scholarly journals Bayesian Estimation for Two Parameters of Weibull Distribution under Generalized Weighted Loss Function

2021 ◽  
Vol 34 (4) ◽  
pp. 116-129
Author(s):  
Abtisam J. Kadhim ◽  
Huda A. Rasheed
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Loss Function ◽  
Simulation Method ◽  
Bayes Estimators ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
The Mean ◽  
Two Parameters

In this paper, Bayes estimators for the shape and scale parameters of Weibull distribution have been obtained using the generalized weighted loss function, based on Exponential priors. Lindley’s approximation has been used effectively in Bayesian estimation. Based on theMonte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s).

scholarly journals Bayesian Estimation for Two Parameters of Gamma Distribution under Generalized Weighted Loss Function

2019 ◽  
Vol 60 (5) ◽  
pp. 1161-1171
Author(s):  
Loaiy F. Naji ◽  
Huda A. Rasheed
Keyword(s):  
Bayesian Estimation ◽  
Gamma Distribution ◽  
Loss Function ◽  
Maximum Likelihood Estimators ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
The Mean ◽  
Two Parameters

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

scholarly journals Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function

2019 ◽  
Vol 32 (1) ◽  
pp. 193 ◽  
Author(s):  
Loaiy F. Naji ◽  
Huda Abdullah Rasheed
Keyword(s):  
Bayesian Estimation ◽  
Gamma Distribution ◽  
Loss Function ◽  
Simulation Method ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
Lindley’S Approximation ◽  
The Mean ◽  
Two Parameters ◽  
Better Than

In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.

scholarly journals Some Bayes Estimators for Maxwell Distribution by Using New Loss Function

2017 ◽  
Vol 28 (1) ◽  
pp. 103
Author(s):  
Huda A. Rasheed ◽  
Zainab N. Khalifa
Keyword(s):  
Monte Carlo Simulation ◽  
Loss Function ◽  
Scale Parameter ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Maxwell Distribution ◽  
Bayes Estimators ◽  
Mean Squared Errors ◽  
The Mean ◽  
Bayesian Estimations

In the current study, we have been derived some Bayesian estimations of the scale parameter of Maxwell distribution using the New loss function (NLF) which it called Generalized weighted loss function, assuming non-informative prior, namely, Jefferys prior and information prior, represented by Inverted Levy prior. Based on Monte Carlo simulation method, those estimations are compared depending on the mean squared errors (MSE's). The results show that, the behavior of Bayesian estimation under New loss function using Inverted Levy prior when (k=0, c=3) is the better behavior than other estimates for all cases.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

Inference about Weibull Distribution Using Upper Record Values

2015 ◽  
Vol 22 (04) ◽  
pp. 1550016
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Weibull Distribution ◽  
Prediction Interval ◽  
Record Values ◽  
Testing Procedures ◽  
Scale Parameters ◽  
Upper Record Values ◽  
Record Value ◽  
Upper Record ◽  
Two Parameters ◽  
Two Parameter

This paper studies the frequentist inference about the shape and scale parameters of the two-parameter Weibull distribution using upper record values. The exact sampling distribution of the MLE of the shape parameter is derived. The asymptotic normality of the MLEs of both parameters are obtained. Based on these results this paper proposes various confidence intervals of the two parameters. Assuming one parameter is known certain testing procedures are proposed. Furthermore, approximate prediction interval for the immediately consequent record value is derived too. Conclusions are made based on intensive simulations.

scholarly journals The Bayes Estimators of the Variance and Scale Parameters of the Normal Model With a Known Mean for the Conjugate and Noninformative Priors Under Stein’s Loss

2022 ◽  
Vol 4 ◽  
Author(s):  
Ying-Ying Zhang ◽  
Teng-Zhong Rong ◽  
Man-Man Li
Keyword(s):  
Loss Function ◽  
Bayes Estimator ◽  
Bayes Estimation ◽  
Normal Model ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Squared Error Loss Function ◽  
Noninformative Priors ◽  
Scale Parameters ◽  
Variance Parameter

For the normal model with a known mean, the Bayes estimation of the variance parameter under the conjugate prior is studied in Lehmann and Casella (1998) and Mao and Tang (2012). However, they only calculate the Bayes estimator with respect to a conjugate prior under the squared error loss function. Zhang (2017) calculates the Bayes estimator of the variance parameter of the normal model with a known mean with respect to the conjugate prior under Stein’s loss function which penalizes gross overestimation and gross underestimation equally, and the corresponding Posterior Expected Stein’s Loss (PESL). Motivated by their works, we have calculated the Bayes estimators of the variance parameter with respect to the noninformative (Jeffreys’s, reference, and matching) priors under Stein’s loss function, and the corresponding PESLs. Moreover, we have calculated the Bayes estimators of the scale parameter with respect to the conjugate and noninformative priors under Stein’s loss function, and the corresponding PESLs. The quantities (prior, posterior, three posterior expectations, two Bayes estimators, and two PESLs) and expressions of the variance and scale parameters of the model for the conjugate and noninformative priors are summarized in two tables. After that, the numerical simulations are carried out to exemplify the theoretical findings. Finally, we calculate the Bayes estimators and the PESLs of the variance and scale parameters of the S&P 500 monthly simple returns for the conjugate and noninformative priors.

scholarly journals Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation

2021 ◽  
pp. 60-71
Author(s):  
Bashiru Omeiza Sule ◽  
Taiwo Mobolaji Adegoke ◽  
Kafayat Tolani Uthman
Keyword(s):  
Loss Function ◽  
Posterior Distribution ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Shape Parameters ◽  
True Parameter ◽  
Squared Error Loss Function ◽  
Scale Parameters

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

scholarly journals Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Farhad Yahgmaei ◽  
Manoochehr Babanezhad ◽  
Omid S. Moghadam
Keyword(s):  
Weibull Distribution ◽  
Scale Parameter ◽  
Loss Functions ◽  
Simulation Studies ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Risk Functions ◽  
Inverse Weibull Distribution ◽  
The Mean ◽  
Mean Square Errors

This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD). Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

scholarly journals Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

scholarly journals Comparison of classical and Bayesian estimators to estimate the parameters in Weibull distribution under weighted general entropy loss function

2021 ◽  
Vol 8 (3) ◽  
pp. 57-62
Author(s):  
Fuad Alduais ◽  
◽  
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Least Squares Method ◽  
Likelihood Estimation ◽  
Simulation Method ◽  
Ordinary Least Squares ◽  
Bayesian Estimator ◽  
Entropy Loss ◽  
General Entropy ◽  
General Entropy Loss Function

In this work, we have developed a General Entropy loss function (GE) to estimate parameters of Weibull distribution (WD) based on complete data when both shape and scale parameters are unknown. The development is done by merging weight into GE to produce a new loss function called the weighted General Entropy loss function (WGE). Then, we utilized WGE to derive the parameters of the WD. After, we compared the performance of the developed estimation in this work with the Bayesian estimator using the GE loss function. Bayesian estimator using square error (SE) loss function, Ordinary Least Squares Method (OLS), Weighted Least Squared Method (WLS), and maximum likelihood estimation (MLE). Based on the Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that the performance of the Bayes estimator under developed method (WGE) loss function is the best for estimating shape parameters in all cases and has good performance for estimating scale parameter.

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