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CLT and sum of gamma random variables

0

$begingroup$

I am having trouble approximating the sum of gamma-distributed variables via CLR.

I know via Gamma that
$X=sum_i=1^n X_i \$ and
$XsimGamma(nalpha,beta) \$

and $CLT: Z_n=fracoverlineX-nmusigmasqrtn$

Let's say n = 300, $X_isimGamma(0.6,0.3) \$
so $X=sum_i=1^n X_i \$, $XsimGamma(300*(0.6),0.3) \$

$mu = fracalphabeta = 600.\
sigma^2 = fracalphabeta^2 = 2000\
sigma = 44.72\$

For $Z_n$, does $nmu$ refer to $300*mu$?

Thanks in advance.

central-limit-theorem gamma-distribution

share|cite|improve this question

asked Mar 27 at 7:34

Sean MciSean Mci

82

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $nmu$ is just $600$.
  $endgroup$
  – Kavi Rama Murthy
  Mar 27 at 7:55
  

  
  
  
  

add a comment | 

0

$begingroup$

I am having trouble approximating the sum of gamma-distributed variables via CLR.

I know via Gamma that
$X=sum_i=1^n X_i \$ and
$XsimGamma(nalpha,beta) \$

and $CLT: Z_n=fracoverlineX-nmusigmasqrtn$

Let's say n = 300, $X_isimGamma(0.6,0.3) \$
so $X=sum_i=1^n X_i \$, $XsimGamma(300*(0.6),0.3) \$

$mu = fracalphabeta = 600.\
sigma^2 = fracalphabeta^2 = 2000\
sigma = 44.72\$

For $Z_n$, does $nmu$ refer to $300*mu$?

Thanks in advance.

central-limit-theorem gamma-distribution

share|cite|improve this question

asked Mar 27 at 7:34

Sean MciSean Mci

82

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $nmu$ is just $600$.
  $endgroup$
  – Kavi Rama Murthy
  Mar 27 at 7:55
  

  
  
  
  

add a comment | 

$begingroup$

I am having trouble approximating the sum of gamma-distributed variables via CLR.

I know via Gamma that
$X=sum_i=1^n X_i \$ and
$XsimGamma(nalpha,beta) \$

and $CLT: Z_n=fracoverlineX-nmusigmasqrtn$

Let's say n = 300, $X_isimGamma(0.6,0.3) \$
so $X=sum_i=1^n X_i \$, $XsimGamma(300*(0.6),0.3) \$

$mu = fracalphabeta = 600.\
sigma^2 = fracalphabeta^2 = 2000\
sigma = 44.72\$

For $Z_n$, does $nmu$ refer to $300*mu$?

Thanks in advance.

central-limit-theorem gamma-distribution

share|cite|improve this question

asked Mar 27 at 7:34

Sean MciSean Mci

82

$endgroup$

share|cite|improve this question

asked Mar 27 at 7:34

Sean MciSean Mci

82

share|cite|improve this question

asked Mar 27 at 7:34

Sean MciSean Mci

82

asked Mar 27 at 7:34

Sean MciSean Mci

82

asked Mar 27 at 7:34

Sean MciSean Mci

82