On 13-May-05 Isobel Clark wrote: > I am a little worried by the statements: > > " As you point out, the sub-sample values should have a normal > distribution. Increasing the number of samples (n) would help. " > > Averages of lognormal (or other highly skewed) data are not Normal. The > lognormal, in particular, does not conform to the Central Limit > Theorem. This is why Sichel in the South African GoldMines and Finney > in the Royal Statistical Society worked out the lognormal estimation > theories.
A short comment, just for the sake of clarifying the above point. The lognormal distribution does indeed, in theory, "conform to the Central Limit Theorem", since it has both mean and variance, which is a sufficient condition. However, as is well known, lognormal distributions can indeed be very skew. Skewness is one of the features of a distribution which has most resistant to being ironed out by the averaging, and so very large samples my be needed before the mean, of some lognormal distributions, begins to look remotely normal. Therefore, while in theory the CLT applies to the lognormal, the skewness may be such that in practice you simply cannot take that large a sample. Best wishes to all, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 13-May-05 Time: 13:59:52 ------------------------------ XFMail ------------------------------
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