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Self-Adaptive Multivariate q-Gaussian-based Capacitor Placement for Reactive Power Compensation in Distribution Feeders
Published in Satyajit Chakrabarti, Ayan Kumar Panja, Amartya Mukherjee, Arun Kr. Bar, Intelligent Electrical Systems: A Step towards Smarter Earth, 2021
Debashis Jana, Ranjita Chowdhury
where c is the matrix that explains the mutation potency in each coordinate j=1,.,m and z→ is an m-dimensional random vector created from a provided multivariate distribution. At this point, an m-dimensional random vector is formed from the multivariate Gaussian distribution (Su, Chan and Chiou, 2005). We proposed to model the random mutation vector z→ from an isotropic q-Gaussian distribution as z→~r→un, where r→ is a uniform random vector configured by sampling a random vector with Gaussian distribution. The random vector may be denoted by z→~χqm, while a random vector of m-dimension can be generated by sampling m self-determining q-Gaussian arbitrary variables xq(0,1). In q-Gaussian distribution self-adaption (Su, Chan and Chiou, 2005) is made of by the parameter q which illuminates the shape of the distribution. The computation has been done for muted child is as follows: () Pgi=Pgi+δPgimax−Pgimin
Experience with valuation methods for the creation of real options enabling diversity of nuclear fuel supply
Published in Journal of Nuclear Science and Technology, 2022
Marcus Seidl, Andreas Wensauer, Wolfgang Faber
There is a rich literature about the derivation of option prices for non-geometric Brownian motion processes, see for example [26–29]. Cassidy et al. used a capped Student-t distribution [30] of degree to obtain an analytic formula for the value of a European call option. Price capping was explained as an appropriate means to force convergence of the option price formula. Borland [31] analyzed the value of a European call option with an underlying Tsallis distribution [32] as the driver of randomness. The Tsallis distribution is known as a q-Gaussian [33] and can be transformed into a Student-t distribution [34]. For q = 1 the Tsallis distribution coincides with a Gaussian and the standard Black-Scholes option price formula follows. For q > 1 the Tsallis distribution exhibit fat tails. The variance of the Tsallis distribution diverges for and therefore in [31] was assumed in order to avoid price capping. Borland used the following partial differential equation (PDE) for the derivation of the option price formula: