Exact forms of Rényi and Shannon entropies are determined for several multivariate distributions, including multivariate t, multivariate Cauchy, multivariate Pearson type VII, multivariate Pearson type II, multivariate symmetric Kotz type, multivariate logistic, multivariate Burr, multivariate...

For order $q$ kernel density estimators we show that the constant $b_q$ in $bias=b_qh^q+o(h^q)$ can be made arbitrarily small, while keeping the variance bounded. A data-based selection of bq is presented and Monte Carlo simulations illustrate the advantages of the method.

Since the 2008 financial crisis, modeling of the extreme values of financial risk has become important. Postgraduate programs and PhD research programs in mathematical finance are cropping up in nearly every university. Additionally, many conferences are being held annually on the topic of...

Blockchain and cryptocurrencies have recently captured the interest of academics and those in industry. Cryptocurrencies are essentially digital currencies that use blockchain technology and cryptography to facilitate secure and anonymous transactions. The cryptocurrency market is currently...