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help for lmose
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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)