Zaktualizowano

Sigmoid Functions:

History and Mathematical Basis:
1. Sigmoid functions have a rich history in mathematics and are widely used in various fields, including statistics, machine learning, and signal processing.
2. The term "sigmoid" originates from the Greek words "sigma" (meaning "S-shaped") and "eidos" (meaning "form" or "type").
3. The sigmoid curve is characterized by its smooth S-shaped appearance, which allows it to map any real-valued input to a bounded output range, typically between 0 and 1.
4. The most common form of the sigmoid function is the logistic function:

Logistic Function (σ):
• Defined as σ(x) = 1 / (1 + e^(-x)), where:
'x' is the input value,
'e' is Euler's number (approximately 2.71828).
• This function was first introduced by Belgian mathematician Pierre François Verhulst in the 1830s to model population growth with limiting factors.
• It gained popularity in the early 20th century when statisticians like Ronald Fisher began using it in regression analysis.

Specific Sigmoid Functions Used in the Indicator:
• sig(val):
The 'sig' function in this indicator is a modified version of the logistic function, clamping a value between 0 and 1 on the sigmoid curve.
• siga(val):
The 'siga' function adjusts values between -1 and 1 on the sigmoid curve, offering a centered variation of the sigmoid effect.
• sigmoid(val):
The 'sigmoid' function provides a standard implementation of the logistic function, calculating the sigmoid value of the input data.

The 'adaptiveSmoothingFactor(gradient, k)' function computes a dynamic smoothing factor for the filter based on the gradient of the price data and the user-defined sensitivity parameter 'k'.

The gradient represents the rate of change in price, calculated as the absolute difference between the current and previous close prices.

• Sensitivity (k):
The 'k' parameter adjusts how quickly the filter reacts to changes in the gradient. Higher values of 'k' lead to a more responsive filter, while lower values result in smoother outputs.

Usage in the Indicator:
The "close" value refers to the closing price of each period in the chart's time frame

• The indicator calculates the gradient by measuring the absolute difference between the current "close" price and the previous "close" price.
• This gradient represents the strength or magnitude of the price movement within the chosen time frame.
• The "close" value plays a pivotal role in determining the dynamic behavior of the "Dynamic Gradient Filter," as it directly influences the smoothing factor.

What Makes This Special:
The "Dynamic Gradient Filter" indicator stands out due to its adaptive nature and responsiveness to changing market conditions.

Dynamic Smoothing Factor:
• The indicator's dynamic smoothing factor adjusts in real-time based on the rate of change in price (gradient) and the user-defined sensitivity '(k)' parameter.
• This adaptability allows the filter to respond promptly to both minor fluctuations and significant price movements.
Smoothed Price Action:
• The final output of the filter is a smoothed representation of the price action, aiding traders in identifying trends and potential reversals.
Customizable Sensitivity:
• Traders can adjust the 'Sensitivity' parameter '(k)' to suit their preferred trading style, making the indicator versatile for various strategies.
Visual Clarity:
• The plotted "Dynamic Gradient Filter" line on the chart provides a clear visual guide, enhancing the understanding of market dynamics.

Usage:

• Identify trends and reversals in price movements.
• Filter out noise and highlight significant price changes.
• Enhance visual analysis with a dynamically adjusting filter line on the chart.

Literature:

Informacje o Wersji:
`m = input.float(1, title="Multiplier",minval=0.01, maxval=10000, step=0.01)`