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01.07.2016

Multivariate mixtures of Erlangs for density estimation under censoring

verfasst von: Roel Verbelen, Katrien Antonio, Gerda Claeskens

Erschienen in: Lifetime Data Analysis | Ausgabe 3/2016

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Abstract

Multivariate mixtures of Erlang distributions form a versatile, yet analytically tractable, class of distributions making them suitable for multivariate density estimation. We present a flexible and effective fitting procedure for multivariate mixtures of Erlangs, which iteratively uses the EM algorithm, by introducing a computationally efficient initialization and adjustment strategy for the shape parameter vectors. We furthermore extend the EM algorithm for multivariate mixtures of Erlangs to be able to deal with randomly censored and fixed truncated data. The effectiveness of the proposed algorithm is demonstrated on simulated as well as real data sets.

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Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723MathSciNetCrossRefMATH

Ampe B, Goethals K, Laevens H, Duchateau L (2012) Investigating clustering in interval-censored udder quarter infection times in dairy cows using a gamma frailty model. Prev Vet Med 106(3):251–257CrossRef

Asmussen S, Nerman O, Olsson M (1996) Fitting phase-type distributions via the EM algorithm. Scand J Stat 23:419–441MATH

Assaf D, Langberg NA, Savits TH, Shaked M (1984) Multivariate phase-type distributions. Oper Res 32(3):688–702MathSciNetCrossRefMATH

Azzalini A, Bowman A (1990) A look at some data on the Old Faithful geyser. Appl Stat 39:357–365

Cossette H, Côté M-P, Marceau E, Moutanabbir K (2013a) Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: aggregation and capital allocation. Insur Math Econ 52(3):560–572MathSciNetCrossRefMATH

Cossette H, Mailhot M, Marceau E, Mesfioui M (2013b) Bivariate lower and upper orthant value-at-risk. Eur Actuar J 3(2):321–357MathSciNetCrossRefMATH

Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Method) 39(1):1–38MathSciNetMATH

Dhaene J, Tsanakas A, Valdez EA, Vanduffel S (2012) Optimal capital allocation principles. J Risk Insur 79(1):1–28CrossRef

Efron B, Tibshirani R (1994) An introduction to the bootstrap. Monographs on statistics & applied probability. Chapman & Hall, London

Eisele K-T (2005) EM algorithm for bivariate phase distributions. In: ASTIN Colloquium, Zurich, Switzerland. http://www.actuaries.org/ASTIN/Colloquia/Zurich/Eisele.pdf

Frees EW, Carriere J, Valdez E (1996) Annuity valuation with dependent mortality. J Risk Insur 63:229–261CrossRef

Georges P, Lamy A-G, Nicolas E, Quibel G, Roncalli T (2001) Multivariate survival modelling: a unified approach with copulas. Unpublished paper, Groupe de Recherche Operationnelle, Credit Lyonnais, France

Goethals K, Ampe B, Berkvens D, Laevens H, Janssen P, Duchateau L (2009) Modeling interval-censored, clustered cow udder quarter infection times through the shared gamma frailty model. J Agric Biol Environ Stat 14(1):1–14MathSciNetCrossRefMATH

Härdle W (1991) Smoothing techniques: with implementation in S. Springer, New YorkCrossRefMATH

Joe H (1997) Multivariate models and multivariate dependence concepts, vol 73. CRC Press, Boca RatonCrossRefMATH

Klugman SA, Panjer HH, Willmot GE (2013) Loss models: further topics. Wiley, HobokenCrossRefMATH

Laevens H, Deluyker H, Schukken Y, De Meulemeester L, Vandermeersch R, De Muelenaere E, De Kruif A (1997) Influence of parity and stage of lactation on the somatic cell count in bacteriologically negative dairy cows. J Dairy Sci 80(12):3219–3226CrossRef

Lee G, Scott C (2012) EM algorithms for multivariate Gaussian mixture models with truncated and censored data. Comput Stat Data Anal 56(9):2816–2829MathSciNetCrossRefMATH

Lee S, McLachlan GJ (2014) Finite mixtures of multivariate skew \(t\)-distributions: some recent and new results. Stat Comput 24(2):181–202MathSciNetCrossRefMATH

Lee SC, Lin XS (2010) Modeling and evaluating insurance losses via mixtures of Erlang distributions. N Am Actuar J 14(1):107–130MathSciNetCrossRef

Lee SC, Lin XS (2012) Modeling dependent risks with multivariate Erlang mixtures. ASTIN Bull 42(1):153–180MathSciNetMATH

Leung K-M, Elashoff RM, Afifi AA (1997) Censoring issues in survival analysis. Annu Rev Public Health 18(1):83–104CrossRef

Li Y, Gillespie BW, Shedden K, Gillespie JA (2015) Calculating profile likelihood estimates of the correlation coefficient in the presence of left, right or interval censoring and missing data. Working paper

Lin TI (2009) Maximum likelihood estimation for multivariate skew normal mixture models. J Multivar Anal 100(2):257–265MathSciNetCrossRefMATH

Mailhot M (2012) Mesures de risque et dépendance. Ph.D. thesis, Université Laval

McLachlan G, Jones P (1988) Fitting mixture models to grouped and truncated data via the EM algorithm. Biometrics 44:571–578CrossRefMATH

McLachlan G, Peel D (2001) Finite mixture models. Wiley, New YorkMATH

McLachlan GJ, Krishnan T (2007) The EM algorithm and extensions, vol 382. Wiley, New YorkMATH

Nair VN (1984) Confidence bands for survival functions with censored data: a comparative study. Technometrics 26(3):265–275CrossRef

Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New YorkMATH

Olsson M (1996) Estimation of phase-type distributions from censored data. Scand J Stat 23:443–460MathSciNetMATH

Peel D, McLachlan G (2000) Robust mixture modelling using the t distribution. Stat Comput 10(4):339–348CrossRef

Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464MathSciNetCrossRefMATH

Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. Chapman & Hall, LondonCrossRefMATH

Tijms HC (1994) Stochastic models: an algorithmic approach. Wiley, New YorkMATH

Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J R Stat Soc Ser B (Method) 38:290–295MathSciNetMATH

Verbelen R, Gong L, Antonio K, Badescu A, Lin XS (2015) Fitting mixtures of Erlangs to censored and truncated data using the EM algorithm. ASTIN Bull 45(3):729–758

Willmot GE, Lin XS (2011) Risk modelling with the mixed Erlang distribution. Appl Stoch Models Bus Ind 27(1):2–16MathSciNetCrossRef

Willmot GE, Woo J-K (2007) On the class of Erlang mixtures with risk theoretic applications. N Am Actuar J 11(2):99–115MathSciNetCrossRef

Willmot GE, Woo J-K (2015) On some properties of a class of multivariate Erlang mixtures with insurance applications. ASTIN Bull 45(01):151–173MathSciNetCrossRef

Zadeh AH, Bilodeau M (2013) Fitting bivariate losses with phase-type distributions. Scand Actuar J 2013(4):241–262MathSciNetCrossRefMATH

Titel: Multivariate mixtures of Erlangs for density estimation under censoring
verfasst von: Roel Verbelen
Katrien Antonio
Gerda Claeskens
Publikationsdatum: 01.07.2016
Verlag: Springer US
Erschienen in: Lifetime Data Analysis / Ausgabe 3/2016
Print ISSN: 1380-7870
Elektronische ISSN: 1572-9249
DOI: https://doi.org/10.1007/s10985-015-9343-y

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