Parameter estimation for the Lomax distribution using the E-Bayesian method

Fitrilia, A.; Fithriani, Ida; Nurrohmah, Siti

doi:10.1088/1742-6596/1108/1/012081

Cited by 3 publications

(4 citation statements)

References 3 publications

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“…0, ],[ , ) +∞ T T ( , according to the conditional density formula, the probability density function of 1 Y can be obtained by 1 ( 1) ( 1)…”

Section: Em Estimatingmentioning

confidence: 99%

“…Next, the parameter β is estimated with the help of the EM algorithm. First, assume that the estimated value of the existing shape parameter in the 1 k + -th iteration is ( ) k β , and a new estimated value of the shape parameter ( 1) k β + can be obtained with the help of the EM algorithm. The specific process is as follows:…”

Section: Em Estimatingmentioning

confidence: 99%

“…Many Scholars have done a lot of research on the statistical properties of Lomax distribution. Fitria et al [1] studied the estimation of Lomax distribution parameters by using the E-Bayesian method; Okasha et al [2] obtained the E-Bayesian estimation of Lomax distribution parameters under Type-II censored data; Long and Zhang [3][4] studied Bayes estimation of shape parameters on Lomax distribution under Type-II censored samples and Bilateral Type-Ⅱ censored data; Long et al [5] Studied the maximum likelihood estimation and Bayes estimation of the shape parameters of Lomax distribution under progressive Type-II censoring; Huang et al [6] studied the estimation of shape parameters of Lomax distribution under left truncated and right censored data by using maximum likelihood method and EM algorithm; Long et al [7] Studied the maximum likelihood estimation of Lomax distribution shape parameters under typeⅠcensoring samples with missing data, proving that the estimation has consistency and asymptotic normality, and gave the corresponding confidence interval and hypothesis test of shape parameters; Type-I censoring is a special case of bilateral Type-I truncation.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Shape Parameter for Lomax Distribution Under Bilateral Type-I Censored Sample

Liu

2022

J. Phys.: Conf. Ser.

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The maximum likelihood estimation of shape parameters of Lomax distribution under bilateral Type-I Censored Sample is studied, the explicit expression of shape parameter estimation cannot be obtained, but it is proved that the maximum likelihood estimation of this parameter is unique. Then the EM estimation of shape parameters is obtained by using EM algorithm, and the asymptotic variance and approximate confidence interval of the EM estimation of shape parameters are also given; Finally, the effects of maximum likelihood estimation and EM estimation of shape parameters of Lomax distribution are numerically simulated. By comparing the relative deviation, it shows that the estimation effect of using EM algorithm to calculate shape parameters is relatively good, and the asymptotic variance and asymptotic confidence interval of EM estimation are given.

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“…0, ],[ , ) +∞ T T ( , according to the conditional density formula, the probability density function of 1 Y can be obtained by 1 ( 1) ( 1)…”

Section: Em Estimatingmentioning

confidence: 99%

Section: Em Estimatingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation of the Shape Parameter for Lomax Distribution Under Bilateral Type-I Censored Sample

Liu

2022

J. Phys.: Conf. Ser.

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“…Monte Carlo simulation is also used to compare new methods with corresponding Bayesian and maximum likelihood techniques [ 5 ]. The E-Bayesian method is used to obtain the likelihood function of the LD in the right-censored data type II and the parameter estimators of the LD in the right-censored data type II [ 6 ]. A new method is developed, to estimate failure probability which is defined based on formulas of the E-Bayesian estimate of the failure probability by [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

E‐Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function

Al‐Bossly

2021

Computational Intelligence and Neuroscience

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The main contribution of this work is the development of a compound LINEX loss function (CLLF) to estimate the shape parameter of the Lomax distribution (LD). The weights are merged into the CLLF to generate a new loss function called the weighted compound LINEX loss function (WCLLF). Then, the WCLLF is used to estimate the LD shape parameter through Bayesian and expected Bayesian (E-Bayesian) estimation. Subsequently, we discuss six different types of loss functions, including square error loss function (SELF), LINEX loss function (LLF), asymmetric loss function (ASLF), entropy loss function (ENLF), CLLF, and WCLLF. In addition, in order to check the performance of the proposed loss function, the Bayesian estimator of WCLLF and the E-Bayesian estimator of WCLLF are used, by performing Monte Carlo simulations. The Bayesian and expected Bayesian by using the proposed loss function is compared with other methods, including maximum likelihood estimation (MLE) and Bayesian and E-Bayesian estimators under different loss functions. The simulation results show that the Bayes estimator according to WCLLF and the E-Bayesian estimator according to WCLLF proposed in this work have the best performance in estimating the shape parameters based on the least mean averaged squared error.

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Bayesian estimation of the Pareto model based on type-II censoring data by employing non-linear programming

AL-Essa,

Al-Duais,

Aydi

et al. 2024

Alexandria Engineering Journal

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Parameter estimation for the Lomax distribution using the E-Bayesian method

Cited by 3 publications

References 3 publications

Estimation of the Shape Parameter for Lomax Distribution Under Bilateral Type-I Censored Sample

Estimation of the Shape Parameter for Lomax Distribution Under Bilateral Type-I Censored Sample

E‐Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function

Bayesian estimation of the Pareto model based on type-II censoring data by employing non-linear programming

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