Quasars: Quasars Data
In DTDA: Doubly Truncated Data Analysis

Description Usage Format Details Source References Examples

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.

1	data(Quasars)

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.

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, … 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.

Vahé Petrosian and Bradley Efron.

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.