pdfkap

The parameters from <code><a rd-options="" href="/link/parkap?package=lmomco&version=2.3.1" data-mini-rdoc="lmomco::parkap">parkap</a></code> or <code><a rd-options="" href="/link/vec2par?package=lmomco&version=2.3.1" data-mini-rdoc="lmomco::vec2par">vec2par</a></code>.

para

This function computes the probability density of the Kappa distribution given parameters ($\xi$, $\alpha$, $\kappa$, and $h$) computed by <code><a rd-options="" href="/link/parkap?package=lmomco&version=2.3.1" data-mini-rdoc="lmomco::parkap">parkap</a></code>. The probability density function is
$$f(x) = \alpha^{-1} [1-\kappa(x - \xi)/\alpha]^{1/k-1} \times [F(x)]^{1-h}$$
where $f(x)$ is the probability density for quantile $x$, $F(x)$ is the cumulative distribution function or nonexceedance probability at $x$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\kappa$ is a shape parameter.

distribution

probability density function

Distribution: Kappa

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 associations.

William Asquith

lmomco

L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions

pdfkap function

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

This function computes the probability density of the Kappa distribution given parameters ($\xi$, $\alpha$, $\kappa$, and $h$) computed by <code><a rd-options='' href='parkap'>parkap</a></code>. The probability density function is
$$f(x) = \alpha^{-1} [1-\kappa(x - \xi)/\alpha]^{1/k-1} \times [F(x)]^{1-h}$$
where $f(x)$ is the probability density for quantile $x$, $F(x)$ is the cumulative distribution function or nonexceedance probability at $x$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\kappa$ is a shape parameter.

pdfkap: Probability Density Function of the Kappa Distribution

Description

Usage

Arguments

Value

References

See Also

Examples