Many distribution functions, can be explored in numerous dimensions with their extended form. In this paper an form of exponential is studied by the quadratic rank transmutation map, called three parameter transmuted distribution, where base two parameters \(\theta\) > 0 and \(\beta\) , shape location respectively. Some statistical properties have been for said including moments, quantile fu...

In fact the Kesten–Stigum theorem [2] only states that the number of nodes will converge to some random variable, the distribution of which depends on the choice of offspring distribution. This random variable has a mean of z , where z is the mean offspring per node and h is the number of generations. Therefore, equation (3.2) in the original manuscript, and the results derived from it, hold in...