cdfst3

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters (\(\xi\), \(\alpha\), \(\nu\)) computed by <code>parst3</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 <code>U</code> = \(\xi\) and <code>A</code> = \(\alpha\) and for \(1.001 \le \nu \le 10^5.5\), one can use <code>pt((X-U)/A, N)</code> for <code>N</code> = \(\nu\). The R function <code>pt</code> is used for the 1-parameter Student t cumulative distribution function. The limits for \(\nu\) stem from study of ability for theoretical integration of the quantile function to produce viable \(\tau_4\) and \(\tau_6\) (see <code>inst/doc/t4t6/studyST3.R</code>).

distribution

cumulative distribution function

Distribution: Student t (3-parameter)

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

cdfst3 function

<dl> <dt>x</dt>
<dd>A real value vector.</dd> <dt>para</dt>
<dd>The parameters from <code>parst3</code> or <code>vec2par</code>.</dd> <dt>paracheck</dt>
<dd>A logical on whether the parameter should be check for validity.</dd></dl>

Arguments

Author

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

<dl>

 <dt>x</dt>
<dd>A real value vector.</dd>

 <dt>para</dt>
<dd>The parameters from <code>parst3</code> or <code>vec2par</code>.</dd>

 <dt>paracheck</dt>
<dd>A logical on whether the parameter should be check for validity.</dd>

</dl>

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

Description

Usage

Value

Arguments

Author

References

See Also

Examples