13_AS_2_lec_a

S cl an interval censored observation s cl s cr a

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Unformatted text preview: left-censored observation 1 − S (CL ) an interval-censored observation, [S (CL ) − S (CR )] ) a left-truncated observation, Sf((tL ) Y if it’s a right-truncated observation, f (t ) 1−S (YR ) if it’s an interval-truncated observation, 8/42 f (t ) [S (YL )−S (YR )] Actuarial Statistics – Module 2: Non-parametric methods Estimating the lifetime distribution: non-parametric approach 1 Introduction 2 Censoring and truncation Censoring Truncation Likelihood for censored and truncated data 3 Estimating the lifetime distribution: non-parametric approach Preliminaries Maximum Likelihood with censoring The likelihood as a function of the discrete hazard function Kaplan-Meier (product limit) estimator Nelson-Aalen estimator 4 Comparing survival functions Introductory example A hypothesis test Special cases 9/42 Actuarial Statistics – Module 2: Non-parametric methods Estimating the lifetime distribution: non-parametric approach Preliminaries 1 Introduction 2 Censoring and truncation Censoring Truncation Likelihood for censored and truncated data 3 Estimating the lifetime distribution: non-parametric approach Preliminaries Maximum Likelihood with censoring The likelihood as a function of the discrete hazard function Kaplan-Meier (product limit) estimator Nelson-Aalen estimator 4 Comparing survival functions Introductory example A hypothesis test Special cases 9/42 Actuarial Statistics – Module 2: Non-parametric methods Estimating the lifetime distribution: non-parametric approach Preliminaries Parametric vs Non-parametric Non-parametric approach: no prior assumptions about the shape or form of the distribution are made Parametric approach: assume that the distribution belongs to a certain family (eg normal or exponential) and use the data to estimate the appropriate parameters. In this module we focus on non-parametric models. 9/42 Actuarial Statistics – Module 2: Non-parametric methods Estimating the lifetime distribution: non-parametric approach Preliminaries Notation 10/42 Population of N lives Observe m deaths; N − m lives are righ...
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