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Quantile functions are used in both statistical applications and Monte Carlo methods. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.
Visualization of the Quantile Regression Averaging (QRA) probabilistic forecasting technique. The quantile regression problem can be written as follows: (|) =, where (|) is the conditional q-th quantile of the dependent variable (), = [, ^,,..., ^,] is a vector of point forecasts of individual models (i.e. independent variables) and β q is a vector of parameters (for quantile q).
Quantile regression expresses the conditional quantiles of a dependent variable as a linear function of the explanatory variables. Crucial to the practicality of quantile regression is that the quantiles can be expressed as the solution of a minimization problem, as we will show in this section before discussing conditional quantiles in the ...
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series .
Common aggregate functions include: Average (i.e., arithmetic mean) Count; Maximum; Median; Minimum; Mode; Range; Sum; Others include: Nanmean (mean ignoring NaN values, also known as "nil" or "null") Stddev; Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain I and outputs an element of an ...
A quantile-parameterized distribution (QPD) is a probability distributions that is directly parameterized by data. They were created to meet the need for easy-to-use continuous probability distributions flexible enough to represent a wide range of uncertainties, such as those commonly encountered in business, economics, engineering, and science.
More abstractly, [4] given two cumulative probability distribution functions F and G, with associated quantile functions F −1 and G −1 (the inverse function of the CDF is the quantile function), the Q–Q plot draws the q-th quantile of F against the q-th quantile of G for a range of values of q.
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.