General expressions of derivative-constrained linear-phase type-I FIR filters

2013 ◽  
Author(s):  
Peng-Hua Wang ◽  
Bo-You Yu ◽  
Po-Ning Chen
Keyword(s):  
Fir Filters ◽  
Type I ◽  
Linear Phase ◽  
Phase Type

scholarly journals Exact boundaries in sequential testing for phase-type distributions

2014 ◽  
Vol 51 (A) ◽  
pp. 347-358
Author(s):  
Hansjörg Albrecher ◽  
Peiman Asadi ◽  
Jevgenijs Ivanovs
Keyword(s):  
Ratio Test ◽  
Type I ◽  
Phase Type Distribution ◽  
Additive Process ◽  
Markov Additive Process ◽  
Scale Functions ◽  
Phase Type ◽  
Sequential Probability ◽  
Decision Boundaries ◽  
Type Ii Errors

Consider Wald's sequential probability ratio test for deciding whether a sequence of independent and identically distributed observations comes from a specified phase-type distribution or from an exponentially tilted alternative distribution. Exact decision boundaries for given type-I and type-II errors are derived by establishing a link with ruin theory. Information on the mean sample size of the test can be retrieved as well. The approach relies on the use of matrix-valued scale functions associated with a certain one-sided Markov additive process. By suitable transformations, the results also apply to other types of distributions, including some distributions with regularly varying tails.

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