Simultaneous Pitman closeness of progressively type-II right-censored order statistics to population quantiles

In this work, we extend prior results concerning the simultaneous Pitman closeness of order statistics (OS) to population quantiles. By considering progressively type-II right-censored samples, we derive expressions for the simultaneous closeness probabilities of the progressively censored OS to population quantiles. Explicit expressions are deduced for the cases when the underlying distribution has bounded and unbounded supports. Illustrations are provided for the cases of exponential, uniform and normal distributions for various progressive type-II right-censoring schemes and different quantiles. Finally, an extension to the case of generalized OS is outlined.

[1]  Narayanaswamy Balakrishnan,et al.  Computation of optimal plotting points based on Pitman closeness with an application to goodness-of-fit for location-scale families , 2012, Comput. Stat. Data Anal..

[2]  N. Balakrishnan,et al.  On Pitman's measure of closeness of k-records , 2011 .

[3]  An odd property of sample median from odd sample sizes , 2010 .

[4]  N. Balakrishnan,et al.  Pitman closeness of current records for location-scale families , 2010 .

[5]  Katherine F. Davies.  Simultaneous Closeness among Order Statistics to Population Quantiles , 2010 .

[6]  N. Balakrishnan,et al.  Pitman closeness of record values to population quantiles , 2009 .

[7]  Narayanaswamy Balakrishnan,et al.  Pitman closeness of sample median to population median , 2009 .

[8]  Narayanaswamy Balakrishnan,et al.  Pitman Closeness of Order Statistics to Population Quantiles , 2009, Commun. Stat. Simul. Comput..

[9]  N. Balakrishnan.  Rejoinder on: Progressive censoring methodology: an appraisal , 2007 .

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

[11]  Udo Kamps,et al.  A concept of generalized order statistics , 1995 .

[12]  Robert L. Mason,et al.  Comparison of Linear Estimators Using Pitman's Measure of Closeness , 1990 .

[13]  R. L. Mason,et al.  Pitman's Measure of Closeness: A Comparison of Statistical Estimators , 1987 .

[14]  E. J. G. Pitman,et al.  The “closest” estimates of statistical parameters , 1937, Mathematical Proceedings of the Cambridge Philosophical Society.