A random variable (r.v.) has a logistic distribution if its survival function is given by \({\left[1+\exp\bigl({X-\mu\over\sigma}\bigr)\right]^{-1}}\), \(x\in K\) where \(\mu\in K\) is a location parameter and \(\sigma>0\) is a scale parameter. Suppose \(X_ 1,X_ 2,\dots,X_ n\) are i.i.d. r.v.'s and \(N\) is an independent geometric r.v. with \(P(N=n)=pq^{n-1}\). The distribution of \(X_ 1\) is said to be min-geometric stable if for any \(p\in(0,1)\), \(\exists\) a vector \(c(p)>0\), such that \((*)\) \(Y+c(p){\buildrel{\text{d}}\over =}X_ 1\), where \(Y\) is the coordinate-wise minimum of \(X_ 1,X_ 2,\dots,X_ n\). In one dimension, \(X_ i\) has a logistic distribution. In the \(k\)-dimensional case under \((*)\), \(X_ i\) has a distribution the marginals of which are logistic. This property has been availed to develop \(k\)-dimensional processes (auto-regressive processes, geometric processes and other processes) having logistic and semi-logistic marginals.