Array Quantile

Shipping

array_quantile

Quantile / percentile of an array with NumPy-style interpolation methods

Signature

Inputs

dataArrayrequired— Any array, flattened to 1-D before the order statistic is taken.

Outputs

valueScalar— The requested quantile of the data.

Parameters

Key	Type	Default	Notes
`q`	float	0.5	Quantile to compute in $[0,1]$; $0.5$ is the median, $0.25$ the lower quartile.
`method`	enum	linear	one of: linear, lower, higher, nearest, midpoint

Description

Array Quantile returns the value at quantile $q \in [0, 1]$ of the flattened input — $q = 0.5$ is the median, $q = 0.25$ the first quartile, $q = 0.99$ the 99th percentile, and so on. When the target rank $h = q (n - 1)$ falls between two samples, the method parameter selects how to combine the bracketing order statistics, following NumPy's percentile conventions:

linear — linearly interpolate between the two neighbours (the default).
lower / higher — take the lower or higher neighbour.
nearest — take the nearest by rank.
midpoint — the average of the two neighbours.

The node is stateless and order-statistic based, so it is robust to a handful of extreme outliers in a way the mean is not.

Mathematics

h = q (n - 1), k = ⌊ h ⌋

Q_{linear} (q) = x_{(k)} + (h - k) (x_{(k + 1)} - x_{(k)})

Examples

Median of an even-length sample

For $[1, 2, 3, 4]$ with q = 0.5, method = linear: rank $h = 0.5 \cdot 3 = 1.5$ , so the result interpolates halfway between $x_{(1)} = 2$ and $x_{(2)} = 3$ , giving value $= 2.5$ .

95th percentile latency

Set q = 0.95 on a Vector of request latencies to read the tail (p95) that most SLAs target, unaffected by a few pathological outliers the mean would inflate.

Applications

Percentile SLAs (p50/p95/p99) on latency or error buffers.
Robust center/spread estimates (median, IQR) resistant to outliers.
Clipping thresholds derived from data quantiles rather than fixed limits.

Neat

The five interpolation modes mirror NumPy's percentile methods exactly, so results reproduce a `numpy.quantile` call bit-for-bit on the same data.

As an order statistic, a single extreme outlier moves the median by at most one rank — unlike the mean, which it can move arbitrarily far.