qlss: Quantile-based Summary Statistics for Location, Scale and...
In Qtools: Utilities for Quantiles

Description Usage Arguments Details Value Author(s) References See Also Examples

This function calculates quantile-based summary statistics for location, scale and shape of a distribution, unconditional or conditional.

qlss(...)
## Default S3 method:
qlss(fun = "qnorm", probs = 0.1, ...)
## S3 method for class 'formula'
qlss(formula, data, type = "rq", tsf = NULL, symm = TRUE, dbounded = FALSE,
lambda.p = NULL, delta.p = NULL, lambda.q = NULL, delta.q = NULL,
probs = 0.1, ci = FALSE, R = 500, predictLs = NULL, ...)
## S3 method for class 'numeric'
qlss(x, probs = 0.1, ...)

`fun`	quantile function.
`probs`	a vector of probabilities.
`formula`	an object of class `formula`: a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
`data`	a data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.
`type`	possible options are `rq` for quantile regression (default) or `rqt` for transformation-based quantile regression.
`tsf`	transformation to be used. Possible options are `mcjI` for Proposal I transformation models (default), `mcjI` for Proposal II transformation models, `bc` for Box-Cox and `ao` for Aranda-Ordaz transformation models.
`symm`	logical flag. If `TRUE` (default) a symmetric transformation is used.
`dbounded`	logical flag. If `TRUE` the response is assumed to be doubly bounded on [a,b]. If `FALSE` the response is assumed to be singly bounded (ie, strictly positive).
`lambda.p, delta.p`	vectors with values of transformation parameters to fit models for quantiles `probs`. Must be the same length as `probs`.
`lambda.q, delta.q`	vectors with values of transformation parameters to fit models for quantiles `1-probs`. Must be the same length as `probs`.
`ci`	logical flag. If `TRUE`, bootstrapped confidence intervals for the predictions are calculated.
`R`	number of bootstrap replications.
`x`	a numeric vector.
`predictLs`	list of arguments for `predict.rq`.
`...`	other arguments for `fun`, `rq` or `tsrq`.

This function computes a number of quantile-based summary statistics for location (median), scale (inter-quartile range), and shape (Bowley skewness and shape index) of a distribution. These statistics can be computed for unconditional and conditional distributions. In the latter case, a formula specifies a linear quantile function, which is fitted with rq. The default qlss function computes the summary statistics of a standard normal distribution or of any other distribution via the argument fun. The latter must be a function with p as its probability argument (see for example qnorm, qt, qchisq, qgamma, etc.)

The argument p

qlss returns an object of class qlss. This is a list that contains three elements:

`location`	summary statistic(s) for location.
`scale`	summary statistic(s) for scale.
`method`	summary statistic(s) for shape.

Marco Geraci

Geraci M and Jones MC. Improved transformation-based quantile regression. Canadian Journal of Statistics 2015;43(1):118-132.

Gilchrist W. Statistical modelling with quantile functions. Chapman and Hall/CRC; 2000.

rq, tsrq, tsrq2

# Compute summary statistics of a normal distribution
qlss()

# Compute summary statistics of a t distribution with 3 df
qlss(fun = "qt", df = 3, probs = 0.05)

# Compute summary statistics for a sample using a sequence of probabilities
x <- rnorm(1000)
qlss(x, probs = c(0.1, 0.2, 0.3, 0.4))

# Compute summary statistics for Volume conditional on Height
trees2 <- trees[order(trees$Height),]
fit <- qlss(Volume ~ Height, data = trees2)
plot(fit, z = trees2$Height, xlab = "height")

# Use a quadratic model for Height
fit <- qlss(Volume ~ poly(Height,2), data = trees2)
plot(fit, z = trees2$Height, xlab = "height")