Quantile Function - Applications

Applications

Quantile functions are used in both statistical applications and Monte Carlo methods.

For statistical applications, users need to know key percentage points of a given distribution. For example, they require the median and 25% and 75% quartiles as in the example above or 5%, 95%, 2.5%, 97.5% levels for other applications such as assessing the statistical significance of an observation whose distribution is known; see the quantile entry. Before the popularization of computers, it was not uncommon for books to have appendices with statistical tables sampling the quantile function (see, e.g., ). Statistical applications of quantile functions are discussed extensively by Gilchrist.

Monte-Carlo simulations employ quantile functions to produce non-uniform random or pseudorandom numbers for use in diverse types of simulation calculations. A sample from a given distribution may be obtained in principle by applying its quantile function to a sample from a uniform distribution. The demands, for example, of simulation methods in modern computational finance are focusing increasing attention on methods based on quantile functions, as they work well with multivariate techniques based on either copula or quasi-Monte-Carlo methods and Monte Carlo methods in finance.