bounder_cooke: Estimate bounds of a distribution using Cooke's method

In ggdist: Visualizations of Distributions and Uncertainty

Estimate bounds of a distribution using Cooke's method

Description

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.

Usage

bounder_cooke(x)

Arguments

x	numeric vector containing a sample to estimate the bounds of.

Details

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 ith order statistic of x (i.e. its ith-smallest value).

Value

A length-2 numeric vector giving an estimate of the minimum and maximum bounds of the distribution that x came from.

References

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")}

See Also

The bounder argument to density_bounded().

Other bounds estimators: bounder_cdf(), bounder_range()

ggdist documentation built on Nov. 27, 2023, 9:06 a.m.