A Semiparametric Two-Sample Hypothesis Testing Problem for Random Graphs

2017 ◽  
Vol 26 (2) ◽  
pp. 344-354 ◽  
Author(s):  
Minh Tang ◽  
Avanti Athreya ◽  
Daniel L. Sussman ◽  
Vince Lyzinski ◽  
Youngser Park ◽  
...  
Bernoulli ◽  
2017 ◽  
Vol 23 (3) ◽  
pp. 1599-1630 ◽  
Author(s):  
Minh Tang ◽  
Avanti Athreya ◽  
Daniel L. Sussman ◽  
Vince Lyzinski ◽  
Carey E. Priebe

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 942 ◽  
Author(s):  
Vali Soltani Masih ◽  
Stanisława Kanas

Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) respectively are lying in the region bounded by the limaçon ( u − 1 ) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given.


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