# AKm02q0 derive q0 from m0 using the Andreev-Kingkade rule of thumb.

### Description

Derive m0 from q0 according to the relevant segment of the Andreev-Kingkade formula. This is elegant because it's an analytic solution, but ugly because, man, look at it. Carl Boe got this from Maple I think. This formula is only necessary because AK start with q0 whereas the HMD starts with m0, so we needed to adapt. This is an auxiliary function, and not likely needed for direct use.

### Usage

1 | ```
AKm02q0(m0, constant, slope)
``` |

### Arguments

`m0` |
the event / exposure infant mortality rate (not IMR) |

`constant` |
the intercept of the relevant Andreev-Kingkade segment |

`slope` |
the slope of the relevant Andreev-Kingkade segment |

### Details

This is based on an MPIDR Working Paper: Andreev, Evgueni M and Kingkade, Ward W (2011) "Average age at death in infancy and infant mortality level: reconsidering the Coale-Demeny formulas at current levels of low mortality". short link: http://goo.gl/b5m5pg.

### Value

q0 the estimate of q0 according to the identity between a0, m0, q0

### Author(s)

Tim Riffe

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