# bfrlmomco: Bonferroni Curve of the Distributions In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 bfrlmomco R Documentation

## Bonferroni Curve of the Distributions

### Description

This function computes the Bonferroni Curve for quantile function x(F) (par2qua, qlmomco). The function is defined by Nair et al. (2013, p. 179) as

B(u) = \frac{1}{\mu u}\int_0^u x(p)\; \mathrm{d}p\mbox{,}

where B(u) is Bonferroni curve for quantile function x(F) and \mu is the conditional mean for quantile u=0 (cmlmomco). The Bonferroni curve is related to the Lorenz curve (L(u), lrzlmomco) by

B(u) = \frac{L(u)}{u}\mbox{.}

### Usage

bfrlmomco(f, para)


### Arguments

 f Nonexceedance probability (0 \le F \le 1). para The parameters from lmom2par or vec2par.

### Value

Bonferroni curve value for F.

W.H. Asquith

### References

Nair, N.U., Sankaran, P.G., and Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

qlmomco, lrzlmomco

### Examples

# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(0.0, 2649, 2.11), type="gov") # so set lower bounds = 0.0

"afunc" <- function(u) { return(par2qua(u,A,paracheck=FALSE)) }
f <- 0.65 # Both computations report: 0.5517342
Bu1 <- 1/(cmlmomco(f=0,A)*f) * integrate(afunc, 0, f)\$value
Bu2 <- bfrlmomco(f, A)


lmomco documentation built on May 29, 2024, 10:06 a.m.