// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("JVOLTYN - Normalized Jurik Volatility", shorttitle="JVOLTYN", overlay=false)

//@function Calculates Normalized Jurik Volatility (0-100 scale)
//@param period Number of bars used in the calculation (>= 2)
//@param src Source series for volatility measurement
//@returns Normalized volatility value (0 = low, 100 = high)
//@optimized Uses adaptive bands with distribution-based normalization

// Inputs
period = input.int(14, "Period", minval=2)
src = input.source(close, "Source")

// Calculate logParam (same as JVOLTY)
len1 = math.max((period - 1) / 2.0, 0)
logParam = len1 > 0 ? math.max(math.log(math.sqrt(len1)) / math.log(2) + 2.0, 0) : 0

// Normalization factor: maps [1, logParam] to [0, 100]
normFactor = logParam > 1 ? 100.0 / (logParam - 1.0) : 100.0

// JVOLTY core parameters
powParam = math.max(logParam - 2.0, 0.5)
sqrtDivider = len1 > 0 ? math.sqrt(len1) * logParam / (math.sqrt(len1) * logParam + 1.0) : 1.0

// State variables
var float upperBand = na
var float lowerBand = na
var float[] voltyBuffer = array.new_float(10, 0.0)
var float[] distBuffer = array.new_float(128, 0.0)
var int distIndex = 0
var int distCount = 0
var float lastValid = 0.0

// Initialize bands
if na(upperBand)
    upperBand := src
    lowerBand := src

// Finite value helper
getFinite(float val, float fallback) =>
    na(val) or not math.isfinite(val) ? fallback : val

price = getFinite(src, lastValid)
lastValid := price

// Calculate deviation from bands
del1 = math.abs(price - nz(upperBand[1], price))
del2 = math.abs(price - nz(lowerBand[1], price))
deviation = math.max(del1, del2) + 1e-10

// Update 10-bar volatility buffer (ring buffer style)
array.shift(voltyBuffer)
array.push(voltyBuffer, deviation)

// Short volatility: 10-bar SMA
shortVolty = array.avg(voltyBuffer)

// Update distribution buffer
if distCount < 128
    array.set(distBuffer, distCount, shortVolty)
    distCount += 1
else
    array.set(distBuffer, distIndex, shortVolty)
distIndex := (distIndex + 1) % 128

// Calculate trimmed mean from distribution
calcTrimmedMean() =>
    if distCount < 16
        array.avg(distBuffer)
    else
        // Sort the buffer
        sorted = array.copy(distBuffer)
        array.sort(sorted)
        
        // Calculate trim indices
        if distCount >= 128
            // Full buffer: use middle 65 values (indices 32-96)
            sum = 0.0
            for i = 32 to 96
                sum += array.get(sorted, i)
            sum / 65.0
        else
            // Partial buffer: adaptive trim
            sampleSize = math.max(5, math.round(0.5 * distCount))
            startIdx = math.floor((distCount - sampleSize) / 2.0)
            sum = 0.0
            for i = 0 to sampleSize - 1
                sum += array.get(sorted, int(startIdx) + i)
            sum / sampleSize

refVolty = calcTrimmedMean()

// Calculate dynamic exponent (raw JVOLTY value)
ratio = refVolty > 0 ? math.abs(shortVolty) / refVolty : 1.0
rawD = math.max(1.0, math.min(math.pow(ratio, powParam), logParam))

// Normalize to 0-100 scale
jvoltyn = (rawD - 1.0) * normFactor

// Update adaptive bands
adapt = math.pow(sqrtDivider, math.sqrt(rawD))
if price > upperBand
    upperBand := price
else
    upperBand := nz(upperBand[1], price) + adapt * (price - nz(upperBand[1], price))

if price < lowerBand
    lowerBand := price
else
    lowerBand := nz(lowerBand[1], price) + adapt * (price - nz(lowerBand[1], price))

// Plot
plot(jvoltyn, "JVOLTYN", color=color.new(color.orange, 0), linewidth=2)

// Reference levels
hline(0, "Min Volatility", color=color.gray, linestyle=hline.style_dotted)
hline(25, "Low", color=color.green, linestyle=hline.style_dotted)
hline(50, "Medium", color=color.yellow, linestyle=hline.style_dotted)
hline(75, "High", color=color.red, linestyle=hline.style_dotted)
hline(100, "Max Volatility", color=color.gray, linestyle=hline.style_dotted)

// Background coloring for volatility regimes
bgcolor(jvoltyn < 25 ? color.new(color.green, 90) : 
        jvoltyn < 50 ? color.new(color.yellow, 90) :
        jvoltyn < 75 ? color.new(color.orange, 90) :
        color.new(color.red, 90))