The Box-Muller transform (by George Edward Pelham Box and Mervin Edgar Muller 1958) is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers. It is commonly expressed in two forms. The basic form as given by Box and Muller takes two samples from the uniform distribution on the interval (0, 1] and maps them to two standard, normally distributed samples. The polar form takes two samples from a different interval, [-1, +1], and maps them to two normally distributed samples without the use of sine or cosine functions. The Box-Muller transform was developed as a more computationally efficient alternative to the inverse transform sampling method. The Ziggurat algorithm gives an even more efficient method. …
A choropleth map is a thematic map in which areas are shaded or patterned in proportion to the measurement of the statistical variable being displayed on the map, such as population density or per-capita income.
The choropleth map provides an easy way to visualize how a measurement varies across a geographic area or it shows the level of variability within a region.
A special type of choropleth map is a prism map, a three-dimensional map in which a given region’s height on the map is proportional to the statistical variable’s value for that region.
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, and yet enables robust estimation in a broader variety of settings, including the previously unstudied problem of robust mean estimation in $\ell_p$-norms. …