Gompertz function

The Gompertz curve or Gompertz function, is a type of mathematical model for a time series and is named after Benjamin Gompertz (1779-1865). 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 regards to detailing populations. The Gompertz curve or Gompertz function, is a type of mathematical model for a time series and is named after Benjamin Gompertz (1779-1865). 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 regards to detailing populations. Benjamin Gompertz originally designed the function to detail his law of human mortality for the Royal Society in 1825. The law rests upon an a priori assumption that a person's resistance to death decreases as his age increases. The model can be written in this way: N ( t ) = N ( 0 ) exp ⁡ ( − c ( exp ⁡ ( a t ) − 1 ) ) {displaystyle N(t)=N(0)exp(-c(exp(at)-1))}