{smcl} {* 13apr2010}{...} {hline} help for {hi:lmose} {hline} {title:Standard errors for L-moments and derived statistics} {p 8 17 2}{cmd:lmose} {it:varname} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{cmd:,} {it:matlist_options} ] {p 4 4 2}{cmd:by ... :} may also be used with {cmd:lmose}: see help on {help by}. {title:Description} {p 4 4 2}{cmd:lmose} calculates standard errors for L-moments and derived statistics for a numeric variable {it:varname}. {title:Remarks} {p 4 4 2}Specifically, the variance matrix of sample L-moments and the standard error vector of sample L-moments and derived ratios is displayed. The variance matrix of sample L-moments is estimated using the exact unbiased distribution-free estimator of Elamir and Seheult (2004). Note that negative estimates of each variance are possible, especially with very small samples. The standard errors of sample L-moments are the square roots of the diagonal elements of that matrix. The standard errors of t, t_3 and t_4 are obtained from the variances of ratios l_2/l_1, l_3/l_2, l_4/l_2 using Taylor-series-based approximations: for a ratio U/V, {p 8 8 2}var(U/V) = {c -(}var(U)/E(U)^2 + var(V)/E(V)^2 - 2 cov(U,V)/(E(U) E(V)){c )-} {c -(}E(U)/E(V){c )-}^2. {p 4 4 2}This information is reported for the one variable only. However, {cmd:by:} may be used to obtain listings of standard errors for each of several groups. This program can be rather slow for larger sample sizes. {title:Options} {p 4 8 2}{it:matlist_options} are options of {help matrix list}. The default display has {cmd:format(%9.3f)}. {title:Examples} {p 4 8 2}{cmd:. lmose price} {title:Saved results} r(V) variance matrix of l_1 ... l_4 r(SE) standard error vector of l_1 ... l_4 t t_3 t_4 {title:Acknowledgments} {p 4 4 2}Allan Seheult kindly provided and discussed reprints of his joint work. William Gould was most helpful over the first version of the Mata code. {title:Author} {p 4 4 2}Nicholas J. Cox, Durham University, U.K.{break} n.j.cox@durham.ac.uk {title:References} {p 4 8 2}{browse "http://www.research.ibm.com/people/h/hosking/lmoments.html": The L-moments page} {p 4 8 2}Elamir, E.A.H. and A.H. Seheult. 2004. Exact variance structure of sample L-moments. {it:Journal of Statistical Planning and Inference} 124: 337{c -}359. {p 4 8 2}Hosking, J.R.M. 1990. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. {it:Journal of the Royal Statistical Society} Series B 52: 105{c -}124. {p 4 8 2}Hosking, J.R.M. 1998. L-moments. In Kotz, S., C.B. Read and D.L. Banks (eds) {it:Encyclopedia of Statistical Sciences Update Volume 2.} New York: Wiley, 357{c -}362. {p 4 8 2}Hosking, J.R.M. and J.R. Wallis. 1997. {it:Regional frequency analysis: an approach based on L-moments.} Cambridge University Press. {p 4 8 2}Royston, P. 1992. Which measures of skewness and kurtosis are best? {it:Statistics in Medicine} 11: 333{c -}343. {title:See also} {p 4 8 2}{help lmo} (if installed); {help lmoments} (if installed; older version with some discontinued features)