distribution (just compressed along the x-axis) ? Or is the Wikipedia entry wrong ? I just find it odd that there would be two 'standard' distributions that are just transforms of one-another, can anyone anyone confirm this ?
Thanks,
Usjes.