Bayesian Estimations from the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Record Values

Abstract

This article discusses Bayesian and non-Bayesian estimations problems of the unknown parameters for the two-parameter bathtub-shaped lifetime distribution based on upper record values. The ML and the Bayes estimates based on record values are derived for the two unknown parameters as well as hazard function. When the Bayesian approach is considered, under the assumption that both parameters are unknown, the Bayes estimators cannot be obtained in explicit forms. An approximation form due to Soland (Soland (1969)) is used for obtaining the Bayes estimates based on a conjugate prior for the first shape parameter and a discrete prior for the second shape parameter of this model. This is done with respect to the squared error loss and LINEX loss functions. The estimation procedure is then applied to real data set and simulation data.

Estimation and prediction for the Kumaraswamy-inverse Rayleigh distribution based on records

“…Bayes estimators for the parameters α and λ and the predicted sth record value are obtained under the SE loss function using informative ( 1 2 1 2 , , , 0 a a b b  for example, 12 ), see [20]. The performance assessment is made by comparing the biases and the mean squared errors (MSE) of the estimators of  and  and the future sth record value s r .…”

“…Furthermore, several authors have studied distribution characteristics based on record value. For example, Selim, [12] studied Bayesian estimation of two parameter of bathtub-shape lifetime distribution based on record values and Nader et. al., [13] inferentially studied record values from the Kumaraswamy distribution.…”

Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values

“…Ahmadi et al [13] studied the Bayesian estimation and the admissibility of some estimators for the two parameters of the exponential distribution based on k-record values under LINEX loss function. More references can be found in [14][15][16][17][18][19].…”

On Bayesian estimation from two parameter Bathtub-Shaped lifetime distribution based on progressive first-failure-censored sampling

“…Also Rastogi et al [13] consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtubshaped distribution on the basis of progressive type-II censored sample by using different symmetric and asymmetric such as LINEX, entropy and squared error loss functions. Sarhan et al [14] discussed Maximum likelihood and Bayes estimates of the two unknown parameters of two parameter bathtub-shaped lifetime distribution or Selim [15] discussed Bayesian and non-Bayesian estimations problems of the unknown parameters for the two-parameter bathtub-shaped lifetime distribution based on record values. In this paper, we assume that shape parameter β is known and used different method of Bayesian estimation to estimate parameter λ and reliability function of two parameter bathtub-shaped lifetime distribution under progressively first-failure-censored samples based on different symmetric and asymmetric loss functions.…”