We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with mo...

The tails of the Taylor series for many standard functions such as arctan and log can be expressed as continued fractions in a variety of ways. A surprising side effect is that some of these continued fractions provide a dramatic acceleration for the underlying power series. These investigations were motivated by a surprising observation about Gregory’s series. Gregory’s series for π, truncated...

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This supplementary appendix provides estimation results for the different tail dependence measures discussed in the main text for all of the fifty individual stocks listed in Table 2. The detailed estimation results reported here are summarized in Tables 5 and 7 in the

An investigation was conducted in the NASA Langley 20-Foot Vertical Spin Tunnel to determine the developed spin and spin-recovery characteristics of a 1/28-scale, free-spinning model of the NASA F-18 HARV (High Alpha Research Vehicle) airplane that can be configured with and without the vertical tails installed. The purpose of the test was to determine what effects, if any, the absence of verti...

Histone amino-terminal tails (N-tails) are required for cellular resistance to DNA damaging agents; therefore, we examined the role of histone N-tails in regulating DNA damage response pathways in Saccharomyces cerevisiae. Combinatorial deletions reveal that the H2A and H3 N-tails are important for the removal of MMS-induced DNA lesions due to their role in regulating the basal and MMS-induced ...

We report on the search for very-high-energy gamma-ray emission from regions around three nearby supersonic pulsars (PSR B0355+54, PSR J0357+3205, and J1740+1000) that exhibit long X-ray tails. To date there is no clear detection of TeV any pulsar tail prominent in or radio. provide upper limits flux, luminosity, also compare these with other wind nebulae detected X-rays model predictions. find...