quatri

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

The parameters from <code><a rd-options="" href="/link/partri?package=lmomco&version=2.3.1" data-mini-rdoc="lmomco::partri">partri</a></code> or <code><a rd-options="" href="/link/vec2par?package=lmomco&version=2.3.1" 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

This function computes the quantiles of the Asymmetric Triangular distribution given parameters ($\nu$, $\omega$, and $\psi$) of the distribution computed by <code><a rd-options="" href="/link/partri?package=lmomco&version=2.3.1" data-mini-rdoc="lmomco::partri">partri</a></code>. The quantile function of the distribution is
$$x(F) = \nu + \sqrt{(\psi - \nu)(\omega - \nu)F}\mbox{,}$$
for $F &lt; P$,
$$x(F) = \psi - \sqrt{(\psi - \nu)(\psi - \omega)(1-F)}\mbox{,}$$
for $F &gt; P$, and
$$x(F) = \omega\mbox{,}$$
for $F = P$
where $x(F)$ is the quantile for nonexceedance probability $F$, $\nu$ is the minimum, $\psi$ is the maximum, and $\omega$ is the mode of the distribution and
$$P = \frac{(\omega - \nu)}{(\psi - \nu)}\mbox{.}$$

distribution

quantile function

Distribution: Asymmetric Triangular

Distribution: Triangular

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 associations.

William Asquith

lmomco

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

quatri function

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

This function computes the quantiles of the Asymmetric Triangular distribution given parameters ($\nu$, $\omega$, and $\psi$) of the distribution computed by <code><a rd-options='' href='partri'>partri</a></code>. The quantile function of the distribution is
$$x(F) = \nu + \sqrt{(\psi - \nu)(\omega - \nu)F}\mbox{,}$$
for $F &lt; P$,
$$x(F) = \psi - \sqrt{(\psi - \nu)(\psi - \omega)(1-F)}\mbox{,}$$
for $F &gt; P$, and
$$x(F) = \omega\mbox{,}$$
for $F = P$
where $x(F)$ is the quantile for nonexceedance probability $F$, $\nu$ is the minimum, $\psi$ is the maximum, and $\omega$ is the mode of the distribution and
$$P = \frac{(\omega - \nu)}{(\psi - \nu)}\mbox{.}$$

quatri: Quantile Function of the Asymmetric Triangular Distribution

Description

Usage

Arguments

Value

See Also

Examples