Sequential Procedures for the Point Estimation of the Mean of an Inverse Gaussian Reliability Model

2017 ◽  
Author(s):  
Sandeep Bhougal ◽  
Sunil Kumar
Keyword(s):  
Point Estimation ◽  
Reliability Model ◽  
Inverse Gaussian ◽  
Sequential Procedures ◽  
The Mean

On Sequential Procedures for the Point Estimation of the Mean Vector

1988 ◽  
Vol 37 (1-2) ◽  
pp. 47-54 ◽  
Author(s):  
R. Karan Singh ◽  
Ajit Chaturvedi
Keyword(s):  
Normal Population ◽  
Stopping Time ◽  
Point Estimation ◽  
Multivariate Normal ◽  
Minimum Risk ◽  
Sequential Procedures ◽  
Multivariate Normal Population ◽  
Bounded Risk ◽  
The Mean ◽  
Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

A degradation model for maintenance improvement in respect of cost and availability

2015 ◽  
Vol 21 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Christophe Letot ◽  
Pierre Dehombreux ◽  
Edouard Rivière-Lorphèvre ◽  
Guillaume Fleurquin ◽  
Arnaud Lesage
Keyword(s):  
Preventive Maintenance ◽  
Residual Life ◽  
Operating Time ◽  
Hitting Times ◽  
Mean Residual Life ◽  
Reliability Model ◽  
Content Type ◽  
Degradation Data ◽  
Specific Item ◽  
The Mean

Purpose – The purpose of this paper is to highlight the need for degradation data in order to improve the reliability and the mean residual life estimation of a specific item of equipment and to adapt the preventive maintenance tasks accordingly. Design/methodology/approach – An initial reliability model which uses a degradation-based reliability model that is built from the collection of hitting times of a failure threshold. The proposed maintenance model is based on the cost/availability criterion. The estimation of both reliability and optimum time for preventive maintenance are updated with all new degradation data that are collected during operating time. Findings – An improvement for the occurrences of maintenance tasks which minimizes the mean cost per unit of time and increases the availability. Practical implications – Inspection tasks to measure the degradation level should be realized at least one time for each item of equipment at a specific time determined by the proposed methodology. Originality/value – The introduction of a criterion which helps the maintainer to decide to postpone or not the preventive replacement time depending on the measured degradation level of a specific item of equipment.

scholarly journals Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

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