bounder_cooke | R Documentation |
Estimate the bounds of the distribution a sample came from using Cooke's method.
Use with the bounder
argument to density_bounded()
.
Supports automatic partial function application.
bounder_cooke(x)
x |
numeric vector containing a sample to estimate the bounds of. |
Estimate the bounds of a distribution using the method from Cooke (1979); i.e. method 2.3 from Loh (1984). These bounds are:
\left[\begin{array}{l}
2X_{(1)} - \sum_{i = 1}^n \left[\left(1 - \frac{i - 1}{n}\right)^n -
\left(1 - \frac{i}{n}\right)^n \right] X_{(i)}\\
2X_{(n)} - \sum_{i = 1}^n \left[\left(1 - \frac{n - i}{n}\right)^n -
\left(1 - \frac{n + 1 - i}{n} \right)^n\right] X_{(i)}
\end{array}\right]
Where X_{(i)}
is the i
th order statistic of x
(i.e. its
i
th-smallest value).
A length-2 numeric vector giving an estimate of the minimum and maximum bounds
of the distribution that x
came from.
Cooke, P. (1979). Statistical inference for bounds of random variables. Biometrika 66(2), 367–374. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/66.2.367")}.
Loh, W. Y. (1984). Estimating an endpoint of a distribution with resampling methods. The Annals of Statistics 12(4), 1543–1550. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1176346811")}
The bounder
argument to density_bounded()
.
Other bounds estimators:
bounder_cdf()
,
bounder_range()
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