### Abstract

This paper describes generalizations of simple growth equations made by assuming that one or more parameters have a probability distribution in the population. Thus, the product of the parental growth equation and the probability density function when integrated over the range of the parameter produces a compound growth function. In most cases, the resulting equations are more complex than the original function, but the new parameters are interpretable directly in terms of the distribution of the parameter in the population. Despite the frequent need for special functions, an effort has been made here to produce simple mathematical forms. An example is provided using some compound growth functions to describe real growth data. This method appears to be a meaningful and useful way to improve the modeling of growth.

Original language | English (US) |
---|---|

Pages (from-to) | 50-63 |

Number of pages | 14 |

Journal | Growth, Development and Aging |

Volume | 51 |

Issue number | 1 |

State | Published - Mar 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)

### Cite this

*Growth, Development and Aging*,

*51*(1), 50-63.

**Generalizing growth functions assuming parameter heterogeneity.** / Piantadosi, S.

Research output: Contribution to journal › Article

*Growth, Development and Aging*, vol. 51, no. 1, pp. 50-63.

}

TY - JOUR

T1 - Generalizing growth functions assuming parameter heterogeneity.

AU - Piantadosi, S.

PY - 1987/3

Y1 - 1987/3

N2 - This paper describes generalizations of simple growth equations made by assuming that one or more parameters have a probability distribution in the population. Thus, the product of the parental growth equation and the probability density function when integrated over the range of the parameter produces a compound growth function. In most cases, the resulting equations are more complex than the original function, but the new parameters are interpretable directly in terms of the distribution of the parameter in the population. Despite the frequent need for special functions, an effort has been made here to produce simple mathematical forms. An example is provided using some compound growth functions to describe real growth data. This method appears to be a meaningful and useful way to improve the modeling of growth.

AB - This paper describes generalizations of simple growth equations made by assuming that one or more parameters have a probability distribution in the population. Thus, the product of the parental growth equation and the probability density function when integrated over the range of the parameter produces a compound growth function. In most cases, the resulting equations are more complex than the original function, but the new parameters are interpretable directly in terms of the distribution of the parameter in the population. Despite the frequent need for special functions, an effort has been made here to produce simple mathematical forms. An example is provided using some compound growth functions to describe real growth data. This method appears to be a meaningful and useful way to improve the modeling of growth.

UR - http://www.scopus.com/inward/record.url?scp=0023302258&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023302258&partnerID=8YFLogxK

M3 - Article

C2 - 3623193

AN - SCOPUS:0023302258

VL - 51

SP - 50

EP - 63

JO - Growth

JF - Growth

SN - 0017-4793

IS - 1

ER -