lmomcau

para


This function estimates the trimmed L-moments of the Cauchy distribution given the parameters ($\xi$ and $\alpha$) from <code><a rd-options="" href="/link/parcau?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::parcau">parcau</a></code>. The trimmed L-moments in terms of the parameters are $\lambda^{(1)}_1 = \xi$, 
$\lambda^{(1)}_2 = 0.698\alpha$, $\tau^{(1)}_3 = 0$, and $\tau^{(1)}_4 = 0.343$. These TL-moments (trim=1) are symmetrical for the first L-moments defined because $\mathrm{E}[X_{1:n}]$ and $\mathrm{E}[X_{n:n}]$ undefined expectations for the Cauchy.


L-moment (distribution)

Distribution: Cauchy

Extensive functions for L-moments (LMs) and probability-weighted moments (PWMs), parameter estimation for distributions, LM computation for distributions, and L-moment ratio diagrams. Maximum likelihood and maximum product of spacings estimation are also available. LMs for right-tail and left-tail censoring by known or unknown threshold and by indicator variable are available. Asymmetric (asy.) trimmed LMs (TL-moments, TLMs) are supported. LMs of residual (resid.) and reversed (rev.) resid. life are implemented along with 13 quantile function operators for reliability and survival analyses.  Exact analytical bootstrap estimates of order statistics, LMs, and variances-covariances of LMs are provided. The Harri-Coble Tau34-squared Normality Test is available. Distribution support with "L" (LMs), "TL" (TLMs) and added (+) support for right-tail censoring (RC) encompasses: 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 Resid. Quantile Function [L], Normal [L], 3-p log-Normal [L], Pearson Type III [L], Rayleigh [L], Rev.-Gumbel [L+RC], Rice/Rician [L], Slash [TL], 3-p Student t [L], Truncated Exponential [L], Wakeby [L], and Weibull [L]. Multivariate sample L-comoments (LCMs) are implemented to measure asymmetric association.

William Asquith

lmomco

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

lmomcau function


This function estimates the trimmed L-moments of the Cauchy distribution given the parameters ($\xi$ and $\alpha$) from <code><a rd-options='' href='parcau'>parcau</a></code>. The trimmed L-moments in terms of the parameters are $\lambda^{(1)}_1 = \xi$, 
$\lambda^{(1)}_2 = 0.698\alpha$, $\tau^{(1)}_3 = 0$, and $\tau^{(1)}_4 = 0.343$. These TL-moments (trim=1) are symmetrical for the first L-moments defined because $\mathrm{E}[X_{1:n}]$ and $\mathrm{E}[X_{n:n}]$ undefined expectations for the Cauchy.


lmomcau: Trimmed L-moments of the Cauchy Distribution

Description

Usage

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References

See Also

Examples