quaemu

Nonexceedance probability ($0 \le F \le 1$).

The parameters from <code><a rd-options="" href="/link/paremu?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::paremu">paremu</a></code> or <code><a rd-options="" href="/link/vec2par?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::vec2par">vec2par</a></code>.

para

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

paracheck

A logical controlling whether the integral by Yacoub (2007) is used for the cumulative distribution function instead of numerical integration of <code><a rd-options="" href="/link/pdfemu?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::pdfemu">pdfemu</a></code>.

yacoubsintegral

A close-enough error term for the recursion process.


This function computes the quantiles of the Eta-Mu ($\eta:\mu$) distribution given $\eta$ and $\mu$) computed by <code><a rd-options="" href="/link/paremu?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::paremu">paremu</a></code>. The quantile function is complex and numerical rooting of the cumulative distribution function (<code><a rd-options="" href="/link/cdfemu?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::cdfemu">cdfemu</a></code>) is used.


distribution

quantile function

Distribution: Eta-Mu

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

quaemu function

The parameters from <code><a rd-options='' href='paremu'>paremu</a></code> or <code><a rd-options='' href='vec2par'>vec2par</a></code>.

A logical controlling whether the integral by Yacoub (2007) is used for the cumulative distribution function instead of numerical integration of <code><a rd-options='' href='pdfemu'>pdfemu</a></code>.


This function computes the quantiles of the Eta-Mu ($\eta:\mu$) distribution given $\eta$ and $\mu$) computed by <code><a rd-options='' href='paremu'>paremu</a></code>. The quantile function is complex and numerical rooting of the cumulative distribution function (<code><a rd-options='' href='cdfemu'>cdfemu</a></code>) is used.


quaemu: Quantile Function of the Eta-Mu Distribution

Description

Usage

Arguments

Value

References

See Also

Examples