Percentile (nearest rank) (PERCENTILE)

Summary

Rolling percentile by the nearest-rank method: sort the trailing window ascending and report the value whose 1-based ordinal rank is the P-th percentile of the window size. The result is always a value that actually occurred in the window, never an interpolation, so it stays on the price scale and never invents a level the series never traded at. At P = 50 with an odd window it is the rolling median; at the extremes it degenerates to the rolling minimum and maximum.

Formula

$W_t = \operatorname{sort}(x_{t-N+1}, \dots, x_t)$; $k = \left\lceil \frac{P \cdot N}{100} \right\rceil$ clamped to $[1, N]$; $PERCENTILE_t = W_t[k]$ (N = optInTimePeriod, P = optInPercentile, $W_t[1]$ the smallest)

Notes

• The nearest-rank method is one of several incompatible percentile conventions. The linear-interpolation family (Hyndman & Fan type 7, the default of most statistical packages, and TradingView's ta.percentile_linear_interpolation) reports a weighted blend of two neighbouring order statistics and can emit a value that never occurred. That is a different indicator, not a mode of this one: PERCENTILE's parameter list is fixed at a window and a percentage, and a method selector cannot be appended to it later without changing the function's arity.
• Every input value in the window must be finite. A NaN makes every comparison against it false, which breaks the ordering the rank index is read from.

Inputs

• inReal — Source series to take the percentile of

Outputs

• outReal — The value at the requested rank within the trailing window

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	30	2–100000	Number of bars in the trailing window
optInPercentile	real	50	0–100	Percentage position within the sorted window

Properties

Numerical Stability: Start-Independent

✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: percentile.c · percentile.yaml

Native	File
C	ta_PERCENTILE.c
Rust	percentile.rs
Java	Core_PERCENTILE.java

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Percentile Nearest Rank, Rolling Percentile, Rolling Quantile, Rolling Median

See Also

MIN · MAX · MEDPRICE · STDDEV

References

• Percentile — nearest-rank method, the ordinal rank definition this function implements.
• Rob J. Hyndman and Yanan Fan, "Sample Quantiles in Statistical Packages", The American Statistician 50(4), 1996 — the nearest-rank rule is their type 1.