A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution

Based on asymmetric loss function, the estimations and their properties of liquid rocket engine are discussed. The UMVUE and bayes estimator for some lifetime parameters, reliability and hazard function are obtained under entropy loss function. And we prove the estimations with the form of cT+d are admissible. At last, the statistical performances are compared through the MSE based on Monte Carlo simulation study. According to these comparisons, it is suggested that the empirical bayes estimators have high-precision.

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Alpha power transformed inverse Lindley distribution: A distribution with an upside-down bathtub-shaped hazard function

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.03.037 ◽

2019 ◽

Vol 348 ◽

pp. 130-145 ◽

Cited By ~ 9

Author(s):

Sanku Dey ◽

Mazen Nassar ◽

Devendra Kumar

Keyword(s):

Hazard Function ◽

Alpha Power ◽

Lindley Distribution ◽

Inverse Lindley Distribution

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Bayesian Analysis of Weibull-Lindley Distribution Using Different Loss Functions

Asian Journal of Advanced Research and Reports ◽

10.9734/ajarr/2020/v8i430205 ◽

2020 ◽

pp. 28-41

Author(s):

Innocent Boyle Eraikhuemen ◽

Olateju Alao Bamigbala ◽

Umar Alhaji Magaji ◽

Bassa Shiwaye Yakura ◽

Kabiru Ahmed Manju

Keyword(s):

Bayesian Analysis ◽

Loss Function ◽

Bayesian Methods ◽

Shape Parameter ◽

Loss Functions ◽

Quadratic Loss ◽

Function Estimation ◽

Lindley Distribution ◽

Method Of Maximum Likelihood ◽

Parameter Values

In the present paper, a three-parameter Weibull-Lindley distribution is considered for Bayesian analysis. The estimation of a shape parameter of Weibull-Lindley distribution is obtained with the help of both the classical and Bayesian methods. Bayesian estimators are obtained by using Jeffrey’s prior, uniform prior and Gamma prior under square error loss function, quadratic loss function and Precautionary loss function. Estimation by the method of Maximum likelihood is also discussed. These methods are compared by using mean square error through simulation study with varying parameter values and sample sizes.

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Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

Entropy ◽

10.3390/e23101256 ◽

2021 ◽

Vol 23 (10) ◽

pp. 1256

Author(s):

Abdullah M. Almarashi ◽

Ali Algarni ◽

Amal S. Hassan ◽

Ahmed N. Zaky ◽

Mohammed Elgarhy

Keyword(s):

Loss Function ◽

Credible Interval ◽

Bayesian Estimator ◽

Residual Entropy ◽

Real World Data ◽

Lindley Distribution ◽

Bayesian Estimates ◽

True Value ◽

Cumulative Residual ◽

Theoretical Results

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

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Valence electron spectroscopy of inhomogeneous media

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130389 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1150-1151

Author(s):

A. Howie ◽

D.W. McComb

Keyword(s):

Specific Gravity ◽

Loss Function ◽

Electron Spectroscopy ◽

Valence Electron ◽

Peak Height ◽

Loss Functions ◽

Loss Peak ◽

High Energies ◽

Valence Electron Density ◽

Electron Microscopist

The bulk loss function Im(-l/ε (ω)), a well established tool for the interpretation of valence loss spectra, is being progressively adapted to the wide variety of inhomogeneous samples of interest to the electron microscopist. Proportionality between n, the local valence electron density, and ε-1 (Sellmeyer's equation) has sometimes been assumed but may not be valid even in homogeneous samples. Figs. 1 and 2 show the experimentally measured bulk loss functions for three pure silicates of different specific gravity ρ - quartz (ρ = 2.66), coesite (ρ = 2.93) and a zeolite (ρ = 1.79). Clearly, despite the substantial differences in density, the shift of the prominent loss peak is very small and far less than that predicted by scaling e for quartz with Sellmeyer's equation or even the somewhat smaller shift given by the Clausius-Mossotti (CM) relation which assumes proportionality between n (or ρ in this case) and (ε - 1)/(ε + 2). Both theories overestimate the rise in the peak height for coesite and underestimate the increase at high energies.

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