pwm.beta2alpha {lmomco}

Conversion of Beta to Alpha Probability-Weighted Moments (PWMs) or Alpha to Beta PWMs

Description

Conversion of “beta” (the well known ones) to “alpha” probability-weighted moments (PWMs) by pwm.beta2alpha or alpha to beta PWMs by pwm.alpha2beta. The relations between the \alpha and \beta PWMs are

\alpha_r = \sum^r_{k=0} (-1)^k {r \choose k} \beta_k\mbox{,}

and

\beta_r = \sum^r_{k=0} (-1)^k {r \choose k} \alpha_k\mbox{.}

Lastly, note that the \beta are almost exclusively used in the literature. Because each is a linear combination of the other, they are equivalent in meaning but not numerically.

Usage

pwm.beta2alpha(pwm)

pwm.alpha2beta(pwm)

Arguments

pwm

A vector of alpha or beta probability-weighted moments depending on which related function is called.

Value

If \beta_r \rightarrow \alpha_r (pwm.beta2alpha), a vector of the \alpha_r. Note that convention is the have a \alpha_0, but this is placed in the first index i=1 vector. Alternatively, if \alpha_r \rightarrow \beta_r (pwm.alpha2beta), a vector of the \beta_r.

Author(s)

W.H. Asquith

References

# NEED

See Also

pwm, pwm2lmom

Examples

X <- rnorm(100)
pwm(X)$betas
pwm.beta2alpha(pwm(X)$betas)
pwm.alpha2beta(pwm.beta2alpha(pwm(X)$betas))