page_title: Gompertz function
section_title: History
hierarchical_section_title: Gompertz function / History
context_page_description: The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz. It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations.
context_section_description: Benjamin Gompertz (1779–1865) was an actuary in London who was privately educated.   He was elected a fellow of the Royal Society in 1819.  The function was first presented in his June 16, 1825 paper at the bottom of page 518.  The Gompertz function reduced a significant collection of data in life tables into a single function.  It is based on the assumption that the mortality rate decreases exponentially as a person ages.   The resulting Gompertz function is for the number of individuals living at a given age as a function of age.
  Earlier work on the construction of functional models of mortality was done by the French mathematician Abraham de Moivre (1667–1754) in the 1750s.   However, Moivre assumed that the mortality rate was constant.   An extension to Gompertz's work was proposed by the English actuary and mathematician  William Matthew Makeham (1826–1891) in 1860, who added a constant background mortality rate to Gompertz’s exponentially decreasing one.
caption: Varying 
    
      
        
          a
        
      
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