000001 0000001 the third dierences are very small the

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Unformatted text preview: 67 0.001290 0.001426 0.001576 o ∆q x 0.00011 0.000123 0.000136 0.000150 o ∆2 q x 0.000012 0.000013 0.000014 o ∆3 q x 0.000001 0.000001 The third differences are very small, the graduated rates are very smooth. 2 x 40 41 42 43 44 o qx 0.000867 0.001018 0.001215 0.001494 0.001701 o ∆q x 0.000151 0.000197 0.000279 0.000207 o ∆2 q x 0.000046 0.000082 -0.00072 o ∆3 q x 0.000036 -0.000154 The third differences are relatively large, the graduated rates are irregular. 11/72 Actuarial Statistics – Module 8: Method of Graduation Statistical tests 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 12/72 Actuarial Statistics – Module 8: Method of Graduation Statistical tests Preliminaries 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 12/72 Actuarial Statistics – Module 8: Method of Graduation Statistical tests Preliminaries Statistical Tests of Adherence to data of a graduation There is no one single test that will provide adequate coverage of every aspect. Will use a multitude of tests, each with their pros and cons. Main Tests include: 1 2 Standardised Deviations Test 3 Sign Test 4 Cumulative Deviations Test 5 Grouping of Signs Test (Stevens’ Test) 6 12/72 Chi-Square Test of t Serial Correlations Test Actuarial Statistics – Module 8: Method of Graduation Statistical tests Preliminaries Assumptions lives are independent no heterogeneity in...
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