Abstract
The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function. We have examined Bayes estimates under various losses such as the balanced squared error (balanced SEL) and balanced LINEX loss functions are considered. We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. The parametric bootstrap method has been used to construct confidence interval for the parameters and reliability function. Progressively type-II censored and k-record values as a special case of GOS are considered. Finally a practical example using real data set was used for illustration.
Highlights
The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations
We develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function
We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases
Summary
Udo Kamps [1,2] has introduced GOS as random variables having certain joint density function, which includes as a special case the joint density functions of many models of ordered random variables such as ordinary order statistics (OS) (David [3], Castillo [4] and Arnold, Balakrishnan and Nagaraja [5]), sequential order statistics (SOS) (Cramer and Kamps [6,7]), record values, Kth record values, and Pfeifer’s records (Nevzorov [8] and Ahsanullah [9]), Progressive Type-II censoring order statistics (PCOS) (Soliman [10,11,12,13], Balakrishnan and Asgharzadeh [14], and Sarhan, Ammar and Abuammoh [15]). The structural similarities of these models are based on the similarity of their joint density function. The conesquences of overestimates, in loss of human life, are much more serious than the consequences of underestimates In this case an asymmetric loss function is more appropriate. In this paper based on n selected GOS from the inverse Weibull model, we consider the problem of Bayesian and non-Bayesian estimation for parameters and reliability function of the model. This was done under assumption of discrete-continous mixture prior for the unknown parameters.
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