Abstract
In this paper, we derive the recurrence relations for the moments of function of single and two order statistics from Lindley distribution. We also consider the maximum likelihood estimation (MLE) of the parameter of the distribution based on multiply type-II censoring. However maximum likelihood estimator does not have an explicit form for the involved parameter. In order to compute the MLE of the parameter, Monte Carlo simulation is used. A comparative study is presented between classical MLE and MLE from multiply type-II censored sample.
Highlights
A random variable X is said to have Lindley distribution if its probability density function is given by f (x) = θ2 (1 + x) e−θx; x > 0, θ > 0, (1)1+θ and it was introduced by Lindley (1952)
Xi, i = 1, 2, · · ·, n from the Lindley distribution with parameter θ one may follow the acceptance-rejection method which can be given by the following algorithm: i
The main aim of this paper is to develop recurrence relations of moments of order statistics for the function of single and two order statistics
Summary
Xi, i = 1, 2, · · · , n from the Lindley distribution with parameter θ one may follow the acceptance-rejection method which can be given by the following algorithm: i. Assume that n items are put on a life test, but only r1-th, · · · , rk-th failures are observed, the rest are unobserved, where r1, · · · , rk are considered to be fixed This is the multiply Type-II censoring, for more details see e.g. Jang et al (2001) and Schenk et al (2011). We let 0 ≤ Xr1:n ≤ Xr2:n ≤ · · · ≤ Xrk:n < ∞ to be a multiply Type-II censored sample from a population with pdf (1) and cdf (2) for θ ∈ Rq, where, 1 ≤ r1 < r2 < · · · < rn ≤ n. 149 RECURRENCE RELATIONS FOR MOMENTS OF MULTIPLY TYPE-II CENSORED ORDER STATISTICS
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Statistics, Optimization & Information Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
