In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get of the strengths and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered estimator are discussed including the study of mentioned expressions. The numerical results are exhibited and put it in tables.
The present paper concerns with the problem of estimating the reliability system in the stress – strength model under the consideration non identical and independent of stress and strength and follows Lomax Distribution. Various shrinkage estimation methods were employed in this context depend on Maximum likelihood, Moment Method and shrinkage weight factors based on Monte Carlo Simulation. Comparisons among the suggested estimation methods have been made using the mean absolute percentage error criteria depend on MATLAB program.
In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors.
Additionally Maximum likelihood estimation method
... Show MoreThis article discusses the estimation methods for parameters of a generalized inverted exponential distribution with different estimation methods by using Progressive type-I interval censored data. In addition to conventional maximum likelihood estimation, the mid-point method, probability plot method and method of moments are suggested for parameter estimation. To get maximum likelihood estimates, we utilize the Newton-Raphson, expectation -maximization and stochastic expectation-maximization methods. Furthermore, the approximate confidence intervals for the parameters are obtained via the inverse of the observed information matrix. The Monte Carlo simulations are used to introduce numerical comparisons of the proposed estimators. In ad
... Show MoreIn this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.
The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.
In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes
... Show MoreThis deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values
The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since
... Show MoreThe paper shows how to estimate the three parameters of the generalized exponential Rayleigh distribution by utilizing the three estimation methods, namely, the moment employing estimation method (MEM), ordinary least squares estimation method (OLSEM), and maximum entropy estimation method (MEEM). The simulation technique is used for all these estimation methods to find the parameters for the generalized exponential Rayleigh distribution. In order to find the best method, we use the mean squares error criterion. Finally, in order to extract the experimental results, one of object oriented programming languages visual basic. net was used