Abstract
In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the scale and location parameters of two parameter reduced Kies distribution. The parameters of the two parameter reduced Kies distribution are estimated under progressive type-II censoring scheme. The model parameters are estimated using the maximum likelihood estimation method. Further, we explore the asymptotic confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. Based on our study, we can conclude that maximum likelihood estimators is decreasing with respect to an increase of the schemes and comparing the three censoring schemes, it is clear that the mean sum of squares, confidence interval lengths are smaller for scheme 1 than schemes 2 and 3.
Highlights
IntroductionThe one parameter reduced Kies (RK) distribution was introduced by Kumar and Dharmaja [1]
The one parameter reduced Kies (RK) distribution was introduced by Kumar and Dharmaja [1]for modeling data and a generalization of Kies distribution
This paper gives recurrence relations for single moments and product moments of progressive type-II censoring order statistics based on one parameter RK distribution
Summary
The one parameter reduced Kies (RK) distribution was introduced by Kumar and Dharmaja [1]. This paper gives recurrence relations for single moments and product moments of progressive type-II censoring order statistics based on one parameter RK distribution. The data arising from such a time-constrained life-test would be of the form Y1:s ≤ · · · ≤ Yr:s with the remaining s − s lifetimes being more than T; here, r is random (0 ≤ r ≤ s) and has a binomial distribution with parameters (s, F ( T )) This situation is referred to as Type-I censoring. Malik and Kumar [25] studied moments of progressively type-II Right censored order statistics from Erlang-truncated exponential distribution. The key role of this article is two fold: first, we derive recurrence relations for the single and product moments of the RK distribution based on progressive type-II right censored order statistics.
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