Affiliation:
1. Department of Mathematics, Institute of Mathematics, Banacha 2, University of Warsaw , Warszawa , Poland
Abstract
Abstract
A family of bivariate copulas given by: for
v
+
2
u
<
2
v+2u\lt 2
,
C
(
u
,
v
)
=
F
(
2
F
−
1
(
v
∕
2
)
+
F
−
1
(
u
)
)
C\left(u,v)=F\left(2{F}^{-1}\left(v/2)+{F}^{-1}\left(u))
, where
F
F
is a strictly increasing cumulative distribution function of a symmetric, continuous random variable, and for
v
+
2
u
≥
2
v+2u\ge 2
,
C
(
u
,
v
)
=
u
+
v
−
1
C\left(u,v)=u+v-1
, is introduced. The basic properties and necessary conditions for absolute continuity of
C
C
are discussed. Several examples are provided.
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability
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