quaemu

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

distribution

quantile function

Distribution: Eta-Mu

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

quaemu function

<dl> <dt>f</dt>
<dd>Nonexceedance probability (\(0 \le F \le 1\)).</dd> <dt>para</dt>
<dd>The parameters from <code>paremu</code> or <code>vec2par</code>.</dd> <dt>paracheck</dt>
<dd>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.</dd> <dt>yacoubsintegral</dt>
<dd>A logical controlling whether the integral by Yacoub (2007) is used for the cumulative distribution function instead of numerical integration of <code>pdfemu</code>.</dd> <dt>eps</dt>
<dd>A close-enough error term for the recursion process.</dd></dl>

Arguments

Author

Quantile Function of the Eta-Mu Distribution — quaemu

<dl>

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

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

 <dt>paracheck</dt>
<dd>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.</dd>

 <dt>yacoubsintegral</dt>
<dd>A logical controlling whether the integral by Yacoub (2007) is used for the cumulative distribution function instead of numerical integration of <code>pdfemu</code>.</dd>

 <dt>eps</dt>
<dd>A close-enough error term for the recursion process.</dd>

</dl>

quaemu: Quantile Function of the Eta-Mu Distribution

Description

Usage

Value

Arguments

Author

References

See Also