Category:Definitions/Quantiles
This category contains definitions related to Quantiles.
Related results can be found in Category:Quantiles.
Informal Definition
Let $S$ be a set of quantitative data.
Let $S$ be arranged in order of size.
Let $q \in \Z_{\ge 1}$ be a strictly positive integer.
Let the range of $S$ be divided into exactly $q$ class intervals such that the probability of an instance of $S$ falling into an arbitrary instance of one of these class intervals is equal to $\dfrac 1 q$.
That is, the class intervals are designed so as to have the same number of elements in them.
Then the class boundaries are known as the quantiles of $X$.
Continuous
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $X$ have probability density function $f_X$.
Let $q \in \Z_{\ge 1}$ be a strictly positive integer.
Then for $k \in \Z: 0 < k < q$, $x$ is the $k$th $q$-quantile if and only if:
| \(\ds \map \Pr {X < x}\) | \(=\) | \(\ds \int_{-\infty}^x \map {f_X} t \rd t\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac k q\) |
Discrete
Subcategories
This category has the following 2 subcategories, out of 2 total.
D
- Definitions/Deciles (1 P)
P
- Definitions/Percentiles (3 P)
Pages in category "Definitions/Quantiles"
The following 6 pages are in this category, out of 6 total.