Tornadoes and related damage costs: statistical modelling with a semi-Markov approach

D’Amico, Guglielmo; Manca, Raimondo; Corini, Chiara; Petroni, Filippo; Prattico, Flavio

doi:10.1080/19475705.2015.1124462

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…An alternative model that may solve those problems is a semi-Markov model, which can be viewed as a natural extension of a Markov model. In recent years, the use of discrete time semi-Markov models became more and more popular in various fields such as reliability and survival analysis [19], DNA analysis [20,21], disability insurance [22], credit risk [23][24][25][26], and wind speed and tornado modeling [27,28]. Moreover, insights regarding discrete time semi-Markov models contribute to the use of continuous time semi-Markov models [29].…”

Section: Introductionmentioning

confidence: 99%

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Verbeken

Guerry

2021

Mathematics

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Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria.

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Section: Introductionmentioning

confidence: 99%

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Verbeken

Guerry

2021

Mathematics

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“…Semi-Markov processes have become important tools in probability and statistical modeling with applications in various domains like survival analysis, biology, reliability, DNA analysis, insurance and finance, earthquake modeling, meteorology studies, etc. ; see, e.g., Heutte and Huber-Carol (2002), Ouhbi and Limnios (2003), Chryssaphinou et al (2008), Janssen and Manca (2006), Votsi et al (2012), D'Amico et al (2013, Votsi et al (2014), D'Amico et al (2016b, Barbu et al (2016), D'Amico et al (2016a for semi-Markov processes in continuous or discrete time with various applications and Sansom and Thomson (2001), Bulla and Bulla (2006), Barbu and Limnios (2008), for hidden semi-Markov models and applications in climatology, finance and DNA analysis.…”

Section: Introductionmentioning

confidence: 99%

SMM: An R Package for Estimation and Simulation of Discrete-time semi-Markov Models

Barbu¹,

Bérard²,

Cellier³

et al. 2019

The R Journal

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Semi-Markov models, independently introduced by Lévy (1954), Smith (1955) and Takacs (1954), are a generalization of the well-known Markov models. For semi-Markov models, sojourn times can be arbitrarily distributed, while sojourn times of Markov models are constrained to be exponentially distributed (in continuous time) or geometrically distributed (in discrete time). The aim of this paper is to present the R package SMM, devoted to the simulation and estimation of discretetime multi-state semi-Markov and Markov models. For the semi-Markov case we have considered: parametric and non-parametric estimation; with and without censoring at the beginning and/or at the end of sample paths; one or several independent sample paths. Several discrete-time distributions are considered for the parametric estimation of sojourn time distributions of semi-Markov chains: Uniform, Geometric, Poisson, Discrete Weibull and Binomial Negative.Few R packages have been developed to handle semi-Markov models or hidden semi-Markov models. For semi-Markov models we have the recent semiMarkov R package (Król and Saint-Pierre, 2015) that performs maximum likelihood estimation for parametric continuous-time semi-Markov processes, where the distribution can be chosen between Exponential, Weibull or exponentiated Weibull. That package computes associated hazard rates; covariates can also be taken into account through the Cox proportional hazard model. Two R packages are also dedicated to hidden semi-Markov models, implementing estimation and prediction methods: the hsmm R package (Bulla et al., 2010) and the mhsmm R package (O'Connell and Højsgaard, 2011).Note that there is no R package developed for discrete-time multi-state semi-Markov models. Thus the purpose of this paper is to present an R package that we have developed, called SMM, which performs parametric and non-parametric estimation and simulation for multi-state discrete-time semi-Markov processes. For the parametric estimation, several discrete distributions are considered

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Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

Kordnoori

Mostafaei

Kordnoori

et al. 2020

Pak.j.stat.oper.res.

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Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.

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Tornadoes and related damage costs: statistical modelling with a semi-Markov approach

Cited by 3 publications

References 26 publications

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

SMM: An R Package for Estimation and Simulation of Discrete-time semi-Markov Models

Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

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