13_AS_8_lec_a

Graduation methods of graduation graphical graduation

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wx (ˆx − µx )2 = µ S= x wx [ˆx − (aµs + b )]2 µ x x The weights should be proportional toc the reciprocal of the variance of the crude rates, ie wx = Ex . µx ˆ So the function to be minimised is S (a, b ) = x 61/72 c Ex [ˆx − (aµs + b )]2 µ x µx ˆ Actuarial Statistics – Module 8: Method of Graduation Methods of graduation Graphical graduation 1 Introduction 2 Testing smoothness 3 Statistical tests Preliminaries Chi-square (χ2 ) test Standardised Deviations Test Signs test Cumulative Deviations Test Grouping of Signs Test Serial Correlations Test 4 Methods of graduation Preliminaries Graduation by Parametric Formula Graduation by Reference to a Standard Table Graphical graduation Statistical Tests The Effect of Duplicate policies 62/72 Actuarial Statistics – Module 8: Method of Graduation Methods of graduation Graphical graduation Graphical Graduation I Procedure 1 plot the crude rates or plot a function (e.g. log) of the crude rates group different ages together if data is scarce choose groups so that the grouped crude rates run more smoothly use evenly-spaced groups, eg 5-year age bands group so that at least 5 deaths are in each group determine average age for the group (weighted versus unweighted) 2 62/72 plot confidence intervals (eg 95% CI intervals) around the plotted crude rates. Rough 95% CI intervals are given by √ √ dx dx qx ± 2 or µx ± 2 c Ex Ex Actuarial Statistics – Module 8: Method of Graduation Methods of graduation Graphical graduation Graphical Graduation II 3 draw a curve through the crude rates, make sure that only about 1 point in 20 deviates outside the CI interval curves the curve is as smooth as possible the curve captures the overall shape of the crude rates 4 5 Test the graduated rates for goodness-of-fit and smoothness 6 Redraw if the graduated rates lack smoothness or adherence to data 7 63/72 determine graduated rates at integer ages from the plotted curve (avoid over accuracy) Once adequate adherence and a reasonable smooth progression have been obtained, handpolish the graduated rates - manually alter the rates to make them smoother steady progression of values Actuarial Statistics – Module 8: M...
View Full Document

Ask a homework question - tutors are online