cdfst3

The parameters from <code><a rd-options="" href="/link/parst3?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::parst3">parst3</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 on whether the parameter should be check for validity.

paracheck

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters ($\xi$, $\alpha$, $\nu$) computed by <code><a rd-options="" href="/link/parst3?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::parst3">parst3</a></code>. There is no explicit solution for the cumulative distribution function for value <code>X</code> but built-in R functions can be used. For $\nu \ge 1000$, one can use <code>pnorm(X, mean=U, sd=A)</code> for <code>U</code> = $\xi$ and <code>A</code> = $\alpha$ and for $1.000001 \le \nu \le 1000$, one can use <code>pt((X-U)/A, N)</code> for <code>N</code> = $\nu$ and where the R function <code>pnorm</code> is for the Normal distribution and the R function <code>pt</code> is the 1-parameter Student t distribution.

distribution

cumulative distribution function

Distribution: Student t (3-parameter)

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

cdfst3 function

The parameters from <code><a rd-options='' href='parst3'>parst3</a></code> or <code><a rd-options='' href='vec2par'>vec2par</a></code>.

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters ($\xi$, $\alpha$, $\nu$) computed by <code><a rd-options='' href='parst3'>parst3</a></code>. There is no explicit solution for the cumulative distribution function for value <code>X</code> but built-in R functions can be used. For $\nu \ge 1000$, one can use <code>pnorm(X, mean=U, sd=A)</code> for <code>U</code> = $\xi$ and <code>A</code> = $\alpha$ and for $1.000001 \le \nu \le 1000$, one can use <code>pt((X-U)/A, N)</code> for <code>N</code> = $\nu$ and where the R function <code>pnorm</code> is for the Normal distribution and the R function <code>pt</code> is the 1-parameter Student t distribution.

cdfst3: Cumulative Distribution Function of the 3-Parameter Student t Distribution

Description

Usage

Arguments

Value

References

See Also

Examples