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Such functions are called decomposable aggregation functions [4] or decomposable aggregate functions. The simplest may be referred to as self-decomposable aggregation functions , which are defined as those functions f such that there is a merge operator ⋄ {\displaystyle \diamond } such that
From its first version Excel supported end-user programming of macros (automation of repetitive tasks) and user-defined functions (extension of Excel's built-in function library). In early versions of Excel, these programs were written in a macro language whose statements had formula syntax and resided in the cells of special-purpose macro ...
For example, in Microsoft Excel one must first select the entire data in the original table and then go to the Insert tab and select "Pivot Table" (or "Pivot Chart"). The user then has the option of either inserting the pivot table into an existing sheet or creating a new sheet to house the pivot table.
A spreadsheet's concatenation ("&") function can be used to assemble complex text strings in a single cell (in this example, XML code for an SVG "circle" element). This concatenation is a variation of the chaining of formulas, for which spreadsheets are commonly used.
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Nested functions can be used for unstructured control flow, by using the return statement for general unstructured control flow.This can be used for finer-grained control than is possible with other built-in features of the language – for example, it can allow early termination of a for loop if break is not available, or early termination of a nested for loop if a multi-level break or ...
For example, suppose P(L = red) = 0.2, P(L = yellow) = 0.1, and P(L = green) = 0.7. Multiplying each column in the conditional distribution by the probability of that column occurring results in the joint probability distribution of H and L, given in the central 2×3 block of entries.
The Gaussian VaR ensures subadditivity: for example, the Gaussian VaR of a two unitary long positions portfolio at the confidence level is, assuming that the mean portfolio value variation is zero and the VaR is defined as a negative loss, = + + where is the inverse of the normal cumulative distribution function at probability level , , are the ...