L-moments (Hosking, J. R. Statis. Soc. B, 52, 105-124, 1990) are summary statistics of probability distributions and data samples, computed from linear combinations of the ordered data values. Like the ordinary moments, the first few sample L-moments of a data set give an indication of possible families of distributions that might fit the data. However, L-moments have several disadvantages: in particular, population L-moments exist even when the variance or higher-order ordinary moments are infinite, and sample L-moments are less affected than the ordinary moments by the presence of outliers in the data sample.
Many financial computations, such as option pricing and calculation of Value at Risk, require knowledge of the distribution of returns on financial instruments. It is generally acknowledged that the naive assumption that returns are Normally distributed is inadequate, but there is little agreement about what other distributions are appropriate. As an example of the use of L-moments with financial data, we analyze the distribution of daily returns on IBM stock and demonstrate the ability of L-moments to identify which heavy-tailed distributions are consistent with the data.
By: J. R. M. Hosking
Published in: RC21466 in 1999
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