A new two-parameter lifetime distribution with decreasing, increasing or upside-down bathtub-shaped failure rate

Abd-Elrahman, Ayman M.

doi:10.1080/03610926.2016.1193198

Cited by 13 publications

(13 citation statements)

References 11 publications

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“…M would be the solution of this equation, which provides a good starting point for (11). This technique have been used by, e.g., Kundu and Howlader [11] and Abd-Elrahman [1].…”

Section: When β Is Knownmentioning

confidence: 99%

“…Onceλ (0) is obtained, an initial value for the parameter β,β (0) , can be calculated as the right hand side of (9) after replacing λ (0) byλ (0) . Based on the initialsβ (0) andλ (0) , an updated value for β,β (1) , can be obtained by using (8). Similarly, based on the pair (β (1) ,λ (0) ), an updated value for λ,λ (1) , can be obtained by using (11), and so on.…”

Section: When β Is Knownmentioning

confidence: 99%

“…Based on the initialsβ (0) andλ (0) , an updated value for β,β (1) , can be obtained by using (8). Similarly, based on the pair (β (1) ,λ (0) ), an updated value for λ,λ (1) , can be obtained by using (11), and so on. As a stopping rule, the iterations will be terminated after some value s < 1000 with a level of accuracy, ≤ 1.2 × 10 −7 , which is defined as…”

Section: When β Is Knownmentioning

confidence: 99%

“…Denote I 0 = lim y → 0 + I (0) (y) = 0.32078, I 1 = lim y → 0 + I (1) (y) = 0.00934 and I 2 = lim y → 0 + I (2) (y) = 0.13177 . Then, (16) can be rewritten as…”

Section: Fisher Information Matrix (Fim)mentioning

confidence: 99%

“…The generalized Bilal (GB) model coincides with the distribution of the median in a sample of size three from the Weibull distribution. It was first introduced by Abd-Elrahman [1]. He showed that its failure rate function can be upside-down bathtub shaped.…”

Section: Introductionmentioning

confidence: 99%

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Reliability estimation under type-II censored data from the generalized Bilal distribution

Abd-Elrahman

2019

J Egypt Math Soc

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The main object of this article is the estimation of the unknown population parameters and the reliability function for the generalized Bilal model under type-II censored data. Both maximum likelihood and Bayesian estimates are considered. In the Bayesian framework, although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibb's sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute the Bayes estimates and also to construct their corresponding credible intervals with the help of two different importance sampling techniques. A simulation study is carried out to examine the accuracy of the resulting Bayesian estimates and compare them with their corresponding maximum likelihood estimates. Application to a real data set is considered for the sake of illustration.

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“…M would be the solution of this equation, which provides a good starting point for (11). This technique have been used by, e.g., Kundu and Howlader [11] and Abd-Elrahman [1].…”

Section: When β Is Knownmentioning

confidence: 99%

Section: When β Is Knownmentioning

confidence: 99%

Section: When β Is Knownmentioning

confidence: 99%

“…Denote I 0 = lim y → 0 + I (0) (y) = 0.32078, I 1 = lim y → 0 + I (1) (y) = 0.00934 and I 2 = lim y → 0 + I (2) (y) = 0.13177 . Then, (16) can be rewritten as…”

Section: Fisher Information Matrix (Fim)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations