Narrow Results

In this work, we consider a recently proposed entropy S defined by a variational relationship as a measure of uncertainty of random variable x. The entropy defined in this way underlies an extension of virtual work principle leading to the maximum entropy . This paper presents an analytical investigation of this maximizable entropy for several distributions such as the stretched exponential distribution, κ-exponential distribution, and Cauchy distribution.

Asymmetrical models like the generalized and q-generalized extreme value distributions have been widely used to describe a variety of random events observed in studies including survival, finance, and dependability. The q-analogues, with the extra parameter q, provide for more modelling freedom. In this paper, Shannon entropy, Varentropy and Varexentropy measures are computed in closed form in cases of generalized and q-generalized extreme value distributions. Maximum likelihood estimation method is applied for computing the values of Shannon entropy, Varentropy and Varexentropy measures.