A Study on LINEX Loss Function with Different Estimating Methods

Khatun, Nazia; Matin, Mohammad A.

doi:10.4236/ojs.2020.101004

Cited by 18 publications

(17 citation statements)

References 9 publications

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“…Varian and Savage [ 9 ] presented a highly useful asymmetric loss function, which has lately been employed in different works [ 10 , 11 ] and [ 12 ]. This function is known as the LINEX loss function, according to linear exponentially.…”

Section: Bayesian and Non-bayesian Estimationmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis–Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

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Section: Bayesian and Non-bayesian Estimationmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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“…Discrete-time events are the focus of the studies in these publications. They discussed how the LINEX error function operated, but still, no specifics or practical solutions were provided on how the LINEX loss function changes the shape variable and error value [ 11 ]. Considering the LINEX loss method's versatility in estimating a location parameter, it does not seem to be useful for estimating scale variables and other values.…”

Section: Introductionmentioning

confidence: 99%

“…In continuous-time processes, the idea of the asymptotic element-wise optimization problem is expanded from discrete-time processes [ 11 ]. Additionally, with a squared error loss, the APO procedures for predicting the intensities of a homogeneity Poisson process are AO for random priors and asymptotically nondeficient for conjugation priors [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Mohammed

Alaziz

Sumati

et al. 2022

Computational Intelligence and Neuroscience

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The LINEX loss function, which climbs exponentially with one-half of zero and virtually linearly on either side of zero, is employed to analyze parameter analysis and prediction problems. It can be used to solve both underestimation and overestimation issues. This paper explained the Bayesian estimation of mean, Gamma distribution, and Poisson process. First, an improved estimator for μ 2 is provided (which employs a variation coefficient). Under the LINEX loss function, a better estimator for the square root of the median is also derived, and an enhanced estimation for the average mean in such a negatively exponential function. Second, giving a gamma distribution as a prior and a likelihood function as posterior yields a gamma distribution. The LINEX method can be used to estimate an estimator λ B L ^ using posterior distribution. After obtaining λ B L ^ , the hazard function h B L ^ and D B L ^ the function of survival estimators are used. Third, the challenge of sequentially predicting the intensity variable of a uniform Poisson process with a linear exponentially (LINEX) loss function and a constant cost of production time is investigated using a Bayesian model. The APO rule is offered as an approximation pointwise optimal rule. LINEX is the loss function used. A variety of prior distributions have already been studied, and Bayesian estimation methods have been evaluated against squared error loss function estimation methods. Finally, compare the results of Maximum Likelihood Estimation (MLE) and LINEX estimation to determine which technique is appropriate for such information by identifying the lowest Mean Square Error (MSE). The displaced estimation method under the LINEX loss function was also examined in this research, and an improved estimation was proposed.

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“…us, an alternative loss function is needed. One of these alternatives is the linear exponential (LINEX) loss function, which many authors have discussed, including Calabria and Pulcini [17], Gencer and Saraçoglu [18], Khatun and Matin [19], and Parsian and Kirmani [20].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

Al-Duais

2021

Mathematical Problems in Engineering

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The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment.

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A Study on LINEX Loss Function with Different Estimating Methods

Cited by 18 publications

References 9 publications

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

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