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Intersection Puzzle

Determine the skewness of a gamma distribution with a coefficient of variation of 1.

Range of coefficient of SkewnessIf the prior distribution of $lambda$ is a gamma distribution with mean 1.4 and std dev of .5 find the appropriate values and $alpha$ and $beta$Maximum Likelihood Estimation with a Gamma distributionFinding the distribution of a dependent function given the mean and coefficient of variation (COV) of the independent parameters.How to find the mode and median of a Gamma distribution?Is there an equation for the maximum of n random draws from a Gamma distributionIs that possible to change any gamma distribution to $Gamma(k=0,theta=1)$Prove the normal approximation of beta distributionGamma Distribution. Estimators. ConsistencyTest if reduction of coefficient of variation is significant

0

$begingroup$

let $alpha =a$ and $beta =b$
If $X$ follows a gamma dist. then $E[X]=fracab$ and $Var[X]=fracab^2$

how do I prove that the mean is equal to the standard deviation, so the coefficient of variation equals one?

statistics

share|cite|improve this question

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

$endgroup$

add a comment | 

0

$begingroup$

let $alpha =a$ and $beta =b$
If $X$ follows a gamma dist. then $E[X]=fracab$ and $Var[X]=fracab^2$

how do I prove that the mean is equal to the standard deviation, so the coefficient of variation equals one?

statistics

share|cite|improve this question

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

$endgroup$

add a comment | 

$begingroup$

let $alpha =a$ and $beta =b$
If $X$ follows a gamma dist. then $E[X]=fracab$ and $Var[X]=fracab^2$

how do I prove that the mean is equal to the standard deviation, so the coefficient of variation equals one?

statistics

share|cite|improve this question

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

$endgroup$

share|cite|improve this question

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

share|cite|improve this question

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

edited Oct 6 '17 at 2:24

IEDC PHY

17712

edited Oct 6 '17 at 2:24

IEDC PHY

17712

asked Oct 6 '17 at 2:10

karlkarl

1

asked Oct 6 '17 at 2:10

karlkarl

1

1 Answer
1

active

oldest

votes

0

$begingroup$

Correct me if I'm wrong, but you're not being asked to prove that the CV of the gamma distribution is equal to one (which isn't generally the case), but to find the skewness assuming that the CV = 1. Now,

$textCV = fracsigmamu$,

so if the CV = 1, it should be obvious that $mu = sigma$. Now, all you have to do is plug in $a/b$ for $mu$ and $sqrta/b^2$ for $sigma$. Solve for $a$, and then you can use the formula for skewness for the gamma distribution (https://en.wikipedia.org/wiki/Gamma_distribution)

share|cite|improve this answer

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

$endgroup$

add a comment | 

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0

$begingroup$

Correct me if I'm wrong, but you're not being asked to prove that the CV of the gamma distribution is equal to one (which isn't generally the case), but to find the skewness assuming that the CV = 1. Now,

$textCV = fracsigmamu$,

so if the CV = 1, it should be obvious that $mu = sigma$. Now, all you have to do is plug in $a/b$ for $mu$ and $sqrta/b^2$ for $sigma$. Solve for $a$, and then you can use the formula for skewness for the gamma distribution (https://en.wikipedia.org/wiki/Gamma_distribution)

share|cite|improve this answer

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

$endgroup$

add a comment | 

0

$begingroup$

Correct me if I'm wrong, but you're not being asked to prove that the CV of the gamma distribution is equal to one (which isn't generally the case), but to find the skewness assuming that the CV = 1. Now,

$textCV = fracsigmamu$,

so if the CV = 1, it should be obvious that $mu = sigma$. Now, all you have to do is plug in $a/b$ for $mu$ and $sqrta/b^2$ for $sigma$. Solve for $a$, and then you can use the formula for skewness for the gamma distribution (https://en.wikipedia.org/wiki/Gamma_distribution)

share|cite|improve this answer

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

$endgroup$

add a comment | 

$begingroup$

Correct me if I'm wrong, but you're not being asked to prove that the CV of the gamma distribution is equal to one (which isn't generally the case), but to find the skewness assuming that the CV = 1. Now,

$textCV = fracsigmamu$,

so if the CV = 1, it should be obvious that $mu = sigma$. Now, all you have to do is plug in $a/b$ for $mu$ and $sqrta/b^2$ for $sigma$. Solve for $a$, and then you can use the formula for skewness for the gamma distribution (https://en.wikipedia.org/wiki/Gamma_distribution)

share|cite|improve this answer

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

$endgroup$

share|cite|improve this answer

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

answered Oct 6 '17 at 2:59

BayesicBayesic

1145

answered Oct 6 '17 at 2:59

BayesicBayesic

1145