DTDA (version 3.0.1)

Quasars: Quasars Data

Description

The original dataset studied by Efron and Petrosian (1999) comprised independlently collected quadruplets of the redshift and the apparent magnitude of a quasar object. Due to experiemtnal constraints, the distribution of each luminosity in a log-scale is truncated to a known interval.

Usage

data(Quasars)

Format

A data frame with 210 observations on the following 3 variables.

y (adj lum)

a numeric vector, the log lominosity values.

u (lower)

a numeric vector, lower truncation limits.

v (upper)

a numeric vector, upper truncation limits.

Details

Quadruplets in the original data set studied by Efron and Petrosian (1999) are of the form \((z_i;m_i; a_i; b_i), i = 1, \ldots n\), where \(z_i\) is the redshift of the ith quasar and \(m_i\) is the apparent magnitude. Due to experimental constraints, the distribution of each luminosity in the log-scale \((y_i = t(z_i, m_i))\) is truncated to a known interval \([a_i; b_i]\), where \(t\) represents a transformation which depends on the cosmological model assumed (see Efron and Petrosian (1999) for details). Quasars with apparent magnitude above \(b_i\) were too dim to yield dependent redshifts, and hence they were excluded from the study. The lower limit \(a_i\) was used to avoid confusion with non quasar stellar objects.

References

Boyle BJ, Fong R, Shanks, T and Peterson, BA (1990) A catalogue of faint, UV-excess objects. Monograph National Royal Astronomical Society 243, 1-56.

Efron B and Petrosian V (1999) Nonparametric methods for doubly truncated data. Journal of the American Statistical Association 94, 824-834.

Examples

# NOT RUN {
data(Quasars)
 str(Quasars)
# }