L-moment

In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution.[1][2][3][4] They are linear combinations of order statistics (L-statistics) analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively (the L-mean is identical to the conventional mean). Standardised L-moments are called L-moment ratios and are analogous to standardized moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments. Sample L-moments can be defined for a sample from the population, and can be used as estimators of the population L-moments.

  1. ^ Hosking, J.R.M. (1990). "L-moments: analysis and estimation of distributions using linear combinations of order statistics". Journal of the Royal Statistical Society, Series B. 52 (1): 105–124. doi:10.1111/j.2517-6161.1990.tb01775.x. JSTOR 2345653.
  2. ^ Hosking, J.R.M. (1992). "Moments or L moments? An example comparing two measures of distributional shape". The American Statistician. 46 (3): 186–189. doi:10.2307/2685210. JSTOR 2685210.
  3. ^ Hosking, J.R.M. (2006). "On the characterization of distributions by their L-moments". Journal of Statistical Planning and Inference. 136: 193–198. doi:10.1016/j.jspi.2004.06.004.
  4. ^ Asquith, W.H. (2011) Distributional analysis with L-moment statistics using the R environment for statistical computing, Create Space Independent Publishing Platform, [print-on-demand], ISBN 1-463-50841-7