Advanced Zscore Pro

# Advanced Statistical Studies Indicator
# 
# DESCRIPTION:
# This comprehensive statistical analysis indicator provides multiple statistical measures
# to evaluate price behavior, probability distributions, and market anomalies. It combines
# Z-scores, percentile rankings, skewness, kurtosis, and probability bands to give traders
# a complete statistical view of market conditions.
#
# FEATURES:
# - Z-Score analysis with multiple lookback periods
# - Percentile ranking system for relative positioning
# - Skewness measurement for distribution asymmetry
# - Kurtosis analysis for tail risk assessment
# - Standard deviation bands and probability zones
# - Mean reversion signals and statistical extremes
# - Customizable statistical parameters and display options
#
# USAGE:
# - Identify statistically extreme price levels for mean reversion trades
# - Assess probability of continued moves vs. reversals
# - Evaluate distribution characteristics for better risk assessment
# - Use statistical extremes for entry/exit timing
# - Monitor market regime changes through statistical shifts
#
# PARAMETERS:
# - Primary Length: Main lookback period for calculations (default: 20)
# - Long Length: Extended period for trend analysis (default: 50)
# - Statistical Method: Choose primary statistical focus
# - Probability Bands: Standard deviation multiples for probability zones
#
# Author: MarketEdgePro
# Version: 1.0

declare lower;

# Input parameters
input primaryLength = 20;
input longLength = 50;
input priceSource = close;
input statisticalMethod = {default "Z_Score", "Percentile_Rank", "Skewness", "Kurtosis", "Composite"};
input showProbabilityBands = yes;
input stdDev1 = 1.0;
input stdDev2 = 2.0;
input stdDev3 = 3.0;
input showMovingAverage = yes;
input maLength = 10;
input extremeThreshold = 90;
input showLabels = yes;
input showBackground = yes;

# Basic statistical calculations
def price = priceSource;
def mean = Average(price, primaryLength);
def longMean = Average(price, longLength);
def stdDeviation = StDev(price, primaryLength);
def variance = Power(stdDeviation, 2);

# Z-Score calculations (multiple timeframes)
def zScore = if stdDeviation != 0 then (price - mean) / stdDeviation else 0;
def longZScore = if StDev(price, longLength) != 0 then 
    (price - longMean) / StDev(price, longLength) else 0;

# Percentile rank calculation
def priceHigh = Highest(price, primaryLength);
def priceLow = Lowest(price, primaryLength);
def percentileRank = if (priceHigh != priceLow) then 
    100 * (price - priceLow) / (priceHigh - priceLow) else 50;

# Skewness calculation (asymmetry of distribution)
def deviation = price - mean;
def cubeDeviation = Power(deviation, 3);
def avgCubeDeviation = Average(cubeDeviation, primaryLength);
def skewness = if Power(stdDeviation, 3) != 0 then 
    avgCubeDeviation / Power(stdDeviation, 3) else 0;

# Kurtosis calculation (tail heaviness)
def fourthDeviation = Power(deviation, 4);
def avgFourthDeviation = Average(fourthDeviation, primaryLength);
def kurtosis = if Power(stdDeviation, 4) != 0 then 
    avgFourthDeviation / Power(stdDeviation, 4) - 3 else 0;

# Composite statistical score
def compositeScore = (zScore * 0.4) + ((percentileRank - 50) / 50 * 0.3) + 
                     (skewness * 0.2) + (kurtosis * 0.1);

# Select primary display based on method
def primaryStat = 
    if statisticalMethod == statisticalMethod."Z_Score" then zScore
    else if statisticalMethod == statisticalMethod."Percentile_Rank" then percentileRank
    else if statisticalMethod == statisticalMethod."Skewness" then skewness * 10
    else if statisticalMethod == statisticalMethod."Kurtosis" then kurtosis * 5
    else if statisticalMethod == statisticalMethod."Composite" then compositeScore
    else zScore;

# Moving average of primary statistic
def statMA = Average(primaryStat, maLength);

# Probability bands (for Z-Score method)
def upperBand1 = if statisticalMethod == statisticalMethod."Z_Score" then stdDev1 else 75;
def upperBand2 = if statisticalMethod == statisticalMethod."Z_Score" then stdDev2 else 90;
def upperBand3 = if statisticalMethod == statisticalMethod."Z_Score" then stdDev3 else 95;
def lowerBand1 = if statisticalMethod == statisticalMethod."Z_Score" then -stdDev1 else 25;
def lowerBand2 = if statisticalMethod == statisticalMethod."Z_Score" then -stdDev2 else 10;
def lowerBand3 = if statisticalMethod == statisticalMethod."Z_Score" then -stdDev3 else 5;

# Statistical extremes detection
def upperExtreme = 
    if statisticalMethod == statisticalMethod."Percentile_Rank" then 
        percentileRank > extremeThreshold
    else primaryStat > upperBand2;

def lowerExtreme = 
    if statisticalMethod == statisticalMethod."Percentile_Rank" then 
        percentileRank < (100 - extremeThreshold)
    else primaryStat < lowerBand2;

