Shift of log-normal distribution and skewness of associated gaussian
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I have a dataset where the best fit (e.g. with MATLAB's fitdist) appears to be a log-normal distribution.
Taking the logarithm of the data however results in a normal distribution with a skewness of -0.3, i.e. a left-skew normal distribution (Figure left).
An iterative algorithm reveals for a 3-parameteric log-normal a shift of -2.8, however, and log(X+2.8) results in
a normal distribution with a skewness close to zero (Figure right):
My questions:
(i) How is the shift of the log-normal distribution (analytically) related to the skewness of the associated normal distribution?
(ii) The original data has values of at least 1. How comes that the shift of the log-normal distribution can be negative, if the shift of the 3-parameter log-normal defines the support of the log-normal distribution?
probability normal-distribution
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
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add a comment |
$begingroup$
I have a dataset where the best fit (e.g. with MATLAB's fitdist) appears to be a log-normal distribution.
Taking the logarithm of the data however results in a normal distribution with a skewness of -0.3, i.e. a left-skew normal distribution (Figure left).
An iterative algorithm reveals for a 3-parameteric log-normal a shift of -2.8, however, and log(X+2.8) results in
a normal distribution with a skewness close to zero (Figure right):
My questions:
(i) How is the shift of the log-normal distribution (analytically) related to the skewness of the associated normal distribution?
(ii) The original data has values of at least 1. How comes that the shift of the log-normal distribution can be negative, if the shift of the 3-parameter log-normal defines the support of the log-normal distribution?
probability normal-distribution
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
$endgroup$
2
$begingroup$
Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52
add a comment |
$begingroup$
I have a dataset where the best fit (e.g. with MATLAB's fitdist) appears to be a log-normal distribution.
Taking the logarithm of the data however results in a normal distribution with a skewness of -0.3, i.e. a left-skew normal distribution (Figure left).
An iterative algorithm reveals for a 3-parameteric log-normal a shift of -2.8, however, and log(X+2.8) results in
a normal distribution with a skewness close to zero (Figure right):
My questions:
(i) How is the shift of the log-normal distribution (analytically) related to the skewness of the associated normal distribution?
(ii) The original data has values of at least 1. How comes that the shift of the log-normal distribution can be negative, if the shift of the 3-parameter log-normal defines the support of the log-normal distribution?
probability normal-distribution
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
$endgroup$
I have a dataset where the best fit (e.g. with MATLAB's fitdist) appears to be a log-normal distribution.
Taking the logarithm of the data however results in a normal distribution with a skewness of -0.3, i.e. a left-skew normal distribution (Figure left).
An iterative algorithm reveals for a 3-parameteric log-normal a shift of -2.8, however, and log(X+2.8) results in
a normal distribution with a skewness close to zero (Figure right):
My questions:
(i) How is the shift of the log-normal distribution (analytically) related to the skewness of the associated normal distribution?
(ii) The original data has values of at least 1. How comes that the shift of the log-normal distribution can be negative, if the shift of the 3-parameter log-normal defines the support of the log-normal distribution?
probability normal-distribution
probability normal-distribution
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
edited Dec 2 '18 at 22:49
LinAlg
8,9411521
8,9411521
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
asked Dec 2 '18 at 19:02
TestGuestTestGuest
405821
405821
2
$begingroup$
Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52
add a comment |
2
$begingroup$
Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52
2
2
$begingroup$
Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52
$begingroup$
Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52
add a comment |
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Note that a normal distribution is not skewed.
$endgroup$
– Jean-Claude Arbaut
Dec 2 '18 at 22:52