Quantile function - Wikipedia
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.
3.6: Distribution and Quantile Functions - Statistics LibreTexts
2022年4月24日 · Roughly speaking, a quantile of order \(p\) is a value where the graph of the distribution function crosses (or jumps over) \(p\). For example, in the picture below, \(a\) is the unique quantile of order \(p\) and \(b\) is the unique quantile of order \(q\).
10.3: The Quantile Function - Statistics LibreTexts
2021年9月13日 · The quantile function for a probability distribution has many uses in both the theory and application of probability. If \(F\) is a probability distribution function, the quantile function may be used to “construct” a random variable having \(F\) as its distributions function.
Quantile of a distribution | Definition, explanation, examples
Learn how the quantile of a distribution is defined. Discover how it is calculated through examples. Find the quantiles of the normal distribution.
This function is important because it makes sense for any type of random variable, regardless of whether the distribution is discrete, continuous, or even mixed, and because it completely determines the distribution of X.
pth quantile of F or X if and only if F(x) ≥ p and P(X ≥ x) ≥ 1−p. A pth quantile x of F is uniquely determined if F is strictly increasing in a neighborhood of x, or if F(x−) < p < F(x).
Quantile Function -- from Wolfram MathWorld
5 天之前 · Given a random variable X with continuous and strictly monotonic probability density function f(X), a quantile function Q_f assigns to each probability p attained by f the value x for which Pr(X<=x)=p. Symbolically, Q_f(p)={x:Pr(X<=x)=p}.
Proof: Quantile function of the normal distribution - The Book …
2020年3月20日 · Then, the quantile function of $X$ is \[\label{eq:norm-qf} Q_X(p) = \sqrt{2}\sigma \cdot \mathrm{erf}^{-1}(2p-1) + \mu\] where $\mathrm{erf}^{-1}(x)$ is the inverse error function.
4.5 Quantile functions | An Introduction to Probability and
The quantile function can be used to create a spinner for a distribution. Basically, the values on the outside boundary of the spinner are scaled based on the quantile function (which is determined by the cdf).
Normal distribution - Wikipedia
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is = (). The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is the variance.