A comparison of various estimators of the mean of an inverse gaussian distribution

References

• Atkinson , A. 1982 . The sumulation of generalized Inverse Gaussian and hyperbolic Random Variables . SIAM J. Sci. Stat. Comput , 3 ( 4 ) : 502 – 515 .
   Web of Science ®Google Scholar
• Bateman , H. 1953 . “ Higher Transcendental Functions I ” . Edited by: Erdelyi , A. NY : McGraw Hill .
   Google Scholar
• Bluementhal , S. 1967 . Proportional sampling in life length studies . Technometrics , 9 : 205 – 218 .
   Web of Science ®Google Scholar
• Chhikara , R.S. and Folks , L. 1989 . The Inverse Gaussian Distribution Theory Methodology and Applications , NY : Marcel Dekker Inc .
   Google Scholar
• Cnaan , A. 1985 . Survival models with two phases and length biased sampling . Communications in Statistics , 14 ( 4 ) : 861 – 886 .
   Google Scholar
• Cox , D.R. 1969 . Some sampling problems in Technology , Edited by: Johnson , N.L. and Smith , H. 506 – 527 . NY : John Wiley & Sons . New Developments in Survey Sampling
   Google Scholar
• Doksum , K.A. and Hoyland , A. 1989 . Models for variable-stress accelerated life testing experiments based on Wiener Processes and the Inverse Gaussian distribution , Trondheim, , Norway : University of Trondheim . Technical Report No. 3/89 Department of Mathematics
   Google Scholar
• Iwase , K. and Seto , N. 1983 . Uniformly minimum variance unbiased estimation of the Inverse Gaussian Distribution . Journal of the American Statistical Assoc , 78 : 660 – 663 .
   Web of Science ®Google Scholar
• Iwase , K. 1987 . UMVU Estimation for the inverse Gaussian Distribution I (μ,cμ2 ) with known c . Communications in Statistics , 16 ( 5 ) : 1315 – 1320 .
   Google Scholar
• Khatri , C.G. and Ratani , R.T. 1981 . On estimation and testing of the parameter Θ in N(Θ,aΘ) . Journal of the Indian Statistical Association , 19 ( 5 ) : 77 – 84 .
   Google Scholar
• Letac , G. and Mora , M. 1990 . Natural real exponential families with cubic variance functions . Ann. Statist , 18 ( 5 ) : 1 – 37 .
   Web of Science ®Google Scholar
• Michael , J.R. , Schucany , W.R. and Haas , R.W. 1976 . Generating random variates using transformations with multiple roots . American Statistician , 30 ( 2 ) : 88 – 90 .
   Web of Science ®Google Scholar
• Morris , C.N. 1982 . Natural exponential families with quadratic variance functions . Ann. Statist , 10 ( 2 ) : 65 – 80 .
   Web of Science ®Google Scholar
• Pandey , B.N. and Malik , H.J. 1988 . Some improved estimators for a measure of dispersion of an Inverse Gaussian distribution . Communications in Statistics , 17 ( 11 ) : 3935 – 3949 .
   Google Scholar
• Pandey , B.N. and Malik , H.J. 1989 . Estimation of the mean and the reciprocal of the mean of the Inverse Gaussian distribution . Communications in Statistics , 18 ( 3 ) : 1187 – 1201 .
   Google Scholar
• Rao , C.R. 1977 . “ Weighted distributions: A Survey of their applications In ” . In Applications of Statistics , Edited by: Krishnaiah , P.R. 383 – 405 . North Holland Pub. Co .
   Google Scholar
• Patil , G.P. and Rao , C.R. 1978 . Weighted distributions and size biased sampling with applications to Wildlife populations and human families . Biometrics , 34 : 179 – 189 .
   Web of Science ®Google Scholar
• Rao , C.R. 1977 . A natural example of a weighted distribution . American Statistician , 31 : 24 – 26 .
   Web of Science ®Google Scholar
• Rao , C.R. 1965 . On discrete distributions arising out of methods of ascertainments , Edited by: Patil , G.P. 320 – 332 . Calcutta : Pergamon Press and Statistical Publishing Society .
   Google Scholar
• Ratani , R.T. 1977 . Estimation of the parameter of a normal distribution N(Theta;,a,Θ) . Gujarat Statistical Review , 4 : 17 – 24 .
   Google Scholar
• Schaeffer , R.L. 1972 . Size biased sampling . Technometrics , 14 : 635 – 644 .
   Web of Science ®Google Scholar
• Simon , R. 1980 . Length biased sampling in etiologic studies . American Journal of Epidemiology , 111 : 444 – 452 .
   PubMed Web of Science ®Google Scholar
• Tripathi , R.C. and Gupta , R.C. 1985 . A comparison between the ordinary and length biased modified power series distributions with applications . Communications in Statistics , 16 ( 4 ) : 1195 – 1206 .
   Google Scholar
• Zelen , M. and Feinleib , M. 1969 . On the theory of screening for chronic diseases . Biometrika , 56 ( 4 ) : 601 – 613 .
   Web of Science ®Google Scholar
• Zelen , M. 1974 . Problems in cell kinetics and early detection of disease , 701 – 726 . Philadelphia : SIAM . Reliability and Biometry
   Google Scholar