Mixing
convention in writing measurement results in log-normal distribution
$begingroup$
from a physical phenomena with log-normal distribution, someone writes a measurement result as $30 pm 13 $ cm.
How do I know whether they are $mu pmsigma$, $mu* pmsigma*$, $E[x] pm SD[X]$?
definition
$X$ = r.v. in original scale
$mu = mean(log(X))$ (additive)
$sigma = sd(log(X))$ (additive)
$mu* = e^mu$ (multiplicative)
$sigma* = e^sigma$ (multiplicative)
$E[x] = e^{(mu + frac{1}{2}sigma^2)}$ (multiplicative??)
$SD[x] = e^{(mu + frac{1}{2}sigma^2)} sqrt{e^{sigma^2}-1}$ (multiplicative??)
I know that $mu*$ and $sigma*$ is multiplicative and I have seen them written as $mu* /. sigma*$.
edit:
after some example calculations and trial end error attempts, I think they are $E[x] pm SD[X]$.
But still need some confirmation and maybe explanation about the convention.
statistics probability-distributions convention
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
$endgroup$
add a comment |
$begingroup$
from a physical phenomena with log-normal distribution, someone writes a measurement result as $30 pm 13 $ cm.
How do I know whether they are $mu pmsigma$, $mu* pmsigma*$, $E[x] pm SD[X]$?
definition
$X$ = r.v. in original scale
$mu = mean(log(X))$ (additive)
$sigma = sd(log(X))$ (additive)
$mu* = e^mu$ (multiplicative)
$sigma* = e^sigma$ (multiplicative)
$E[x] = e^{(mu + frac{1}{2}sigma^2)}$ (multiplicative??)
$SD[x] = e^{(mu + frac{1}{2}sigma^2)} sqrt{e^{sigma^2}-1}$ (multiplicative??)
I know that $mu*$ and $sigma*$ is multiplicative and I have seen them written as $mu* /. sigma*$.
edit:
after some example calculations and trial end error attempts, I think they are $E[x] pm SD[X]$.
But still need some confirmation and maybe explanation about the convention.
statistics probability-distributions convention
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
$endgroup$
add a comment |
$begingroup$
from a physical phenomena with log-normal distribution, someone writes a measurement result as $30 pm 13 $ cm.
How do I know whether they are $mu pmsigma$, $mu* pmsigma*$, $E[x] pm SD[X]$?
definition
$X$ = r.v. in original scale
$mu = mean(log(X))$ (additive)
$sigma = sd(log(X))$ (additive)
$mu* = e^mu$ (multiplicative)
$sigma* = e^sigma$ (multiplicative)
$E[x] = e^{(mu + frac{1}{2}sigma^2)}$ (multiplicative??)
$SD[x] = e^{(mu + frac{1}{2}sigma^2)} sqrt{e^{sigma^2}-1}$ (multiplicative??)
I know that $mu*$ and $sigma*$ is multiplicative and I have seen them written as $mu* /. sigma*$.
edit:
after some example calculations and trial end error attempts, I think they are $E[x] pm SD[X]$.
But still need some confirmation and maybe explanation about the convention.
statistics probability-distributions convention
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
$endgroup$
from a physical phenomena with log-normal distribution, someone writes a measurement result as $30 pm 13 $ cm.
How do I know whether they are $mu pmsigma$, $mu* pmsigma*$, $E[x] pm SD[X]$?
definition
$X$ = r.v. in original scale
$mu = mean(log(X))$ (additive)
$sigma = sd(log(X))$ (additive)
$mu* = e^mu$ (multiplicative)
$sigma* = e^sigma$ (multiplicative)
$E[x] = e^{(mu + frac{1}{2}sigma^2)}$ (multiplicative??)
$SD[x] = e^{(mu + frac{1}{2}sigma^2)} sqrt{e^{sigma^2}-1}$ (multiplicative??)
I know that $mu*$ and $sigma*$ is multiplicative and I have seen them written as $mu* /. sigma*$.
edit:
after some example calculations and trial end error attempts, I think they are $E[x] pm SD[X]$.
But still need some confirmation and maybe explanation about the convention.
statistics probability-distributions convention
statistics probability-distributions convention
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
edited Jan 31 at 4:13
Codelearner777
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
asked Jan 31 at 2:06
Codelearner777Codelearner777
427
427
add a comment |
add a comment |
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