Characterizations of inequality orderings by means of dispersive orderings

The generalized Lorenz order and the absolute Lorenz order are used in economics to compare income distributions in terms of social welfare. In Section 2, we show that these orders are equivalent to two stochastic orders, the concave order and the dilation order, which are used to compare the dispersion of probability distributions. In Section 3, a sufficient condition for the absolute Lorenz order, which is often easy to verify in practice, is presented. This condition is applied in Section 4 to the ordering of generalized gamma distributions with different parameters

The proportional likelihood ratio order and applications

In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property). As an application, we show that the IPLR and DPLR properties are sufficient conditions for the Lorenz ordering of truncated distributions

Characterizations of inequality orderings by means of dispersive orderings

The generalized Lorenz order and the absolute Lorenz order are used in economics to compare income distributions in terms of social welfare. In Section 2, we show that these orders are equivalent to two stochastic orders, the concave order and the dilation order, which are used to compare the dispersion of probability distributions. In Section 3, a sufficient condition for the absolute Lorenz order, which is often easy to verify in practice, is presented. This condition is applied in Section 4 to the ordering of generalized gamma distributions with different parameters

BeppoSAX observation of the X-ray binary pulsar Vela X-1

We report on the spectral (pulse averaged) and timing analysis of the ~ 20 ksec observation of the X-ray binary pulsar Vela X-1 performed during the BeppoSAX Science Verification Phase. The source was observed in two different intensity states: the low state is probably due to an erratic intensity dip and shows a decrease of a factor ~ 2 in intensity, and a factor 10 in Nh. We have not been able to fit the 2-100 keV continuum spectrum with the standard (for an X--ray pulsar) power law modified by a high energy cutoff because of the flattening of the spectrum in ~ 10-30 keV. The timing analysis confirms previous results: the pulse profile changes from a five-peak structure for energies less than 15 keV, to a simpler two-peak shape at higher energies. The Fourier analysis shows a very complex harmonic component: up to 23 harmonics are clearly visible in the power spectrum, with a dominant first harmonic for low energy data, and a second one as the more prominent for energies greater than 15 keV. The aperiodic component in the Vela X-1 power spectrum presents a knee at about 1 Hz. The pulse period, corrected for binary motion, is 283.206 +/- 0.001 sec.Comment: 5 pages, 4 PostScript figure, uses aipproc.sty, to appear in Proceedings of Fourth Compton Symposiu