Improvement of expectation-maximization algorithm for phase-type distributions with grouped and truncated data

2012 ◽  
Vol 29 (2) ◽  
pp. 141-156 ◽  
Author(s):  
Hiroyuki Okamura ◽  
Tadashi Dohi ◽  
Kishor S. Trivedi
Keyword(s):  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Truncated Data ◽  
Phase Type ◽  
Phase Type Distributions

Multivariate finite-support phase-type distributions

2020 ◽  
Vol 57 (4) ◽  
pp. 1260-1275
Author(s):  
Celeste R. Pavithra ◽  
T. G. Deepak
Keyword(s):  
Distribution Function ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Finite Support ◽  
Marginal Distributions ◽  
New Class ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Support Phase

AbstractWe introduce a multivariate class of distributions with support I, a k-orthotope in $[0,\infty)^{k}$ , which is dense in the set of all k-dimensional distributions with support I. We call this new class ‘multivariate finite-support phase-type distributions’ (MFSPH). Though we generally define MFSPH distributions on any finite k-orthotope in $[0,\infty)^{k}$ , here we mainly deal with MFSPH distributions with support $[0,1)^{k}$ . The distribution function of an MFSPH variate is computed by using that of a variate in the MPH $^{*} $ class, the multivariate class of distributions introduced by Kulkarni (1989). The marginal distributions of MFSPH variates are found as FSPH distributions, the class studied by Ramaswami and Viswanath (2014). Some properties, including the mixture property, of MFSPH distributions are established. Estimates of the parameters of a particular class of bivariate finite-support phase-type distributions are found by using the expectation-maximization algorithm. Simulated samples are used to demonstrate how this class could be used as approximations for bivariate finite-support distributions.

scholarly journals PHASE-TYPE DISTRIBUTIONS FOR CLAIM SEVERITY REGRESSION MODELING

2022 ◽  
pp. 1-32
Author(s):  
Martin Bladt
Keyword(s):  
Expectation Maximization ◽  
Regression Models ◽  
Heavy Tails ◽  
Proportional Hazards ◽  
Expectation Maximization Algorithm ◽  
Third Party ◽  
Covariate Information ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Entire Distribution

Abstract 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.

Ordered subset expectation maximization algorithm for image reconstruction applied to zero-flow or low-flow mimicking brain phantom

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S678-S678
Author(s):  
Yasuhiro Akazawa ◽  
Yasuhiro Katsura ◽  
Ryohei Matsuura ◽  
Piao Rishu ◽  
Ansar M D Ashik ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Low Flow ◽  
Brain Phantom ◽  
Zero Flow

scholarly journals Environmental Sensitivity and Awareness as Differentiating Factors in the Purchase Decision-Making Process in the Smartphone Industry—Case of Polish Consumers

2021 ◽  
Vol 13 (1) ◽  
pp. 348
Author(s):  
Lukasz Skowron ◽  
Monika Sak-Skowron
Keyword(s):  
Expectation Maximization ◽  
Cross Validation ◽  
Expectation Maximization Algorithm ◽  
Decision Making Process ◽  
Environmental Sensitivity ◽  
Significance Level ◽  
On Line ◽  
Purchase Process ◽  
The Impact ◽  
Fold Cross Validation

The first of the research objectives discussed in this article was to analyze the differences related to the valuation of particular factors influencing the purchase process in the smartphone industry, expressed by respondents with different sensitivity and environmental awareness, as well as the assessment of their knowledge about the impact of smartphones on the natural environment. The second objective of the research was to determine whether the level of environmental sensitivity, awareness and knowledge about the impact of smartphones on the environment has a statistically significant influence on the respondents’ choice of smartphone brand. The survey was conducted using an on-line questionnaire, distributed by a specialized research agency on a representative sample of over 1000 Polish residents. In order to identify the various customers clusters, the expectation-maximization algorithm and the v-fold cross-validation were used. Additionally, in order to analyze the significance level of differences between clusters the nonparametric Mann-Whitney U-test was carried out. The results show unequivocally that people with a different approach to ecological issues demonstrate statistically significant differences in their purchasing behaviors in the smartphone industry. Furthermore, it was noticed that in the case of comparing some smartphones brands, there is a statistically confirmed difference in the environmental sensitivity and awareness of the customers who use them. Moreover, the research has shown that in Polish customers’ consciousness smartphones are mistakenly considered to be relatively safe and environmentally friendly products.

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