Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Mukhopadhyay, Nitis; Bapat, Sudeep R.
• Is Part Of: Sequential analysis. Volume 35:Issue 3(2016)
• Page Start: 387
• Page End: 412
• Publication Date: 2016-07-02
• Subjects: Cancer research -- first-order properties -- Linex loss -- location parameter -- modified Linex -- modified two-stage -- negative exponential -- nonlinear renewal theory -- purely sequential -- real data -- reliability analysis -- risk per unit cost -- scale parameter -- second-order properties -- simulations -- two-stage; 62L12 -- 62L05 -- 62G20 -- 62F10 -- 62P10 -- 62P30; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1206386
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: We have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016, Sequential Analysis ). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984, Canadian Journal of Statistics ) and Mukhopadhyay and Darmanto (1988, Sequential Analysis ). We have resorted to Mukhopadhyay and Duggan (1997, Sankhya, Series A ) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977, 1979, Annals of Statistics ) and Woodroofe (1977, Annals of Statistics ) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.