qua.ostat

This function computes a specified quantile by nonexceedance probability $F$ for the $j$th-order statistic of a sample of size $n$ for a given distribution. Let the quantile function (inverse distribution) of the Beta distribution be
$$ \mathrm{B}^{(-1)}(F,j,n-j+1) \mbox{,} $$
and let $x(F,\Theta)$ represent the quantile function of the given distribution and $\Theta$ represents a vector of distribution parameters. The quantile function of the distribution of the $j$th-order statistic is
$$ x\bigl(\mathrm{B}^{(-1)}(F,j,n-j+1),\Theta\bigr) \mbox{.} $$

order statistics (misc.)

order statistics (quantile function of)

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

qua.ostat function

<dl> <dt>f</dt>
<dd>The nonexceedance probability $F$ for the quantile.</dd> <dt>j</dt>
<dd>The $j$th-order statistic $x_{1:n} \le x_{2:n} \le \ldots \le x_{j:n} \le x_{n:n}.$</dd> <dt>n</dt>
<dd>The sample size.</dd> <dt>para</dt>
<dd>A distribution parameter list from a function such as <code>lmom2par</code> or <code>vec2par</code>.</dd></dl>

Arguments

Author

Compute the Quantiles of the Distribution of an Order Statistic — qua.ostat

<dl>

 <dt>f</dt>
<dd>The nonexceedance probability $F$ for the quantile.</dd>

 <dt>j</dt>
<dd>The $j$th-order statistic $x_{1:n} \le x_{2:n} \le \ldots \le x_{j:n} \le x_{n:n}.$</dd>

 <dt>n</dt>
<dd>The sample size.</dd>

 <dt>para</dt>
<dd>A distribution parameter list from a function such as <code>lmom2par</code> or <code>vec2par</code>.</dd>

</dl>

qua.ostat: Compute the Quantiles of the Distribution of an Order Statistic

Description

Usage

Value

Arguments

Author

References

See Also