3,981 research outputs found
A Geometric Derivation of the Irwin-Hall Distribution
The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution’s history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length.The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed
CLT for non-Hermitian random band matrices with variance profiles
We show that the fluctuations of the linear eigenvalue statistics of a
non-Hermitian random band matrix of increasing bandwidth with a
continuous variance profile converges to a
, where
and is the test function. When , we obtain an explicit
formula for , which depends on , and variance profile
. When , the formula is consistent with Rider, and Silverstein
(2006). We also independently compute an explicit formula for
i.e., when the bandwidth grows slower compared to
. In addition, we show that as
.Comment: Typos corrected; a few more explanations and a couple of pictures
have been adde
The SuperCOSMOS Sky Survey. Paper III: Astrometry
In this, the third in a series of three papers concerning the SuperCOSMOS Sky
Survey, we describe the astrometric properties of the database. We describe the
algorithms employed in the derivation of the astrometric parameters of the
data, and demonstrate their accuracies by comparison with external datasets
using the first release of data, the South Galactic Cap survey. We show that
the celestial coordinates, which are tied to the International Celestial
Reference Frame via the Tycho-2 reference catalogue, are accurate to better
than +/- 0.2 arcsec at J,R=19,18 rising to +/- 0.3 arcsec at J,R=22,21 with
positional dependent systematic effects from bright to faint magnitudes at the
+/- 0.1 arcsec level. The proper motion measurements are shown to be accurate
to typically +/- 10 mas/yr at J,R=19,18 rising to +/- 50 mas/yr at J,R=22,21
and are tied to zero using the extragalactic reference frame. We show that the
zeropoint errors in the proper motions are 17 and are no
larger than 10 mas/yr for R < 17 mas/yr.Comment: 15 pages, 12 figures; accepted for publication in MNRA
The total assessment profile, volume 2
Appendices are presented which include discussions of interest formulas, factors in regionalization, parametric modeling of discounted benefit-sacrifice streams, engineering economic calculations, and product innovation. For Volume 1, see
Analysis of Neptune's 2017 Bright Equatorial Storm
We report the discovery of a large (8500 km diameter) infrared-bright
storm at Neptune's equator in June 2017. We tracked the storm over a period of
7 months with high-cadence infrared snapshot imaging, carried out on 14 nights
at the 10 meter Keck II telescope and 17 nights at the Shane 120 inch reflector
at Lick Observatory. The cloud feature was larger and more persistent than any
equatorial clouds seen before on Neptune, remaining intermittently active from
at least 10 June to 31 December 2017. Our Keck and Lick observations were
augmented by very high-cadence images from the amateur community, which
permitted the determination of accurate drift rates for the cloud feature. Its
zonal drift speed was variable from 10 June to at least 25 July, but remained a
constant m s from 30 September until at least 15
November. The pressure of the cloud top was determined from radiative transfer
calculations to be 0.3-0.6 bar; this value remained constant over the course of
the observations. Multiple cloud break-up events, in which a bright cloud band
wrapped around Neptune's equator, were observed over the course of our
observations. No "dark spot" vortices were seen near the equator in HST imaging
on 6 and 7 October. The size and pressure of the storm are consistent with
moist convection or a planetary-scale wave as the energy source of convective
upwelling, but more modeling is required to determine the driver of this
equatorial disturbance as well as the triggers for and dynamics of the observed
cloud break-up events.Comment: 42 pages, 14 figures, 6 tables; Accepted to Icaru
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