The sigmoid curve is the curve whose formula is the sigmoid function. Members of the family of curves obtained by linear scaling and translation of the sigmoid curve are called logistic curves, and are found in a range of fields, from biology to economics.

Table of contents

1 The sigmoid function 2 History 3 See also 4 Bibliography 5 External links

The sigmoid function

The sigmoid function is

• the rate of reproduction is proportional to the existing population, all else being equal
• the rate of reproduction is proportional to the amount of available resources, all else being equal

The sigmoid function is the inverse of the logit function. The conversion from the log-likelihood ratio of two alternatives to a probability takes the form of a sigmoid curve.

History

The Verhulst equation, (1), was first published by Pierre F. Verhulst in 1838, after he had read Thomas Malthus' Essay on the Principle of Population. Verhulst derived his logistique equation (logistic equation) to describe the self-limiting growth of a biological population. The equation is also sometimes called the Verhulst-Pearl equation following its rediscovery in 1920. A. J. Lotka derived the equation again in 1925, calling it the law of population growth.

See also

• Hubbert curve
• Logistic regression
• Generalised logistic curve
• log-likelihood ratio
• logistic map