Logistic Equation

logistic_equation(first_constant, second_constant, third_constant, precision=4)

Generates a logistic function to provide evaluations at variable inputs

Parameters

  • first_constant (int or float) – Carrying capacity of the resultant logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • second_constant (int or float) – Growth rate of the resultant logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • third_constant (int or float) – Value of the sigmoid’s midpoint of the resultant logistic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

  • TypeError – First three arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

evaluation – Function for evaluating a logistic equation when passed any integer or float argument

Return type

func

See also

logistic_derivatives(), logistic_integral(), logistic_roots(), logistic_model()

Notes

  • Standard form of a logistic function: \(f(x) = \frac{a}{1 + \text{e}^{-b\cdot(x - c)}}\)

  • Logistic Functions

Examples

Import logistic_equation function from regressions library
>>> from regressions.analyses.equations.logistic import logistic_equation
Create a logistic function with coefficients 2, 3, and 5, then evaluate it at 10
>>> evaluation_first = logistic_equation(2, 3, 5)
>>> print(evaluation_first(10))
2.0
Create a logistic function with coefficients 100, 5, and 11, then evaluate it at 10
>>> evaluation_second = logistic_equation(100, 5, 11)
>>> print(evaluation_second(10))
0.6693
Create a logistic function with all inputs set to 0, then evaluate it at 10
>>> evaluation_zero = logistic_equation(0, 0, 0)
>>> print(evaluation_zero(10))
0.0001