bfrlmomco

This function computes the Bonferroni Curve for quantile function $x(F)$ (<code>par2qua</code>, <code>qlmomco</code>). 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 $u=0$ (<code>cmlmomco</code>). The Bonferroni curve is related to the Lorenz curve ($L(u)$, <code>lrzlmomco</code>) by
$$B(u) = \frac{L(u)}{u}\mbox{.}$$

quantile function

The lmomco functions

Bonferroni curve

lifetime/reliability analysis

Extensive functions for Lmoments (LMs) and probability-weighted moments (PWMs),
distribution parameter estimation, LMs for distributions, LM ratio diagrams, multivariate
Lcomoments, and asymmetric (asy) trimmed LMs (TLMs). Maximum likelihood and
maximum product spacings estimation are available. Right-tail and left-tail LM censoring
by threshold or indicator variable are available. LMs of residual (resid) and reversed
(rev) residual life are implemented along with 13 quantile operators for reliability analyses.
Exact analytical bootstrap estimates of order statistics, LMs, and LM var-covars are available.
Harri-Coble Tau34-squared Normality Test is available. Distributions with L, TL, and added
(+) support for right-tail censoring (RC) encompass: Asy Exponential (Exp) Power [L],
Asy Triangular [L], Cauchy [TL], Eta-Mu [L], Exp. [L], Gamma [L], Generalized (Gen) Exp
Poisson [L], Gen Extreme Value [L], Gen Lambda [L, TL], Gen Logistic [L], Gen Normal [L],
Gen Pareto [L+RC, TL], Govindarajulu [L], Gumbel [L], Kappa [L], Kappa-Mu [L],
Kumaraswamy [L], Laplace [L], Linear Mean Residual Quantile Function [L], Normal [L],
3p log-Normal [L], Pearson Type III [L], Polynomial Density-Quantile 3 and 4 [L],
Rayleigh [L], Rev-Gumbel [L+RC], Rice [L], Singh Maddala [L], Slash [TL], 3p Student t [L],
Truncated Exponential [L], Wakeby [L], and Weibull [L].

William Asquith

lmomco

L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions

bfrlmomco function

<dl> <dt>f</dt>
<dd>Nonexceedance probability ($0 \le F \le 1$).</dd> <dt>para</dt>
<dd>The parameters from <code>lmom2par</code> or <code>vec2par</code>.</dd></dl>

Arguments

Author

Bonferroni Curve of the Distributions — bfrlmomco

<dl>

 <dt>f</dt>
<dd>Nonexceedance probability ($0 \le F \le 1$).</dd>

 <dt>para</dt>
<dd>The parameters from <code>lmom2par</code> or <code>vec2par</code>.</dd>

</dl>

bfrlmomco: Bonferroni Curve of the Distributions

Description

Usage

Value

Arguments

Author

References

See Also

Examples