Asymptotic Behavior of the Hazard Rate Kernel Estimator Under Truncated and Censored Data

2007 ◽  
Vol 36 (1) ◽  
pp. 155-173 ◽  
Author(s):  
Mohamed Lemdani ◽  
Elias Ould-Saïd
Keyword(s):  
Asymptotic Behavior ◽  
Censored Data ◽  
Hazard Rate ◽  
Kernel Estimator ◽  
Truncated And Censored Data

Kumaraswamy odd Burr G family of distributions with applications to reliability data

2018 ◽  
Vol 55 (1) ◽  
pp. 94-114
Author(s):  
Arslan Nasir ◽  
Hassan S. Bakouch ◽  
Farrukh Jamal
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Censored Data ◽  
Hazard Rate ◽  
Moment Generating Function ◽  
Density Functions ◽  
Censored Samples ◽  
The Family ◽  
Rate Functions ◽  
Family Of Distributions

We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including rth moments, mth incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.

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