Meixner distribution with PDF Mean and Variance
MeixnerDistribution[a, b, m, d]
Mean[MeixnerDistribution[a, b, m, d]]
→ m + a*d*Tan[b/2]PDF[MeixnerDistribution[a, b, m, d], x]
→ (2^(-1 + 2*d)*E^((b*(-m + x))/a)*Cos[b/2]^(2*d)*Gamma[d - (I*(-m + x))/a]*Gamma[d + (I*(-m + x))/a])/(a*Pi*Gamma[2*d])Variance[MeixnerDistribution[a, b, m, d]]
→ (a^2*d*Sec[b/2]^2)/2