I saw a post from someone saying that if a distribution is bounded by zero, such as a lognormal distribution, that it doesn’t exhibit properties of kurtosis…is this true?
I think they will only exhibit positive excess kurtosis. (No negative values)
oh no sorry…that’s would be skeweness won’t it?.. need some sleep!!!
since lognormal is bounded by zero don’t think it can be negatively skewed don’t see why it could not exhibit leptokurtic or platykurtic properties
A distribution with excess (+ or - ) KURT by definition is not normally or lognormally distributed. The statement is true.
Conquistador07 Wrote: ------------------------------------------------------- > A distribution with excess (+ or - ) KURT by > definition is not normally or lognormally > distributed. The statement is true. No, the statement is absolutely not true. Almost all distributions have kurtosis. It is defined as the 4th moment of the distribution. Normal distributions happen to have kurtosis of 3, but there is no reason why a distribution that has a zero bound wouldn’t have any higher moments defined.
wyantjs Wrote: ------------------------------------------------------- > Conquistador07 Wrote: > -------------------------------------------------- > ----- > > A distribution with excess (+ or - ) KURT by > > definition is not normally or lognormally > > distributed. The statement is true. > > > No, the statement is absolutely not true. Almost > all distributions have kurtosis. It is defined as > the 4th moment of the distribution. Normal > distributions happen to have kurtosis of 3, but > there is no reason why a distribution that has a > zero bound wouldn’t have any higher moments > defined. Right, the lognormal distribution does have kurtosis, but no excess kurtosis, otherwise it wouldn’t be lognormally distributed. Key word in my statement was “excess”, as in <>3.
Conquistador07 Wrote: ------------------------------------------------------- > wyantjs Wrote: > -------------------------------------------------- > ----- > > Conquistador07 Wrote: > > > -------------------------------------------------- > > > ----- > > > A distribution with excess (+ or - ) KURT by > > > definition is not normally or lognormally > > > distributed. The statement is true. > > > > > > No, the statement is absolutely not true. > Almost > > all distributions have kurtosis. It is defined > as > > the 4th moment of the distribution. Normal > > distributions happen to have kurtosis of 3, but > > there is no reason why a distribution that has > a > > zero bound wouldn’t have any higher moments > > defined. > > > > Right, the lognormal distribution does have > kurtosis, but no excess kurtosis, otherwise it > wouldn’t be lognormally distributed. Key word in > my statement was “excess”, as in <>3. Wrong again. The lognormal density’s excess kurtosis is given by: exp(4*var) + 2*exp(3*var) + 3*exp(2*var) - 6 where var is variance. It would be nice if people would not come on this board and speak of topics they know nothing about as if they did.
I’m wrong. A log normal distribution CAN have excess kurtosis. To the original poster, the statement is wrong. http://en.wikipedia.org/wiki/File:Lognormal_distribution_PDF.png
