Set $K=\mathbb{Q}(i)$ and suppose that $c\in \mathbb{Z}[i]$ is a square-free algebraic integer with $c\equiv 1 \imod{\langle16\rangle}$. Let $L(s,\chi_{c})$ denote the Hecke $L$-function associated quartic residue character modulo $c$. For $\sigma>1/2$, we prove an asymptotic distribution function $F_{\sigma}$ for values of logarithm \begin{equation*} L_c(s)= L(s,\chi_c)L(s,\overline{\chi}_{c})...

Distribution design for databases usually addresses the problems of fragmentation, allocation and replication. However, the main purposes of distribution are to improve performance and to increase system reliability. The former aspect is particularly relevant in cases where the desire to distribute data originates from the distributed nature of an organization with many data needs only arising ...

The amount of capital necessary to support a portfolio of debt securities depends on the probability distribution of the portfolio loss. Consider a portfolio of loans, each of which is subject to default resulting in a loss to the lender. Suppose the portfolio is financed partly by equity capital and partly by borrowed funds. The credit quality of the lender's notes will depend on the probabili...

The amount of capital necessary to support a portfolio of debt securities depends on the probability distribution of the portfolio loss. Consider a portfolio of loans, each of which is subject to default resulting in a loss to the lender. Suppose the portfolio is financed partly by equity capital and partly by borrowed funds. The credit quality of the lender's notes will depend on the probabili...

W data is col lected, in order to make sense of it, the data needs to be organised in a manner which shows the various values and the frequencies at which these values have occurred, that is the “pattern that the values form after they are organised” and this is called a distribution. A distribution guides how raw data can be converted into meaningful information and also influences the choice ...

We will look at the case of a single-item First Price Auction. Our goal will be to estimate the distribution of valuations of the players, by observing samples of bid vectors of players from multiple first price auctions. In particular, we consider the case where we have a data set of m First Price Auctions, each among n bidders. The value v i of each bidder i in each first price auction t, is ...