This function converts the cumulative distribution function of \(F(x)\) to a conditional cumulative distribution function \(P(x)\) based on the probability level of the left-hand threshold. It is recommended that this threshold (as expressed as a probability) be that value returned from x2xlo in element pp. The conversion is simple
$$
P(x) <- (F(x) - pp)/(1-pp)\mathrm{,}
$$
where the term \(\mathrm{pp}\) corresponds to the estimated probability or plotting position of the left-hand threshold.
This function is particularly useful for applications in which zero values in the data set require truncation so that logarithms of the data may be used. But also this function contributes to the isolation of the right-hand tail of the distribution for analysis. Finally, f <- f[f >= pp] for type="ge" or f <- f[f > pp] for type="gt" is used internally for probability subsetting, so the user does not have to do that with the nonexceedance probability before calling this function. The function f2f does similar subsetting without converting \(F(x)\) to \(P(x)\). Users are directed to Examples under par2qua2lo and carefully note how f2flo and f2f are used.
f2flo(f, pp=NA, xlo=NULL, type=c("ge", "gt"))A vector of conditional nonexceedance probabilities.
A vector of nonexceedance probabilities.
The plotting position of the left-hand threshold and recommended to come from x2xlo.
An optional result from x2xlo from which the pp will be take instead of from the argument pp.
The type of the logical construction gt means greater than the pp and ge means greater than or equal to the pp for the computations. There can be subtle variations in conceptualization of the truncation need or purpose and hence this argument is provided for flexibility.
W.H. Asquith
x2xlo, flo2f, f2f, xlo2qua