# Quantile¶

Quantile is an algorithm to analyze the distribution of observations. Quantiles are the values that divide the distribution so that a given portion of observations is below the quantile.

## Details¶

Given a set $$X$$ of $$p$$ features $$x_1 = (x_{11}, \ldots, x_{1p}), \ldots x_n = (x_{n1}, \ldots, x_{np})$$ and the quantile orders $$\beta = \beta_1, \ldots, \beta_m$$, the problem is to compute $$z_{ik}$$ that meets the following conditions:

$P\{ \xi_i \leq z_{ik} \} \geq \beta_k$
$P\{\xi_i > z_{ik} \} \leq 1 - \beta_k$

In the equations above:

• $$x_i = (x_{1i}, \ldots, x_{ni})$$ are observations of a random variable $$\xi_i$$ that represents the $$i$$-th feature

• $$P$$ is the probability measure

• $$i = 1, \ldots, p$$

• $$k = 1, \ldots, m$$

## Batch Processing¶

### Algorithm Input¶

The quantile algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Algorithm Input for Quantile (Batch Processing)

Input ID

Input

data

Pointer to the $$n \times p$$ numeric table that contains the input data set. This table can be an object of any class derived from NumericTable.

### Algorithm Parameters¶

The quantile algorithm has the following parameters:

Algorithm Parameters for Quantile (Batch Processing)

Parameter

Default Value

Description

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Performance-oriented computation method, the only method supported by the algorithm.

quantileOrders

$$0.5$$

The $$1 \times m$$ numeric table with quantile orders.

### Algorithm Output¶

The quantile algorithm calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Algorithm Output for Quantile (Batch Processing)

Result ID

Result

quantiles

Pointer to the $$p \times m$$ numeric table with the quantiles.

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

## Examples¶

Batch Processing: