Inequalities for Expected Current Record Statistics

2007 ◽  
Vol 36 (7) ◽  
pp. 1367-1380 ◽  
Author(s):  
Mohammad Z. Raqab
2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.


2018 ◽  
Vol 611 ◽  
pp. A25 ◽  
Author(s):  
E. E. E. Gall ◽  
R. Kotak ◽  
B. Leibundgut ◽  
S. Taubenberger ◽  
W. Hillebrandt ◽  
...  

We present photometry and spectroscopy of nine Type II-P/L supernovae (SNe) with redshifts in the 0.045 ≲ z ≲ 0.335 range, with a view to re-examining their utility as distance indicators. Specifically, we apply the expanding photosphere method (EPM) and the standardized candle method (SCM) to each target, and find that both methods yield distances that are in reasonable agreement with each other. The current record-holder for the highest-redshift spectroscopically confirmed supernova (SN) II-P is PS1-13bni (z = 0.335−0.012+0.009), and illustrates the promise of Type II SNe as cosmological tools. We updated existing EPM and SCM Hubble diagrams by adding our sample to those previously published. Within the context of Type II SN distance measuring techniques, we investigated two related questions. First, we explored the possibility of utilising spectral lines other than the traditionally used Fe iiλ5169 to infer the photospheric velocity of SN ejecta. Using local well-observed objects, we derive an epoch-dependent relation between the strong Balmer line and Fe iiλ5169 velocities that is applicable 30 to 40 days post-explosion. Motivated in part by the continuum of key observables such as rise time and decline rates exhibited from II-P to II-L SNe, we assessed the possibility of using Hubble-flow Type II-L SNe as distance indicators. These yield similar distances as the Type II-P SNe. Although these initial results are encouraging, a significantly larger sample of SNe II-L would be required to draw definitive conclusions.


2007 ◽  
Vol 3 (S246) ◽  
pp. 291-300 ◽  
Author(s):  
Scott M. Ransom

AbstractGlobular clusters produce orders of magnitude more millisecond pulsars per unit mass than the Galactic disk. Since the first cluster pulsar was uncovered 20 years ago, at least 138 have been identified – most of which are binary millisecond pulsars. Because their origins involve stellar encounters, many of the systems are exotic objects that would never be observed in the Galactic disk. Examples include pulsar-main sequence binaries, extremely rapid rotators (including the current record holder), and millisecond pulsars in highly eccentric orbits. These systems are allowing new probes of the interstellar medium, the equation of state of material at supra-nuclear density, the masses of neutron stars, and globular cluster dynamics.


2013 ◽  
Vol 101 (1) ◽  
pp. 10003 ◽  
Author(s):  
Shashi C. L. Srivastava ◽  
Arul Lakshminarayan ◽  
Sudhir R. Jain

Paleobiology ◽  
2015 ◽  
Vol 41 (4) ◽  
pp. 610-632 ◽  
Author(s):  
Phoebe A. Cohen ◽  
Francis A. Macdonald

AbstractProterozoic strata host evidence of global “Snowball Earth” glaciations, large perturbations to the carbon cycle, proposed changes in the redox state of oceans, the diversification of microscopic eukaryotes, and the rise of metazoans. Over the past half century, the number of fossils described from Proterozoic rocks has increased exponentially. These discoveries have occurred alongside an increased understanding of the Proterozoic Earth system and the geological context of fossil occurrences, including improved age constraints. However, the evaluation of relationships between Proterozoic environmental change and fossil diversity has been hampered by several factors, particularly lithological and taphonomic biases. Here we compile and analyze the current record of eukaryotic fossils in Proterozoic strata to assess the effect of biases and better constrain diversity through time. Our results show that mean within assemblage diversity increases through the Proterozoic Eon due to an increase in high diversity assemblages, and that this trend is robust to various external factors including lithology and paleogeographic location. In addition, assemblage composition changes dramatically through time. Most notably, robust recalcitrant taxa appear in the early Neoproterozoic Era, only to disappear by the beginning of the Ediacaran Period. Within assemblage diversity is significantly lower in the Cryogenian Period than in the preceding and following intervals, but the short duration of the nonglacial interlude and unusual depositional conditions may present additional biases. In general, large scale patterns of diversity are robust while smaller scale patterns are difficult to discern through the lens of lithological, taphonomic, and geographic variability.


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