par2qua2 {lmomco} | R Documentation |
This function combines two distributions into one by weighting of the two quantile functions by the nonexceedance probability. The distributions are specified by the parameter arguments. The left-tail parameter object is the distribution governing the left tail; the right-tail parameter object is the distribution governing the right tail. The quantile function algebra is
Q(F) = (1-F) times Q_{lefttail}(F) + F times Q_{righttail}(F)
where Q(F) is the equivalent quantile for nonexceedance probability F computed by the tail weigthing. Q_{lefttail}(F) is the left-tail quantile function; Q_{righttail} is the right-tail quantile function. Parameter objects are discussed in vec2par
and lmom2par
functions. If the optional weight
argument is provided, then the multiplication of 1-F
or F
is replaced by 1-weight
or weight
, respectively. If weight=0
, then the quantiles for the right tail are returned, and if weight=1
, then the quantiles for the left tail are returned.
A word of caution. The resulting weighted quantile function is not checked for monotonic increase with F. This is a required property of quantile functions.
par2qua2(f,leftpara,rightpara,weight=NULL,...)
f |
Nonexceedance probability (0 <= F <= 1). |
leftpara |
The left-tail parameters from lmom2par or similar. |
rightpara |
The right-tail parameters from lmom2par or similar. |
weight |
An optional weighting argument to use in lieu of F . |
... |
The additional arguments are passed to the quantile function such as paracheck = FALSE for the generalized Lambda distribution (quagld ). |
Quantile value for F from the two distributions.
W.H. Asquith
par2qua
, lmom2par
, and par2cdf2
# Contrived example lmr <- lmom.ub(rnorm(20)) leftpara <- parnor(lmr) rightpara <- pargev(lmr) combined.median <- par2qua2(0.5,leftpara,rightpara) # Bigger example--using Kappa fit to whole sample # for the right tail and Normal fit to whole sample # for the left tail D <- c(123,523,345,356,2134,345,2365,235,12,235,61) LM <- lmom.ub(D) KAP <- parkap(LM) NOR <- parnor(LM) PP <- pp(D) plot(PP,sort(D),ylim=c(-500,2300)) lines(PP,par2qua(PP,KAP),col=2) lines(PP,par2qua(PP,NOR),col=3) lines(PP,par2qua2(PP,NOR,KAP))