Fisher information and statistical inference for phase-type distributions

Bladt, Mogens; Esparza, Luz Judith R.; Nielsen, Bo Friis

doi:10.1239/jap/1318940471

Cited by 17 publications

(8 citation statements)

References 8 publications

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“…Observe that we have deliberately omitted inference for the PH parameters π and T. The reason being, this is a particularly difficult task due to the nonidentifiability issue of PH distributions, namely that several representations can result in the same model. Papers such as Bladt et al (2011) and Zhang et al, 2021 provide methods of recovering the information matrix for these parameters, but the validity of the conclusions drawn from such approach are not fully understood. Consequently, and similarly to other regression models, we will only perform estimation on the regression coefficients themselves and use the distributional parameters merely as a vehicle to obtain β.…”

Section: Inference For Phase-type Regression Modelsmentioning

confidence: 99%

Phase-Type Distributions for Claim Severity Regression Modeling

Bladt¹

2022

ASTIN Bull.

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This paper addresses the task of modeling severity losses using segmentation when the data distribution does not fall into the usual regression frameworks. This situation is not uncommon in lines of business such as third-party liability insurance, where heavy-tails and multimodality often hamper a direct statistical analysis. We propose to use regression models based on phase-type distributions, regressing on their underlying inhomogeneous Markov intensity and using an extension of the expectation–maximization algorithm. These models are interpretable and tractable in terms of multistate processes and generalize the proportional hazards specification when the dimension of the state space is larger than 1. We show that the combination of matrix parameters, inhomogeneity transforms, and covariate information provides flexible regression models that effectively capture the entire distribution of loss severities.

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Section: Inference For Phase-type Regression Modelsmentioning

confidence: 99%

Phase-Type Distributions for Claim Severity Regression Modeling

Bladt¹

2022

ASTIN Bull.

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show abstract

“…The reason being, this is a particularly difficult task due to the non-identifiability issue of PH distributions, namely that several representations can result in the same model. Papers such as Bladt et al (2011); Zhang et al (2021) provide methods of recovering the information matrix for these parameters, but the validity of the conclusions drawn from such approach are not fully understood. Consequently, and similarly to other regression models, we will only perform estimation on the regression coefficients themselves, and use the distributional parameters merely as a vehicle to obtain β β β.…”

Section: 41mentioning

confidence: 99%

Phase-type distributions for claim severity regression modeling

Bladt¹

2021

Preprint

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This paper addresses the task of modeling severity losses using segmentation when the distribution of the data does not fall into the usual regression frameworks. This is not an uncommon situation in lines of business such as third party liability insurance, where heavy-tails and multimodality often hamper a direct statistical analysis. We propose to use regression models based on phase-type distributions, regressing on their underlying inhomogeneous Markov intensity using an extension of the EM algorithm. These models are tailored for survival analysis, but are shown to be well suited for loss data modeling as well. Contrary to the common belief that the distribution of a model is irrelevant if we only wish to estimate the mean, we show that correct segmentation can be obscured or revealed depending on the quality of the baseline distribution.

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“…Asmussen et al (1996) have presented a procedure for fitting CPH distributions via the EM algorithm. Using uniformization method, Bladt et al (2011) developed an alternative method to compute the E-step in the EM algorithm, and is called as EM unif algorithm.…”

Section: Estimation Of Parameters Of Cph Distributionmentioning

confidence: 99%

“…Asmussen et al (1996) introduced expectation maximization (EM) algorithm for fitting phase-type distribution. Expectation Maximization uniformization (EM unif) algorithm was developed by Bladt et al (2011) as an improvement over EM algorithm.…”

Section: Introductionmentioning

confidence: 99%

Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution

Jose

Drisya

2021

Rev. colomb. estad.

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The time-dependent stress-strength reliability models deal with systems whose strength or the stress imposed on it or both are time-dependent. In this paper, we consider time-dependent stress-strength reliability model which is subjected to constant stress and it causes a change in the strength of the system over each run of the system. Assuming a continuous phase- type distribution for the initial strength and exponential distribution for the duration of each run of the system called cycle time we derived the expression for the stress-strength reliability of the system at time t. The model is further extended to the cases where cycle time distribution is Gamma and Weibull. Simulation studies are conducted to assess the variations in stress-strength reliability, R(t) at diﬀerent time points, corresponding to the changes in the initial strength distribution and cycle time distribution.

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Fisher information and statistical inference for phase-type distributions

Cited by 17 publications

References 8 publications

Phase-Type Distributions for Claim Severity Regression Modeling

Phase-Type Distributions for Claim Severity Regression Modeling

Phase-type distributions for claim severity regression modeling

Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution

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