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Jan Karman
Middelburg (Neth)

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Jan Karman
Last revised: January 2023

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The B-Toe

How it started
One of my most favorite melodies of Bach, that I play on my flute, is his Alto Aria from Cantate BWV 170, "Vergnügte Ruh, beliebte Seelenlust". Transcribed for his Oboe Concerto, it is written in D major, with this passage, going down to B.

How would I ever be able to play this on my flute, i.e. one with just a C-foot?
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Otium cum dignitate

"Reshuffling chaos"

Graduation of Mortality
(from: samples | Kx | Show | Mortality)
Free Download (193Kb)
See also: My article in Vector

Mortality tables are usually graduated for either practical or scientific purposes. The formulae, in which the mortality is expressed as a function of x (= age) are often of the type (Makeham's law):
   mx = A + B.cx (force of mortality)
with A, B and c as parameters. Finding the values of those parameters from the crude material is the hard part.
King-Hardy's method is a suitable way to transform this power function into a linear equation system; it is solved here by way of a least square K-runtime function.
See also E.Zwinggi - Versicherungsmathematik
When invoked, one will find four controls in the bottom part. The first two controls act like a spinbox, the two right most controls simulate the Windows-locator. The challenge is to find as large as possible ranges for making the "law" valid.
Later, famous methods came from Thorvald N. Thiele, published posthumously in 1910, and more recent approaches and remarks can be found at W.J. Willemse.

Recommended for Africa:
G.M.K. Kpedekpo - Essentials of Demographic Analysis for Africa

Jan Karman LinkedIn
Middelburg (Neth), November 2006

Fugues Genevan Psalter
 My harpsichord
Actuarial & financial applications:
 Actuarial Factors
 Annuity Loan
 Graduation of Mortality
 Profit & Loss in Stocks
 The Price of Bonds
 Afronding van sterftetafels
 Ausgleichung von Sterbetafeln
LinkedIn:      Profile
Art: Art Gallery Orsmaal