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Showing 6 results for Estimation.
Ali Shadrokh, Shahram Yaghoobzadeh, Masoud Yarmohammadi,
Volume 12, Issue 1 (9-2018)
Abstract
In this article, with the help of exponentiated-G distribution, we obtain extensions for the Probability density function and Cumulative distribution function, moments and moment generating functions, mean deviation, Racute{e}nyi and Shannon entropies and order Statistics of this family of distributions. We use maximum liklihood method of estimate the parameters and with the help of a real data set, we show the Risti$acute{c}-Balakrishnan-G family of distributions is a proper model for lifetime distribution.
Vahid Nekoukhou, Ashkan Khalifeh, Eisa Mahmoudi,
Volume 13, Issue 2 (2-2020)
Abstract
In this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.
Shahram Yaghoobzadeh,
Volume 14, Issue 1 (8-2020)
Abstract
In this study, the E-Bayesian estimation of the reliability parameter, R = P(Y < X < Z), when X, Y and Z are three independent inverse Rayleigh distribution with different parameters, were estimated based on ranked set sampling method. To assess the efficiency of the obtained estimates, we compute the average absolute bias and relative efficiency of the derived estimates and compare them with those based on the corresponding simple random sample through Monte Carlo simulations. Also, E-Bayesian estimation of R is compared with its maximum likelihood estimation in each method. Finally, three real data sets are used to analyze the estimation methods.
Mehdi Balui, Einolah Deiri, Farshin Hormozinejad, Ezzatallah Baloui Jamkhaneh,
Volume 15, Issue 2 (3-2022)
Abstract
In most practical cases, to increase parameter estimation accuracy, we need an estimator with the least risk. In this, contraction estimators play a critical role. Our main purpose is to evaluate the efficiency of some shrinkage estimators of the shape parameter of the Pareto-Rayleigh distribution under two classes of shrinkage estimators. In this research, the purpose estimators' efficiency will be compared with the unbiased estimator obtained under the quadratic loss function. The relationship between these two classes of shrinkage estimators was examined, and then the relative efficiency of the proposed estimators was discussed and concluded via doing a Monte Carlo simulation.
Ali Rostami, Mohammad Khanjari Sadegh, Mohammad Khorashadizadeh,
Volume 17, Issue 1 (9-2023)
Abstract
This article considers the stress-strength reliability of a coherent system in the state of stress at the component level. The coherent series, parallel and radar systems are investigated. For 2-component series or parallel systems and radar systems, this reliability based on Exponential distribution is estimated by maximum likelihood, uniformly minimum variance unbiased and Bayes methods. Also, simulation studies have been done to check estimators' performance, and real data are analyzed.
Shahram Yaghoobzadeh,
Volume 19, Issue 2 (4-2025)
Abstract
Studying various models in queueing theory is essential for improving the efficiency of queueing systems. In this paper, from the family of models {E_r/M/c; r,c in N}, the E_r/M/3 model is introduced, and quantities such as the distribution of the number of customers in the system, the average number of customers in the queue and in the system, and the average waiting time in the queue and in the system for a single customer are obtained. Given the crucial role of the traffic intensity parameter in performance evaluation criteria of queueing systems, this parameter is estimated using Bayesian, E‑Bayesian, and hierarchical Bayesian methods under the general entropy loss function and based on the system’s stopping time. Furthermore, based on the E‑Bayesian estimator, a new estimator for the traffic intensity parameter is proposed, referred to in this paper as the E^2‑Bayesian estimator. Accordingly, among the Bayesian, E‑Bayesian, hierarchical Bayesian, and the new estimator, the one that minimizes the average waiting time in the customer queue is considered the optimal estimator for the traffic intensity parameter in this paper. Finally, through Monte Carlo simulation and using a real dataset, the superiority of the proposed estimator over the other mentioned estimators is demonstrated.
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