On the record values and its predictions from Exponentiated Inverted Weibull distribution and associated inference

2021 ◽  
pp. 1-22
Author(s):  
Jagdish Saran ◽  
Narinder Pushkarna ◽  
Kanika Verma
Keyword(s):  
Weibull Distribution ◽  
Record Values

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 Bayesian Estimates Based On Record Values Under Weighted LINEX Loss Function

2020 ◽  
pp. 11-19 ◽  
Author(s):  
Fuad Al-Duais ◽  
Mohammed Alhagyan
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Reliability Function ◽  
Record Values ◽  
Linex Loss Function ◽  
Asymmetric Loss ◽  
Bayes Estimates ◽  
Linex Loss ◽  
Asymmetric Loss Function

In this paper, we developed linear exponential (LINEX) loss function by emerging weights to produce weighted linear exponential (WLINEX) loss function. Then we utilized WLINEX to derive scale parameter and reliability function of the Weibull distribution based on record values when the shape parameter is known. After, we estimated scale parameter and reliability function of Weibull distribution by using maximum likelihood (ML) estimation and by several Bayes estimations.  The Bayes estimates were obtained with respect to symmetric loss function (squared error loss (SEL)), asymmetric loss function (LINEX) and asymmetric loss function (WLINEX). The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. The result of simulation mentioned that the proposed WLINEX loss function is promising and can be used in real environment especially at the case of underestimate where it revealed better performance than LINEX loss function for estimating scale parameter.

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