The free tangent law

Application of the Free Tangent Law in Quantification of Household Satisfaction from Durable Consumer Goods

“…The free tangent law is a notion postulated in [ 9 ]. Before we proceed with a detailed presentation of this type of distribution, it may be useful to recall some of the basic concepts of the free probability theory, developed in the early 1980s in [ 13 ].…”

“…In [ 9 ], we postulate the examination of asymptotics of quadratic forms in free random variables. This approach introduces a distribution of free tangents as limits of free commutators.…”

“…The main objective of this paper is the effective evaluation of satisfaction from material affluence among households. It is a well-established idea that people assess their welfare relative to some “comparison group” such as neighbours or co-workers (e.g., [ 9 , 10 ]. This paper presents a new approach to the measurement of living conditions, observably different from the pool of the available solutions, c.f.…”

“…The most notable difference is the elimination of the pecuniary value of household effects; instead, the method examines their role in the satisfaction of household needs and requirements. Another important distinction of the postulated approach is the application of the free tangent law [ 9 ] for the analytical evaluations of responses.…”

Special matrices used in the analysis of the Boolean quadratic forms

“…Then many, new theorems appeared about the Boolean probability ( [1], [2], [4], [6], [7], [8], [9]). In [3] Ejsmont and Hęćka show that the limit of mixed sums of commutators and anti-commutators…”