Question

Is there any link between gamma distribution and normal distribution?
Please, help

Answer 1

ok , im not expert but in my opinion i think they are different things , not derived from each other although both are used to convert sample to universe .

Answer 2

Thanks friend, I review for final, just want to make the life easier. :)

Answer 3

good luck all the best :)

Answer 4

:)

Answer 5

see
http://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Relationships_among_some_of_univariate_probability_distributions.jpg/1280px-Relationships_among_some_of_univariate_probability_distributions.jpg

Answer 6

WWWWWWWWWWWHHHHHHHHHAAAt?? I don't want to study anymore. I go to sell Hoagies. :)

Answer 7

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Answer 8

lol

Answer 9

\[f(x)= \frac{1}{2\sqrt{2\pi}}e^{(-1/8)x^2}\]
\[F(x)=\int_{-\infty}^{x} f(t)dt=\int_{-\infty}^{x}\frac{1}{2\sqrt{2\pi}}e^{(-1/8)t^2}dt\]
\(W = X^2\)
\[G(W)= F(\sqrt w)- F(-\sqrt w)\]
\[G'(W)= F'(\sqrt w)- F'(-\sqrt w)\]
the last line is
\[G'(W) = g(w) = f(\sqrt w) ((1/2)w^{-1/2} - f(-\sqrt w)((1/2)((-1/2)w^{-1/2}\]
I don't get the last line, please, explain me

Answer 10

I type the last line wrong, it is

Answer 11

\[G'(W) = g(w) = f(\sqrt w) ((1/2)w^{-1/2}) - f(-\sqrt w)((-1/2)w^{-1/2})\]

Answer 12

I have group study now, appreciate any tips. Please, leave your guide here. I'll be back right after class. :)

Answer 13

the last line is derived from using chain rule
\[f(x) = F'(x)\]
\[(\pm \sqrt{w})' = \pm (1/2)w^{-1/2}\]

regarding your question on distributions
the gamma distribution can resemble the normal distribution as k-> infinity

"For large k the gamma distribution converges to Gaussian distribution with mean μ = kθ and variance σ2 = kθ2."

http://en.wikipedia.org/wiki/Gamma_distribution#Others

Answer 14

Thank you. :)