LOGISTIC FUNCTION Meaning and
Definition
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A logistic function, also referred to as the sigmoid function, is a mathematical function that models the growth or decline of a variable over time. It is commonly used in fields such as biology, economics, and physics to describe and analyze the behavior of various phenomena.
The logistic function takes the form of a continuous S-shaped curve, which represents the gradual change of the variable being studied. It is characterized by two distinct asymptotes – one at the upper limit and the other at the lower limit – signifying the ultimate boundaries within which the variable can vary. The function is confined within these limits, never exceeding or falling below them.
The logistic function is symmetric around its midpoint, where it undergoes a smooth and gradual transition from a slow growth rate to a rapid growth rate. This midpoint, also known as the inflection point, denotes the moment when the variable's growth rate is at its maximum. As the variable moves away from this point, its growth rate gradually decreases until it approaches zero, eventually reaching a steady state.
The logistic function is widely used in logistic regression, a statistical technique used to model the relationship between a dependent variable and one or more independent variables. It is also employed in applications such as population dynamics, marketing, and prediction models. The versatility and behavior of the logistic function make it a valuable tool for understanding and predicting various phenomena that involve gradual growth or decline over time.
Etymology of LOGISTIC FUNCTION
The word "logistic" in "logistic function" originates from the Greek word "logistikos", which means "skilled in calculating". It is derived from the Greek word "logizesthai", meaning "to reason" or "to calculate". This term was adopted and used in mathematical contexts to refer to calculations and reasoning related to the logistic function. The logistic function itself was initially developed by mathematician Pierre-François Verhulst in the 19th century to describe population growth, and the term "logistic function" became commonly used to describe this specific mathematical function.
