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# List of Mathematical Symbols

## List of Mathematical Symbols

This section lists the mathematical symbols that are used in Technical Studies Reference.

### Parameters

Parameters are variables whose values are either entered by the user as Inputs, calculated from Input values, automatically generated by Auto Looping, or automatically generated by internal looping.

- \(c\) - Smoothing Constant - Appears in several moving averages, such as Moving Average - Adaptive and Moving Average - Exponential. This may be subscripted, e.g. \(c_F\), \(c_S\), etc.
- \(i\) - Variable Index Value - Usually varies from some past value of the Index up to the Current Index Value \(t\).
- \(\lambda\) - Lag - Appears in Moving Average - Zero Lag Exponential.
- \(\mu\) - ATR Multiplier - Appears in Volatility Trend Indicator.
- \(n\) - Length - This may be subscripted, e.g. \(n_1\), \(n_{RSI}\).
- \(t\) - Current Index Value

### Random Variables

Random Variables are variables whose values are determined by the outcome of an experiment. For our purposes, Random Variables are almost always volumes, prices or Statistical Functions of prices.

- \(C\) - Closing Price
- \(H\) - High Price
- \(L\) - Low Price
- \(N\) - Number of Trades - This may be subscripted, e.g. \(N_{ask}\), \(N_{bid}\), etc.
- \(O\) - Opening Price
- \(P\) - Price - This may be subscripted, e.g. \(P_{ask}\), \(P_{bid}\), etc.
- \(V\) - Volume - This may be subscripted, e.g. \(V_{ask}\), \(V_{bid}\), etc.
- \(X\) - Input Data - These may be superscripted, e.g. \(X^{(1)}\), \(X^{(2)}\).

When we refer to the value of a Random Variable at Index \(t\), we use a subscript to indicate this. For instance, the value of the Random Variable **Input Data** \(X\) at Index \(t\) is denoted as \(X_t\).

### Statistical Functions

Statistical Functions take on a value at each Current Index Value \(t\). Unless otherwise stated, the value of a Statistical Function is 0 prior to the starting value of \(t\). We refer to the value of a Statistical Function at Index \(t\) by using a subscript, and we write any Inputs for the Statistical Function in parentheses. For instance, the value of the Statistical Function **Moving Average - Simple** of **Input Data** \(X\) with **Length** \(n\) at Index \(t\) is denoted as \(MA_t(X,n)\).