# Plot primary statistical measure
plot PrimaryStatLine = primaryStat;
PrimaryStatLine.SetDefaultColor(Color.BLUE);
PrimaryStatLine.SetLineWeight(2);

# Plot moving average
plot StatMovingAvg = if showMovingAverage then statMA else Double.NaN;
StatMovingAvg.SetDefaultColor(Color.ORANGE);
StatMovingAvg.SetStyle(Curve.LONG_DASH);

# Plot probability bands
plot UpperBand1Line = if showProbabilityBands then upperBand1 else Double.NaN;
UpperBand1Line.SetDefaultColor(Color.GRAY);
UpperBand1Line.SetStyle(Curve.SHORT_DASH);

plot UpperBand2Line = if showProbabilityBands then upperBand2 else Double.NaN;
UpperBand2Line.SetDefaultColor(Color.RED);
UpperBand2Line.SetStyle(Curve.SHORT_DASH);

plot LowerBand1Line = if showProbabilityBands then lowerBand1 else Double.NaN;
LowerBand1Line.SetDefaultColor(Color.GRAY);
LowerBand1Line.SetStyle(Curve.SHORT_DASH);

plot LowerBand2Line = if showProbabilityBands then lowerBand2 else Double.NaN;
LowerBand2Line.SetDefaultColor(Color.GREEN);
LowerBand2Line.SetStyle(Curve.SHORT_DASH);

# Zero/midpoint line
plot ZeroLine = if statisticalMethod == statisticalMethod."Z_Score" or 
                   statisticalMethod == statisticalMethod."Composite" then 0
                else if statisticalMethod == statisticalMethod."Percentile_Rank" then 50
                else 0;
ZeroLine.SetDefaultColor(Color.DARK_GRAY);
ZeroLine.SetStyle(Curve.LONG_DASH);

# Color coding based on extremes
PrimaryStatLine.AssignValueColor(
    if upperExtreme then Color.RED
    else if lowerExtreme then Color.GREEN
    else if primaryStat > 0 or (statisticalMethod == statisticalMethod."Percentile_Rank" and primaryStat > 50) 
        then Color.BLUE
    else Color.CYAN
);

# Background shading for extreme zones
AddCloud(
    if showBackground and upperExtreme then upperBand2 else Double.NaN,
    if showBackground and upperExtreme then primaryStat else Double.NaN,
    Color.RED,
    Color.RED
);

AddCloud(
    if showBackground and lowerExtreme then lowerBand2 else Double.NaN,
    if showBackground and lowerExtreme then primaryStat else Double.NaN,
    Color.GREEN,
    Color.GREEN
);

# Statistical summary labels
AddLabel(showLabels, "Primary: " + 
    (if statisticalMethod == statisticalMethod."Z_Score" then "Z-Score"
     else if statisticalMethod == statisticalMethod."Percentile_Rank" then "Percentile"
     else if statisticalMethod == statisticalMethod."Skewness" then "Skewness"
     else if statisticalMethod == statisticalMethod."Kurtosis" then "Kurtosis"
     else "Composite") + ": " + Round(primaryStat, 2), Color.Gray);

AddLabel(showLabels, "Z-Score: " + Round(zScore, 2), 
    if AbsValue(zScore) > 2 then Color.RED
    else if AbsValue(zScore) > 1 then Color.BLUE
    else Color.Gray);

AddLabel(showLabels, "Percentile: " + Round(percentileRank, 0) + "%", 
    if percentileRank > 90 then Color.RED
    else if percentileRank < 10 then Color.GREEN
    else Color.Gray);

AddLabel(showLabels, "Skew: " + Round(skewness, 2), 
    if AbsValue(skewness) > 1 then Color.ORANGE else Color.gray);

AddLabel(showLabels, "Kurt: " + Round(kurtosis, 2), 
    if AbsValue(kurtosis) > 1 then Color.MAGENTA else Color.GRAY);

# Extreme condition alerts
AddLabel(showLabels and upperExtreme, "STATISTICAL HIGH", Color.RED);
AddLabel(showLabels and lowerExtreme, "STATISTICAL LOW", Color.GREEN);

# Distribution analysis using numeric codes
def distributionCode = 
    if AbsValue(skewness) < 0.5 and AbsValue(kurtosis) < 1 then 1 # Normal
    else if skewness > 0.5 then 2 # Right Skewed
    else if skewness < -0.5 then 3 # Left Skewed
    else if kurtosis > 1 then 4 # Heavy Tails
    else if kurtosis < -1 then 5 # Light Tails
    else 6; # Mixed

AddLabel(showLabels, 
    "Dist: " + 
    (if distributionCode == 1 then "NORMAL"
     else if distributionCode == 2 then "R-SKEWED"
     else if distributionCode == 3 then "L-SKEWED"
     else if distributionCode == 4 then "HEAVY-TAIL"
     else if distributionCode == 5 then "LIGHT-TAIL"
     else "MIXED"), 
    if distributionCode == 1 then Color.Gray else Color.Blue);