quantilerelated

Quantilerelated is a term used to describe topics and methods centered on quantiles and quantile-based analysis across statistics, data science, finance, and related disciplines. Quantiles are values that partition a distribution into equal-sized intervals; the p-th quantile is the value x such that the probability of observing a value at most x equals p. The inverse of the distribution function, the quantile function or inverse CDF, maps probabilities to outcomes. Common quantiles include quartiles, deciles, and percentiles, with the interquartile range serving as a robust measure of spread.

In statistical practice, quantiles are used for descriptive summaries, outlier detection, and robust benchmarking. Order statistics underpin many quantile estimators, and nonparametric methods often rely on ranks rather than distributional assumptions. Quantile estimation can be pointwise or conditional, the latter leading to modeling approaches that describe how quantiles of a response variable vary with predictors.

Quantilerelated research includes quantile regression, where conditional quantiles of a response are modeled as functions of covariates. Introduced to capture heterogeneous effects beyond the mean, this approach complements traditional mean regression and is robust to outliers and skewed distributions. Other topics include distribution-free confidence intervals for quantiles, bootstrap methods, and the study of asymptotic properties of quantile estimators.

Applications span finance (risk measures such as Value at Risk), meteorology and hydrology (thresholds and extreme quantiles), quality control, psychology and medicine (normative percentiles), and general data analysis. Tools for quantile-related work appear in statistical software and libraries, enabling estimation, visualization, and inference without heavy distributional assumptions.

See also: quantile regression, order statistics, inverse CDF, percentile, interquartile range.