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docs/indicators/averages/ema/calculation.md

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+## EMA - Calculation Method
+
+The EMA calculation utilizes a weighting multiplier, typically denoted as the smoothing factor ($alpha$). This factor is calculated as:
+
+$alpha = \frac{2}{period + 1}$
+
+where 'period' represents the chosen period for the EMA.
+
+The general formula for EMA required for arithmetic operations:
+
+$EMA_n = (data_{n} \times alpha) + (EMA_{n-1} \times (1 - alpha))$
+
+or in optimized form (requires only three arithmetic operations instead of four):
+
+$EMA_n = {alpha}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1}$
+
+
+
+When calculating the Exponential Moving Average (EMA) and there is not enough data (n < period), several approaches can be considered. Each method has its own pros and cons:
+
+#### 1. Assume all previous values were 0
+
+$EMA_0 = 0$ \
+$EMA_n = alpha \times (data_n - EMA_{n-1}) + EMA_{n-1}$
+
+- Will lead to significant underestimation of EMA in early periods
+
+#### 2. Calculate as if all previous values were the same as the first value
+
+$EMA_0 = data_0$ \
+$EMA_n = alpha \times (data_n - EMA_{n-1}) + EMA_{n-1}$
+
+- Will overestimate early EMA if initial data point is far from representative
+
+#### 3. Use SMA instead of EMA for the first period
+
+$EMA_n = \left\{ \begin{array}{cl}
+\frac{1}{p}\left( data_{n}-data_{n-p}\right)+SMA_{n-1} & : \ n \leq period \\
+{alpha}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1} & : \ n > period
+\end{array} \right.$
+
+- Creates a discontinuity when switching from SMA to EMA
+
+
+
+### Conclusion
+
+The choice of method depends on the specific requirements of the application:
+
+- Method 1 is suitable for applications where underestimation in early periods is acceptable.
+- Method 2 is beneficial when a smooth transition is crucial and the initial data point is representative.
+- Method 3 is appropriate when simplicity is preferred and a clear distinction between SMA and EMA is acceptable.
+- Method 4 offers a good balance between adaptability and maintaining the EMA concept, but may require additional explanation to users.
+
+