Logspline Density Estimation - 1992 version

Probability density function (doldlogspline), distribution function (poldlogspline), quantiles (qoldlogspline), and random samples (roldlogspline) from a logspline density that was fitted using the 1992 knot deletion algorithm (oldlogspline). The 1997 algorithm using knot deletion and addition is available using the logspline function.

doldlogspline(q, fit) 
poldlogspline(q, fit) 
qoldlogspline(p, fit) 
roldlogspline(n, fit)

Arguments

q

vector of quantiles. Missing values (NAs) are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

n

sample size. If length(n) is larger than 1, then length(n) random values are returned.

fit

oldlogspline object, typically the result of oldlogspline.

Value

Densities (doldlogspline), probabilities (poldlogspline), quantiles (qoldlogspline), or a random sample (roldlogspline) from an oldlogspline density that was fitted using knot deletion.

Details

Elements of q or p that are missing will cause the corresponding elements of the result to be missing.

References

Charles Kooperberg and Charles J. Stone. Logspline density estimation for censored data (1992). Journal of Computational and Graphical Statistics, 1, 301–328.

Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K. Truong. The use of polynomial splines and their tensor products in extended linear modeling (with discussion) (1997). Annals of Statistics, 25, 1371–1470.

Author

Charles Kooperberg clk@fredhutch.org.

Examples

x <- rnorm(100)
fit <- oldlogspline(x)
qq <- qoldlogspline((1:99)/100, fit)
plot(qnorm((1:99)/100), qq)                  # qq plot of the fitted density

pp <- poldlogspline((-250:250)/100, fit)
plot((-250:250)/100, pp, type = "l")
lines((-250:250)/100, pnorm((-250:250)/100)) # asses the fit of the distribution

dd <- doldlogspline((-250:250)/100, fit)
plot((-250:250)/100, dd, type = "l")
lines((-250:250)/100, dnorm((-250:250)/100)) # asses the fit of the density

rr <- roldlogspline(100, fit)                # random sample from fit