- \(a_t(X,n)\) - Intercept of Least Squares Regression Line - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(ACDC_t(X,n_1,n_2,n_3,n_4)\) - AC/DC Histogram
- \(AD_t\) - Accumulation/Distribution
- \(ADF_t\) - Accumulation/Distribution Flow
- \(\overline{ADF}_t(n)\) - Moving Average of Accumulation/Distribution Flow
- \(AMA_t(X,n,c_F,c_S)\) - Moving Average - Adaptive
- \(AMAHigh_t(X,n,c_F,c_S)\) - Appears in Moving Average - Adaptive Binary Wave
- \(AMALow_t(X,n,c_F,c_S)\) - Appears in Moving Average - Adaptive Binary Wave
- \(AO_t(n_1,n_2)\) - Awesome Oscillator, aka Bill Williams Awesome Oscillator
- \(b_t(X,n)\) - Slope of Least Squares Regression Line - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(BW_t(X,n,c_F,c_S,f)\) - Binary Wave - Appears in Moving Average - Adaptive Binary Wave
- \(c_t(X,n)\) - Smoothing Constant - Appears in Moving Average - Adaptive
- \(D_t(X)\) - Downward Change in \(X\) - Appears in RSI
- \(\Delta MA_t(X,n_1,n_2)\) - Moving Average Difference - Also appears in AC/DC Histogram
- \(DEMA_t(X,n)\) - Moving Average - Double Exponential
- \(Dir_t(X,n)\) - Direction - Appears in Moving Average - Adaptive
- \(Dir_t(X,n,\mu,DPL_{\max})\) - Direction - Appears in Volatility Trend Indicator - Differs from the function that appears in Moving Average - Adaptive
- \(DPL_t(X,n,\mu,DPL_{\max})\) - Dynamic Period Length - Appears in Volatility Trend Indicator
- \(DR_t(H,L)\) - Daily Range - Appears in Average Daily Range
- \(\overline{DR}_t(n)\) - Average Daily Range
- \(EMA_t(X,n)\) - Moving Average - Exponential
- \(EMA_t^{(j)}(X,n)\) - \(j-\)fold composition of the Exponential Moving Average with itself - Appears in T3
- \(FT_t(X,n)\) - Fisher Transform
- \(HMA_t(X,n)\) - Moving Average - Hull
- \(HVR_t(C,n_S,n_L)\) - Historical Volatility Ratio
- \(LR_t(C)\) - Logarithmic Return - Appears in Historical Volatility Ratio
- \(LRI_t(X,n)\) - Linear Regression Indicator - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(LRMA_t(X,n)\) - Linear Regression Moving Average - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(M_t(X,n)\) - Momentum
- \(MA_t(X,n)\) - Moving Average - Simple
- \(MACD_t(X,n_F,n_S)\) - Moving Average Convergence/Divergence (MACD)
- \(MACDDiff_t(X,n_F,n_S,n_M)\) - MACD Difference - Appears in Moving Average Convergence/Divergence (MACD)
- \(MACDMA_t(X,n_F,n_S,n_M)\) - MACD Moving Average - Appears in Moving Average Convergence/Divergence (MACD)
- \(MaxRSI_t(C,n,n_{HL})\) - Maximum RSI - Appears in Stochastic RSI
- \(MinRSI_t(C,n,n_{HL})\) - Minimum RSI - Appears in Stochastic RSI
- \(MMed_t(X,n)\) - Moving Median
- \(\pi^{(i)}_t(X,n,\mu,DPL_{\max})\), \(i = 1,2,3\) - Period 1, 2, and 3 - Appear in Volatility Trend Indicator
- \(RV_t\) - Range Volume - Appears in Accumulation/Distribution
- \(\sigma_t(X,n)\) - Standard Deviation
- \(StochRSI_t(C,n,n_{HL})\) - Stochastic RSI
- \(sum_t(T)\) - Sum over Time values - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(sum_t(TX)\) - Sum over product of Time values and Input Data values - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(sum_t(X)\) - Sum over Input Data values - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(SWWMA_t(X,n)\) - Moving Average - Sine Wave Weighted
- \(SZMA_t(X,n)\) - Moving Average - Simple Skip Zeros
- \(T_3(X,n,v)\) - T3
- \(TEMA_t(X,n_1,n_2)\) - Moving Average - Triple Exponential
- \(TMA_t(X,n_1,n_2)\) - Moving Average - Triangular
- \(TR_t(H,L,C)\) - True Range
- \(\overline{TR}_t(n)\) - Average True Range
- \(U_t(X)\) - Upward Change in \(X\) - Appears in RSI
- \(Var_t(X,n)\) - Variance - Appears in Standard Deviation
- \(Vol_t(X,n)\) - Volatility - Appears in Moving Average - Adaptive
- \(VR_t\) - Volume Ratio - Appears in Bid Ask Volume Ratio
- \(\overline{VR}_t(n)\) - Average Volume Ratio - Appears in Bid Ask Volume Ratio
- \(VTI_t(X,n,\mu,DPL_{\max})\) - Volatility Trend Indicator
- \(VWMA_t(X,n)\) - Moving Average - Weighted
- \(WMA_t(X,n)\) - Moving Average - Weighted
- \(WWMA_t(X,n)\) - Moving Average - Welles Wilders
- \(\xi_t(X,n)\) - First transformation of Price data - Appears in Fisher Transform
- \(\xi^*_t(X,n)\) - Second transformation of Price data - Appears in Fisher Transform
- \(Z_t(X,n_{\mu},n_{\sigma})\) - Z-Score
- \(ZLEMA_t(X,n)\) - Moving Average - Zero Lag Exponential

When a Statistical Function is used as a Random Variable for another Statistical Function, we indicate this by omitting its subscript. For instance, the value of the Exponential Moving Average of \(X\) with **Length** \(n\) at Index \(t\) is denoted as \(EMA_t(X,n)\). If we take the Exponential Moving Average of \(EMA_t(X,n)\), again with **Length** \(n\), we denote its value at Index \(t\) as \(EMA_t(EMA(X,n),n)\). Here, \(EMA(X,n)\) is a random variable corresponding to the first Exponential Moving Average.

*Last modified Wednesday, 16th August, 2017.