help for lmose

Standard errors for L-moments and derived statistics

lmose
varname
[if exp]
[in range]
[,
matlist_options
]

by ... : may also be used with lmose:
see help on by.

Description

lmose calculates standard errors for L-moments and derived
statistics for a numeric variable varname.

Remarks

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,

var(U/V) = {var(U)/E(U)^2 + var(V)/E(V)^2 - 2 cov(U,V)/(E(U) E(V))} {E(U)/E(V)}^2.

This information is reported for the one variable only.
However, 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.

Options

matlist_options are options of matrix list.
The default display has format(%9.3f).

Examples

. lmose price

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

Acknowledgments

Allan Seheult kindly provided and discussed reprints of his
joint work. William Gould was most helpful over the first version of
the Mata code.

Author

Nicholas J. Cox, Durham University, U.K.

n.j.cox@durham.ac.uk

References

The L-moments page

Elamir, E.A.H. and A.H. Seheult. 2004.
Exact variance structure of sample L-moments.
Journal of Statistical Planning and Inference 124: 337-359.

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: 105-124.

Hosking, J.R.M. 1998. L-moments. In Kotz, S., C.B. Read and
D.L. Banks (eds) Encyclopedia of Statistical Sciences Update Volume 2.
New York: Wiley, 357-362.

Hosking, J.R.M. and J.R. Wallis. 1997.
Regional frequency analysis: an approach based on L-moments.
Cambridge University Press.

Royston, P. 1992.
Which measures of skewness and kurtosis are best?
Statistics in Medicine 11: 333-343.

See also

lmo (if installed); lmoments (if installed; older version with some discontinued features)