Non-Parametric Estimation of Component Life Time Distributions of a Parallel System

1993 ◽  
Vol 43 (3-4) ◽  
pp. 199-212 ◽  
Author(s):  
Anup Dewanji ◽  
D. Dhar
Keyword(s):  
Competing Risks ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Parallel Systems ◽  
Life Time ◽  
Parallel System ◽  
Parametric Estimation ◽  
Data Set ◽  
Failure Times ◽  
Non Parametric Estimation

In many practical situations dealing with parallel systems, the failure times of the components are not observable unless that is the last one resulting in the failure of the system. Based on observation on the life time of the system, nonparametric estimation of the life time distributions of the components is considered. Dealing with a parallel system with two components, a competing risks framework is developed and an algorithm of the EM type for maximum likelihood estimation is obtained. The method is illustrated with a simulated data set.

scholarly journals Construction of a Genetic Linkage Map in Tetraploid Species Using Molecular Markers

Genetics ◽  
2001 ◽  
Vol 157 (3) ◽  
pp. 1369-1385 ◽  
Author(s):  
Z W Luo ◽  
C A Hackett ◽  
J E Bradshaw ◽  
J W McNicol ◽  
D Milbourne
Keyword(s):  
Molecular Markers ◽  
Linkage Map ◽  
Recombination Frequency ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Lod Score ◽  
Data Set ◽  
Independent Segregation ◽  
The Em Algorithm ◽  
Small Set

Abstract This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel System

2012 ◽  
Vol 8 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Nitin Gupta ◽  
Neeraj Gandotra ◽  
Rakesh Bajaj
Keyword(s):  
Residual Life ◽  
Sufficient Conditions ◽  
Parallel Systems ◽  
Life Time ◽  
Parallel System ◽  
Time Data ◽  
Stochastic Comparisons ◽  
Aging Properties ◽  
Inactivity Time ◽  
In Series

Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel SystemThe concepts of residual life time and inactivity time are extensively used in reliability theory for modeling life time data. In this paper we prove some new results on stochastic comparisons of residual life time and inactivity time in series and parallel systems. These results are in addition to the existing results of Li & Zhang (2003) and Li & Lu (2003). We also present sufficient conditions for aging properties of the residual life time and inactivity life time of series and parallel systems. Some examples from Weibull and Gompertz distributions are provided to support the results as well.

MCMC in Analysis of Progressively First Failure Censored Competing Risks Data for Gompertz Model

2016 ◽  
Vol 13 (10) ◽  
pp. 6662-6670 ◽  
Author(s):  
R. A Bakoban ◽  
G. A Abd-Elmougod
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Life Time ◽  
Real Data ◽  
Asymptotic Distributions ◽  
Type Ii ◽  
Data Set ◽  
Type Ii Censoring ◽  
Gamma Density ◽  
Special Cases

In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. So in this paper, we consider the competing risks model with very general censoring scheme, namely progressive first-failure censored scheme under the Gompertz life time distribution. The results in each of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are a special cases. We provide different methods for the analysis of the model under the assumption of independent causes of failure and Gompertz distribution lifetimes. The maximum likelihood estimators (MLE’s) of the different parameters as well as approximate confidence intervals are presented. Bayesian estimation using MCMC method under the joint prior density as a product of a conditional gamma density and inverted gamma density for unknown Gompertz parameters are presented. The analysis of a real data set to assess the performance of all these estimators, confidence intervals are developed using asymptotic distributions and Bayesian credible intervals for the parameters. The different methods are compared through a simulation study.

scholarly journals A New Quantile Estimation Method of Weibull-Rayleigh Distribution

2020 ◽  
pp. 28-37
Author(s):  
A. S. Ogunsanya ◽  
E. E. E. Akarawak ◽  
W. B. Yahya
Keyword(s):  
Parameter Estimation ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Absolute Error ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Estimation Methods ◽  
Data Set ◽  
Total Deviation

In this paper, we compared different Parameter Estimation method of the two parameter Weibull-Rayleigh Distribution (W-RD) namely; Maximum Likelihood Estimation (MLE), Least Square Estimation method (LSE) and three methods of Quartile Estimators. Two of the quartile methods have been applied in literature, while the third method (Q1-M) is introduced in this work. The methods have been applied to simulate data. These methods of estimation were compared using Error, Mean Square Error and Total Deviation (TD) which is also known as Sum Absolute Error Estimate (SAEE). The analytical results show that the performances of all the parameter estimation methods were satisfactory with data set of Weibull-Rayleigh distribution while degree of accuracy is determined by the sample size. The proposed quartile (Q1-M) method has the least Total Deviation and MSE. In addition, the quartile methods perform better than MLE for the simulated data. In particular, the proposed quartile methods (Q1-M) have an added advantage of simplicity in usage than MLE methods.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks

2006 ◽  
Vol 342 (1) ◽  
pp. 63-68
Author(s):  
Vilijandas Bagdonavičius ◽  
Algimantas Bikelis ◽  
Vytautas Kazakevičius ◽  
Mikhail Nikulin
Keyword(s):  
Competing Risks ◽  
Parametric Estimation ◽  
Degradation Data ◽  
Non Parametric Estimation ◽  
Non Parametric
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