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Original Articles

Improved Estimation of Inverse Gaussian Shape Parameter and Measure of Dispersion with Prior Information

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Pages 205-226 | Received 01 Jul 2006, Published online: 30 Nov 2011

References

  • Antoniadis , A. , Besbeas , P. and Sapatinas , T. 2001 . Wavelet shrinkage for natural exponential families with cubic variance functions . Sankhyā , 63, A ( 3 ) : 309 – 327 .
  • Banerjee , A. K. and Bhattacharya , G. K. 1976 . A purchase incidence model with Inverse Gaussian interpurchase times . Journal of American Statistical Association , 71 : 823 – 829 .
  • Chhikara , R. S. and Folks , J. L. 1974 . Estimation of the Inverse Gaussian distribution function . Journal of American Statistical Association , 69 : 250 – 254 .
  • Chhikara , R. S. 1975 . Optimum test for the comparison of two Inverse Gaussian means . Journal of American Statistical Association , 17 : 77 – 83 .
  • Chhikara , R. S. and Folks , J. L. 1975 . Statistical distribution related to the Inverse Gaussian . Communication in Statistics , 4 : 1081 – 1091 .
  • Chhikara , R. S. and Folks , J. L. 1976 . Optimum procedure for the mean of the first passage time in Brownian motion with positive drift . Technometric , 18 : 189 – 193 .
  • Chhikara , R. S. and Folks , J. L. 1977 . The Inverse Gaussian distribution as a lifetime model . Technometrics , 19 : 461 – 468 .
  • Chhikara , R. S. and Folks , J. L. 1989 . “ The Inverse Gaussian distribution theory, methodology and application -Statistics ” . In Textbooks and Monographs , 95 New York : Marcel Dekker .
  • Ebrahimi , N. and Hosmane , B. 1987 . On shrinkage estimation of the exponential location parameter . Communication in Statistics, Theory and Methods , 16 ( 9 ) : 2623 – 2637 .
  • Folks , J. L. and Chhikara , R. S. 1978 . The Inverse Gaussian distribution and its application, a review . Journal of the Royal Statistical Society, B , 40 : 263 – 289 .
  • Hasofer , A. M. 1964 . A dam with Inverse Gaussian input . Proc. Camb. Phil. Soc. , 60 : 931 – 933 .
  • Hawkins , D. and Olwell , D. 1997 . Inverse Gaussian cumulative sum control charts for location and shape . Journal of the Royal Statistical Society , 46D : 323
  • Hirano , K. and Iwase , K. 1989 . Minimum risk scale equivariant estimator -Estimating the mean of an Inverse Gaussian distribution with known coefficient of variation . Communication in Statistics , 18 ( 1 ) : 189 – 197 .
  • Howlader , H. A. 1985 . Approximate Bayes estimation of reliability of two parameter Inverse Gaussian distribution . Communication in Statistics, Theory and Methods , 14 ( 4 ) : 937 – 946 .
  • Iwase , K. and Seto , N. 1983 . UMVUE's for the Inverse Gaussian distribution . Journal of American Statistical Association , 78 : 660 – 663 .
  • Iwase , K. and Seto , N. 1985 . UMVU estimators of the mode and limits of an interval for the Inverse Gaussian distribution . Communication in Statistics, Theory and Methods , 14 : 1151 – 1161 .
  • Iwase , K. 1987 . UMVU estimation for the Inverse Gaussian distribution I (μ, cμ2) with known C . Communication in Statistics , 16 ( 5 ) : 1315 – 1320 .
  • Iyenger , S. and Patwardhan , G. 1988 . Handbook of Statistics , Edited by: Krishnaiah . 7 Academic press .
  • James , W. and Stein , C. (A basic paper on Stein -type estimators) . Proceedings of the 4th Berkeley Symposium on Mathematical Statistics,1 . Berkeley : University of California Press . CA.361–379
  • Jani , P. N. 1991 . A class of shrinkage estimators for the scale parameter of exponential distribution . IEEE Transaction on Reliability , 40 : 60 – 70 .
  • Joshi , S. and Shah , M. 1991 . Estimating the mean of an Inverse Gaussian distribution with known coefficient of variation . Communication in Statistics, Theory and Methods , 20 ( 9 ) : 2907 – 2912 .
  • Korwar , R. M. 1980 . On the UMVUE's of the variance and its reciprocal of an Inverse Gaussian distribution . Journal of American Statistical Association , 75 : 734 – 735 .
  • Kourouklis , S. 1994 . Estimation in the two parameter exponential distribution with prior information . IEEE Transaction on reliability , 43 ( 3 ) : 446 – 450 .
  • Lancaster , A. 1972 . A stochastic model for the duration of a strike . Journal of the Royal Statistical Society, A , 135 : 257 – 271 .
  • Mehta , J. S. and Srinivasan , S. R. 1971 . Estimation of the mean by shrinkage to a point . Journal of American Statistical Association , 66 : 86 – 90 .
