mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
84 lines
2.8 KiB
Plaintext
84 lines
2.8 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("Skewness (SKEW)", "SKEW", overlay=false, precision=6)
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//@function Calculates the skewness of a source series over a specified period.
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// Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
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// This implementation calculates the population skewness (Fisher-Pearson coefficient g1).
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//@param src The source series.
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//@param len The lookback period. Must be > 2.
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//@returns The skewness value.
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//@optimized Uses efficient rolling calculations for mean, variance, and the third central moment.
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skew(series float src, simple int len) =>
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if len <= 2
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runtime.error("Length must be greater than 2 for Skewness calculation.")
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var float sum_m = 0.0
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var array<float> buffer_m = array.new_float(len)
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var int head_m = 0
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if bar_index >= len
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sum_m -= array.get(buffer_m, head_m)
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float current_src_nz = nz(src)
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sum_m += current_src_nz
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array.set(buffer_m, head_m, current_src_nz)
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head_m := (head_m + 1) % len
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float mean_val = na
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if bar_index >= len - 1
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mean_val := sum_m / len
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else
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mean_val := sum_m / (bar_index + 1)
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float dev = src - mean_val
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var float sum_v = 0.0
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var array<float> buffer_v = array.new_float(len)
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var int head_v = 0
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float dev_sq_nz = nz(math.pow(dev, 2))
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if bar_index >= len
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sum_v -= array.get(buffer_v, head_v)
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sum_v += dev_sq_nz
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array.set(buffer_v, head_v, dev_sq_nz)
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head_v := (head_v + 1) % len
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float variance_val = na
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if bar_index >= len - 1
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variance_val := sum_v / len
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else
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variance_val := sum_v / (bar_index + 1)
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float stddev_val = variance_val > 1e-9 ? math.sqrt(variance_val) : 0.0
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var float sum_s3 = 0.0
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var array<float> buffer_s3 = array.new_float(len)
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var int head_s3 = 0
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float dev_cubed_nz = nz(math.pow(dev, 3))
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if bar_index >= len
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sum_s3 -= array.get(buffer_s3, head_s3)
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sum_s3 += dev_cubed_nz
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array.set(buffer_s3, head_s3, dev_cubed_nz)
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head_s3 := (head_s3 + 1) % len
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float m3 = na
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if bar_index >= len - 1
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m3 := sum_s3 / len
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else
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m3 := sum_s3 / (bar_index + 1)
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float skew_val = na
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if not na(m3) and not na(stddev_val)
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if stddev_val > 1e-9
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float stddev_cubed = math.pow(stddev_val, 3)
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if stddev_cubed != 0
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skew_val := m3 / stddev_cubed
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else
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skew_val := 0.0
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else
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skew_val := 0.0
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skew_val
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// ---------- Main loop ----------
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// Inputs
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i_source = input.source(close, "Source")
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i_length = input.int(20, "Length", minval=3) // Minval 3 for skewness
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// Calculation
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skewValue = skew(i_source, i_length)
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// Plot
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plot(skewValue, "Skewness", color=color.yellow, linewidth=2)
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