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The concept of $\phi$-complete mixability and $\phi$-joint mixability wasfirst introduced in Bignozzi and Puccetti (2015), which is an extension ofcomplete and joint mixability. Following Bignozzi and Puccetti (2015), weconsider two more general cases of $\phi$ and investigate the $\phi$-jointmixability for elliptical distributions and logarithmic ellipticaldistributions. Some sufficient conditions for the $\phi$-joint mixability ofsome distributions are investigated. In addition, a conjecture on theuniqueness of the center of $\phi$-joint mixability and the forms of thedensities for some elliptical distributions are given.

The mixability of elliptical distributions and log-elliptical distributions