cdfpdq3

This function computes the cumulative probability or nonexceedance probability of the Polynomial Density-Quantile3 (PDQ3) distribution given parameters (\(\xi\), \(\alpha\), \(\kappa\)) computed by <code>parpdq4</code>. The cumulative distribution function has no explicit form and requires numerical methods. The R function <code><a href="/link/uniroot()?package=lmomco&version=2.4.14" data-mini-rdoc="lmomco::uniroot()">uniroot()</a></code> is used to root the quantile function <code>quapdq3</code> to compute the nonexceedance probability. The distribution's canonical definition is in terms of the quantile function (<code>quapdq3</code>).

distribution

cumulative distribution function

Distribution: Polynomial Density-Quantile3

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

cdfpdq3 function

<dl> <dt>x</dt>
<dd>A real value vector.</dd> <dt>para</dt>
<dd>The parameters from <code>parpdq3</code> or <code>vec2par</code>.</dd> <dt>paracheck</dt>
<dd>A logical switch as to whether the validity of the parameters should be checked. Default is <code>paracheck=TRUE</code>. This switch is made so that the root solution needed for <code>cdfpdq3</code> shows an extreme speed increase because of the repeated calls to <code>quapdq3</code>.</dd></dl>

Arguments

Author

This function computes the cumulative probability or nonexceedance probability of the Polynomial Density-Quantile3 (PDQ3) distribution given parameters (\(\xi\), \(\alpha\), \(\kappa\)) computed by <code>parpdq4</code>. The cumulative distribution function has no explicit form and requires numerical methods. The R function <code><a href='https://rdrr.io/r/stats/uniroot.html'>uniroot()</a></code> is used to root the quantile function <code>quapdq3</code> to compute the nonexceedance probability. The distribution's canonical definition is in terms of the quantile function (<code>quapdq3</code>).

Cumulative Distribution Function of the Polynomial Density-Quantile3 Distribution — cdfpdq3

<dl>

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

 <dt>para</dt>
<dd>The parameters from <code>parpdq3</code> or <code>vec2par</code>.</dd>

 <dt>paracheck</dt>
<dd>A logical switch as to whether the validity of the parameters should be checked. Default is <code>paracheck=TRUE</code>. This switch is made so that the root solution needed for <code>cdfpdq3</code> shows an extreme speed increase because of the repeated calls to <code>quapdq3</code>.</dd>

</dl>

cdfpdq3: Cumulative Distribution Function of the Polynomial Density-Quantile3 Distribution

Description

Usage

Value

Arguments

Author

References

See Also