  • Padmanabhan , P. 1978 . Application of the Inverse Gaussian distribution in evaluation and estimation of conversion probabilities for convertible securities , Mc.Gill Quebec : University Montreal . MBA research paper
  • Padgett , W. J. 1979 . Confidence bounds on reliability of the Inverse Gaussian model . IEEE Transaction on Reliability , R-28 : 165 – 168 .
  • Padgett , W. J. 1981 . Bayes estimation of reliability for the Inverse Gaussian models . IEEE Transaction on Reliability , R-30 : 384 – 385 .
  • Pandey , B. N. and Malik , H. J. 1987 . Some improved estimators for a measure of dispersion of an Inverse Gaussian distribution . Communication in Statistics, Theory and Methods , A7 ( 11 ) : 3935 – 3949 .
  • Pandey , B. N. and Malik , H. J. 1988 . Some improved estimators for a measure of dispersion of an Inverse Gaussian distribution . Communication in Statistics-Theory and Methods , 17 ( 11 ) : 3935 – 3949 .
  • Pandey , B. N. and Malik , H. J. 1989 . Estimation of the mean and the reciprocal of the mean of the Inverse Gaussian distribution . Communication in Statistics and Simulation , 18 ( 3 ) : 1187 – 1201 .
  • Patel , M. N. 1998 . Progressively censored sample from Inverse Gaussian distribution . Aligarh Journal of Statistics , 17 & 18 : 28 – 34 .
  • Pandit , S. 2004 . Estimation of parameters of Inverse Gaussian distribution with prior information , M.Phil. Thesis Ujjain, (M.P.), , India : Vikram University . submitted to
  • Saxena , S. and Singh , H. P. 2004 . Estimating various measures in Normal population through a single class of estimators . Journal of the Korean Statistical Society , 33 ( 3 ) : 323 – 337 .
  • Schrödinger , E. 1915 . Zur Theorie Der Fall-und Steigversu che an Teilchenmit Brownscher Bewegung . Physikali Sche Zeitschrift , 16 : 289 – 295 .
  • Seshadri , R. 1999 . “ The Inverse Gaussian distribution ” . In Statistical Theory and Application , New York : Springer Verlag .
  • Sen , A. and Khattree , R. 2000 . Revisiting the problem of estimating the Inverse Gaussian parameters . IAPQR Transactions , 25 ( 2 ) : 63 – 79 .
  • Shah , M. M. and Joshi , S. M. 2003 . Bounds for minimum risk scale equivariant and UMVUE estimators . Journal of Indian Statistical Association , 41 ( 1 ) : 105 – 116 .
  • Sheppard , C. W. 1962 . Basic principles of the Tracer methods , New York : Wiley .
  • Singh , H. P. and Shukla , S. K. 2000 . Estimation in the two-parameter Weibull distribution with prior information . IAPQR. Transactions , 25 ( 2 ) : 107 – 117 .
  • Singh , H. P. and Saxena , S. 2001 . Improved estimation in one-parameter Exponential distribution with prior information . Gujarat Statistical Review , 28 ( 1–2 ) : 25 – 35 .
  • Singh , H. P. and Saxena , S. 2002 . Improved estimation of Weibull shape parameter with prior information in censored sampling . IAPQR Transactions , 27 ( 1 ) : 51 – 61 .
  • Singh , H. P. and Pandit , S. 2006 . “ Estimation of shape parameter and measure of dispersion of Inverse Gaussian distribution using prior information ” . In Communicated to Communication in Statistics -Theory and Methods, USA
  • Thompson , J. R. 1968 . Some shrinkage technique for estimating the mean . Journal of American Statistical Association , 63 : 113 – 123 .
  • Travedi , R. J. and Ratani , R. T. 1990 . On estimation of reliability function for Inverse Gaussian distribution with known coefficient of variation . IAPQR, Transactions , 5 ( 2 ) : 29 – 37 .
  • Tweedie , M. C.K. 1945 . Inverse Statistical Variate . Nature , 155 : 453
  • Tweedie , M. C.K. 1956 . Some statistical properties of Inverse Gaussian distribution . Virginia Journal Science , 7 : 160 – 165 .
  • Tweedie , M. C.K. 1957a . Statistical properties of Inverse Gaussian distribution I . Annals of Mathematical Statististics , 28 : 326 – 377 .
  • Tweedie , M. C.K. 1957b . Statistical properties of Inverse Gaussian distribution II . Annals of Mathematical Statististics , 28 : 696 – 705 .
  • Voinov , V. G. 1985 . “Unbiased estimation of powers of the inverse of the mean and related problems” . Sankhyā, B , 47 : 354 – 364 .
  • Wald , A. 1947 . “Sequential Analysis” , New York : John Wiley & Sons .
  • Whitmore , G. A. 1976 . Management applications of the Inverse Gaussian distribution . International Journal of Management Science , 4 : 215 – 223 .
  • Whitmore , G. A. 1979 . An Inverse Gaussian model for labour turnover . Journal of the Royal Statistical Society, A , 142 : 468 – 478 .

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