scholarly journals Regression Analysis under Inverse Gaussian Model: Repeated Observation Case

2004 ◽  
Vol 1 (1) ◽  
pp. 31-50
Author(s):  
Reza Meshkani ◽  
Keyword(s):  
Regression Analysis ◽  
Gaussian Model ◽  
Inverse Gaussian ◽  
Repeated Observation

A normal inverse Gaussian model for a risky asset with dependence

2012 ◽  
Vol 82 (1) ◽  
pp. 109-115 ◽  
Author(s):  
N.N. Leonenko ◽  
S. Petherick ◽  
A. Sikorskii
Keyword(s):  
Gaussian Model ◽  
Risky Asset ◽  
Inverse Gaussian ◽  
Normal Inverse Gaussian

A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability

2005 ◽  
Vol 288 (1) ◽  
pp. H424-H435 ◽  
Author(s):  
Riccardo Barbieri ◽  
Eric C. Matten ◽  
AbdulRasheed A. Alabi ◽  
Emery N. Brown
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Gaussian Model ◽  
Quantitative Measure ◽  
Local Maximum ◽  
Inverse Gaussian ◽  
Design Of Algorithms

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

scholarly journals The Reciprocal Generalized Inverse Gaussian Frailty with Application in Life Annuity Business

2020 ◽  
pp. 112-131
Author(s):  
Walter Onchere ◽  
Richard Tinega ◽  
Patrick Weke ◽  
Jam Otieno
Keyword(s):  
Simulation Study ◽  
Unobserved Heterogeneity ◽  
Survival Curve ◽  
Gaussian Model ◽  
Frailty Models ◽  
Residual Lifetime ◽  
Longevity Risk ◽  
Inverse Gaussian ◽  
Life Annuity ◽  
Valuation Of Life

Aims: As shown in literature, several authors have adopted various individual frailty mixing distributions as a way of dealing with possible heterogeneity due to unobserved covariates in a group of insurers. This research contribution is to generalize the frailty mixing distribution to nest other classes of frailty distributions not in literature and apply the proposed distributions in valuation of life annuity business. Methodology: A simulation study is done to assess the performance of the aforementioned models. The baseline parameters is estimated using Bayesian Inference and a better model is suggested for valuation of life annuity business. Results: As a result of generalizing the frailty some new classes of frailty distributions are constructed such as; the Reciprocal Inverse Gaussian Frailty, the Inverse Gamma Frailty, the Harmonic Frailty and the Positive Hyperbolic Frailty. From the simulation study, the proposed new frailty models shows that ignoring frailty leads to an underestimation of future residual lifetime since the survival curve shifts to the right when heterogeneity is accounted for. This is consistent with frailty literature. The Reciprocal Inverse Gaussian model closely represents the Association of Kenya Insurers graduated rates with a slight increase in survival due to longevity risk. Conclusion: The proposed new frailty models show an increase in the insurers expected liability when unobserved heterogeneity is accounted for. This is consistent with frailty literature and thus can be applied to avoid underestimating the insurer’s liability in the context of life annuity business. The RIG model as proposed in estimating future liability by directly adjusting the AKI mortality rates shows an increase in longevity risk. The extent of heterogeneity of the insured group determines the level of risk. The RIG frailties should be considered for multivariate cases where the insureds are clustered in groups.

Inverse Gaussian Model and Its Applications in Reliability and Survival Analysis

2010 ◽  
pp. 433-453 ◽  
Author(s):  
Boris Yu. Lemeshko ◽  
Stanislav B. Lemeshko ◽  
Kseniya A. Akushkina ◽  
Mikhail S. Nikulin ◽  
Noureddine Saaidia
Keyword(s):  
Survival Analysis ◽  
Gaussian Model ◽  
Inverse Gaussian

ROLLER-COASTER FAILURE RATES AND MEAN RESIDUAL LIFE FUNCTIONS WITH APPLICATION TO THE EXTENDED GENERALIZED INVERSE GAUSSIAN MODEL

2010 ◽  
Vol 25 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Ramesh C. Gupta ◽  
Weston Viles
Keyword(s):  
Failure Rate ◽  
Generalized Inverse ◽  
Residual Life ◽  
Gaussian Model ◽  
Change Points ◽  
Mean Residual Life ◽  
Additional Parameter ◽  
Inverse Gaussian ◽  
Generalized Inverse Gaussian ◽  
The Relationship

The investigation in this article was motivated by an extended generalized inverse Gaussian (EGIG) distribution, which has more than one turning point of the failure rate for certain values of the parameters. In order to study the turning points of a failure rate, we appeal to Glaser's eta function, which is much simpler to handle. We present some general results for studying the reationship among the change points of Glaser's eta function, the failure rate, and the mean residual life function (MRLF). Additionally we establish an ordering among the number of change points of Glaser's eta function, the failure rate, and the MRLF. These results are used to investigate, in detail, the monotonicity of the three functions in the case of the EGIG. The EGIG model has one additional parameter, δ, than the generalized inverse Gaussian (GIG) model's three parameters; see Jorgensen [7]. It has been observed that the EGIG model fits certain datasets better than the GIG of Jorgensen [7]. Thus, the purpose of this article is to present some general results dealing with the relationship among the change points of the three functions described earlier. The EGIG model is used as an illustration.

Quality Improvement by Using Inverse Gaussian Model in Robust Engineering

2006 ◽  
Vol 40 (2) ◽  
pp. 157-174 ◽  
Author(s):  
M. Bameni Moghadam ◽  
F. Eskandari
Keyword(s):  
Quality Improvement ◽  
Gaussian Model ◽  
Inverse Gaussian
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