quast3

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

The parameters from <code><a href="/link/parst3?package=lmomco&version=2.0.1" rd-options="" data-mini-rdoc="lmomco::parst3">parst3</a></code> or similar.

para

A logical on whether the parameter should be check for validity.

paracheck

This function computes the quantiles of the 3-parameter Student T distribution given parameters ($\xi$, $\alpha$, $\nu$) of the distribution computed by <code><a href="/link/parst3?package=lmomco&version=2.0.1" rd-options="" data-mini-rdoc="lmomco::parst3">parst3</a></code>. There is no explicit solution for the quantile function for nonexceedance probability <code>F</code> but built-in Rfunctions can be used. For $\nu \ge 1000$, <code>qnorm(F, mean=U, sd=A)</code> for <code>U</code> = $\xi$ and <code>A</code> = $\alpha$ for $1.000001 \le \nu \le 1000$, <code>U + A*qt(F, N)</code> for <code>N</code> = $\nu$ and where <code>qnorm()</code> is for the Normal distribution and <code>qt()</code> is the 1-parameter Student T distribution.

distribution

quantile function

The package is a comparatively comprehensive implementation of the theory of L-moments. L-moment, probability-weighted moment (PWM), and parameter estimation for numerous familiar and not-so-familiar distributions are provided. L-moment estimate for the same distributions are provided. L-moments are analogous to product moments; however, L-moments have many advantages including unbiasedness, robustness, and consistency. L-moments can outperform maximum likelihood for small to moderate samples. The package originally was originally oriented around circa 1996-FORTRAN algorithms by Hosking, and the nomenclature parallels that of Hosking. The Hosking algorithms later became available in the lmom package. However, vast extensions, components, concepts, more distributions, L-moment curiosities, and research topics are added. Such extensions the Sen weighted mean, Gini mean difference, plotting positions, and conditional probability adjustments. L-moment ratio diagrams are supported. L-moment support for right-tail and left-tail censoring by known or unknown censoring threshold and also by indicator variable. Asymmetric trimmed L-moments are supported as are numerical integration to dynamically compute trajectories of select TL-moment ratios for the construction of TL-moment ratio diagrams. L-moments have multi-variate analogs; the sample L-comoments are implemented and might have considerable application with copulas because L-comoments measure asymmetric association and higher comoments or comovements of variables. Support exists for exact analytical boot-strap estimates of order statistics, L-moments, and variances-covariances of L-moments. The Harri-Coble Tau34-squared Test for Normality using sample L-skew and L-kurtosis is available. Support for the following distributions, with moment type shown as "L" (L-moments) or "TL" (trimmed L-moments) and additional support for right-tail censoring ([RC]) include, is available: Asymmetric Exponential Power (L), Cauchy (TL), Eta-Mu (L), Exponential (L), Gamma (L), Generalized Extreme Value (L), Generalized Lambda (L & TL), Generalized Logistic (L), Generalized Normal (L), Generalized Pareto (L[RC] & TL), Govindarajulu (L), Gumbel (L), Kappa (L), Kappa-Mu (L), Kumaraswamy (L), Laplace (L), Normal (L), 3-parameter log-Normal (L), Pearson Type III (L), Rayleigh (L), Reverse Gumbel (L[RC]), Rice/Rician (L), Slash (TL), 3-parameter Student T (L), Truncated Exponential (L), Wakeby (L), and Weibull (L).

quast3: Quantile Function of the 3-Parameter Student T Distribution

Description

Usage

Arguments

Value

References

See Also

Examples