Computational aspects of statistical intervals based on two Type-II censored samples

Abstract In this paper, we propose an efficient branch and bound procedure to compute exact nonparametric statistical intervals based on two Type-II right censored data sets. The procedure is based on some recurrence relations for the distribution and density functions of progressively Type-II censored order statistics which can be applied to compute the coverage probabilities. We illustrate the method for both confidence and prediction intervals of a given level.

[1]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

[2]  Luis A. Escobar,et al.  Statistical Intervals: A Guide for Practitioners , 1991 .

[3]  B. Arnold,et al.  A first course in order statistics , 1994 .

[4]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[5]  E. Cramer.  Balakrishnan, Narayanaswamy ; Aggarwala, Rita: Progressive censoring : theory, methods, and applications / N. Balakrishnan ; Rita Aggarwala. - Boston ; Basel ; Berlin, 2000 , 2000 .

[6]  Udo Kamps,et al.  On distributions Of generalized order statistics , 2001 .

[7]  H. N. Nagaraja,et al.  Order Statistics, Third Edition , 2005, Wiley Series in Probability and Statistics.

[8]  Wayne B. Nelson,et al.  Applied Life Data Analysis: Nelson/Applied Life Data Analysis , 2005 .

[9]  Narayanaswamy Balakrishnan,et al.  Progressive censoring methodology: an appraisal , 2007 .

[10]  Hsiuying Wang,et al.  Computational Statistics and Data Analysis Coverage Probability of Prediction Intervals for Discrete Random Variables , 2022 .

[11]  E. Cramer.  Hermite interpolation polynomials and distributions of ordered data , 2009 .

[12]  Narayanaswamy Balakrishnan,et al.  Exact two-sample nonparametric confidence, prediction, and tolerance intervals based on ordinary and progressively type-II right censored data , 2010 .

[13]  Narayanaswamy Balakrishnan,et al.  Exact nonparametric confidence, prediction and tolerance intervals based on multi-sample Type-II right censored data , 2010 .

[14]  E. Beutner,et al.  NONPARAMETRIC META‐ANALYSIS FOR MINIMAL‐REPAIR SYSTEMS , 2010 .

[15]  Narayanaswamy Balakrishnan,et al.  Exact nonparametric meta-analysis for multiple independent doubly Type-II censored samples , 2012, Comput. Stat. Data Anal..

[16]  M. Salehi,et al.  Record ranked set sampling scheme , 2014 .

[17]  Elham Mirfarah,et al.  Pitman closeness of $$k$$k-records from two sequences to progressive Type-II censored order statistics , 2014, Comput. Stat..