samlmu | R Documentation |

Computes the “unbiased” sample (trimmed) `L`

-moments
and `L`

-moment ratios of a data vector.

```
samlmu(x, nmom=4, sort.data=TRUE, ratios=sort.data, trim=0)
samlmu.s(x, nmom=4, sort.data=TRUE, ratios=sort.data, trim=0)
.samlmu(x, nmom=4)
```

`x` |
A numeric vector. |

`nmom` |
Number of |

`sort.data` |
Logical: whether the |

`ratios` |
Logical. If |

`trim` |
Degree of trimming.
If a single value, symmetric trimming of the specified degree will be used.
If a vector of length 2, the two values
indicate the degrees of trimming at the lower and upper ends of the
“conceptual sample” (Elamir and Seheult, 2003) of order statistics
that is used to define the trimmed |

`samlmu`

and `samlmu.s`

are functionally identical.
`samlmu`

calls a Fortran routine internally, and is usually faster.
`samlmu.s`

is written entirely in the S language; it is provided
so that users can conveniently see how the calculations are done.

`.samlmu`

is a “bare-bones” version for use in programming.
It gives an error if `x`

contains missing values,
computes `L`

-moment ratios and not `L`

-moments,
does not give a warning if all the elements of `x`

are equal,
and returns its result in an unnamed vector.

Sample `L`

-moments are defined in Hosking (1990).
Calculations use the algorithm given in Hosking (1996, p.14).

Trimmed sample `L`

-moments are defined as in Hosking (2007), eq. (15)
(a small extension of Elamir and Seheult (2003), eq. (16)).
They are calculated from the untrimmed sample `L`

-moments
using the recursions of Hosking (2007), eqs. (12)-(13).

If `ratios`

is `TRUE`

, a numeric vector containing
the `L`

-moments and `L`

-moment ratios,
in the order `\ell_1`

, `\ell_2`

, `t_3`

, `t_4`

, etc.
If `ratios`

is `FALSE`

, a numeric vector containing the `L`

-moments
in the order `\ell_1`

, `\ell_2`

, `\ell_3`

, `\ell_4`

, etc.

The term “trimmed” is used in a different sense from
its usual meaning in robust statistics.
In particular, the first trimmed `L`

-moment is in general not equal to
any trimmed mean of the data sample.

J. R. M. Hosking jrmhosking@gmail.com

Elamir, E. A. H., and Seheult, A. H. (2003). Trimmed L-moments.
*Computational Statistics and Data Analysis*, **43**, 299-314.

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. (1996).
Fortran routines for use with the method of `L`

-moments, Version 3.
Research Report RC20525, IBM Research Division, Yorktown Heights, N.Y.

Hosking, J. R. M. (2007). Some theory and practical uses of trimmed L-moments.
*Journal of Statistical Planning and Inference*, **137**, 3024-3039.

```
data(airquality)
samlmu(airquality$Ozone, 6)
# Trimmed L-moment ratios
samlmu(airquality$Ozone, trim=1)
```

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