Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-07T20:34:22.952Z Has data issue: false hasContentIssue false

Solutions for Chapter 3

Published online by Cambridge University Press:  05 June 2012

David C. M. Dickson
Affiliation:
University of Melbourne
Mary R. Hardy
Affiliation:
University of Waterloo, Ontario
Howard R. Waters
Affiliation:
Heriot-Watt University, Edinburgh
Get access

Summary

3.1 Figures S3.1, S3.2 and S3.3 are graphs of μx, lx and dx, respectively, as functions of age x up to x = 100. Each graph has been drawn using the values from ELT 15, Males and Females.

(a) The key feature of Figure S3.1 is that the value of μx is very low until around age 55, from where it increases steeply. Numerically, μx is very close to qx provided qx is reasonably small, so that the features in Figure S3.1 are very similar to those shown in Figure 3.1 in AMLCR. The features at younger ages show up much better in Figure 3.1 in AMLCR because the y-axis there is on a logarithmic scale. Note that the near-linearity in Figure 3.1 in AMLCR for ages above 35 is equivalent to the near-exponential growth we observe in Figure S3.1.

(b) The key feature of Figure S3.2 is that, apart from a barely perceptible drop in the first year due to mortality immediately following birth, the graph is more or less constant until around age 55 when it starts to fall at an increasing rate before converging towards zero at very high ages. This reflects the pattern seen in Figure S3.1.

(c) The function dx is the expected number of deaths between exact ages x and x + 1 out of l0 lives aged 0. The relatively high mortality in the first year of life shows clearly in Figure S3.3, as does the increase in the expected number of deaths for males in the late teenage years – the so-called ‘accident hump’.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×