Inferential Procedures on the Shape Parameter of a Gamma Distribution from Censored Data

References

• Bain , L. J. and Engelhardt , M. E. 1975 . “A Two-Moment Chi-Square Approximation for the Statistic log ,” . Journal of the American Statistical Association , 70 : 948 – 950 .
   Web of Science ®Google Scholar
• Barlow , R. E. and Proschan , F. 1965 . Mathematical Theory of Reliability , New York : John Wiley & Sons .
   Google Scholar
• Basu , D. 1955 . “On Statistics Independent of a Complete Sufficient Statistic” . Sankhyā, Ser. A , 15 : 377 – 380 .
   Google Scholar
• Bishop , D. J. and Nair , U. S. 1939 . “A Note on Certain Methods of Testing for the Homogeneity of a Set of Estimated Variances” . Journal of the Royal Statistical Society, Ser. B, Supplement , 6 ( 1 ) : 89 – 99 .
   Google Scholar
• Box , G. E.P. 1954 . “Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in One-Way Classification” . Annals of Mathematical Statistics , 25 : 290 – 302 .
   Google Scholar
• Chernoff , H. , Gastwirth , J. L. and Johns , M. V. 1967 . “Asymptotic Distribution of Linear Combinations of Functions of Order Statistics With Applications to Estimation” . Annals of Mathematical Statistics , 38 : 52 – 72 .
   Google Scholar
• Engelhardt , Max . 1975a . “Simple Linear Estimation of the Parameters of the Logistic Distribution From a Complete or Censored Sample” . Journal of the American Statistical Association , 70 : 899 – 902 .
   Web of Science ®Google Scholar
• Engelhardt , Max . 1975b . “On Simple Estimation of the Parameters of the Weibull or Extreme-Value Distribution” . Technometrics , 17 : 369 – 374 .
   Web of Science ®Google Scholar
• Engelhardt , Max and Bain , Lee J. 1977 . “Simplified Statistical Procedures for the Weibull or Extreme-Value Distribution” . Technometrics , 19 : 323 – 331 .
   Web of Science ®Google Scholar
• Glaser , R. E. 1976 . “The Ratio of the Geometric Mean to the Arithmetic Mean for a Random Sample From a Gamma Distribution” . Journal of the American Statistical Association , 71 : 480 – 487 .
   Web of Science ®Google Scholar
• Guenther , William C. 1972 . “On the Use of the Incomplete Gamma Table to Obtain Unbiased Tests and Unbiased Confidence Intervals for the Variance of a Normal Distribution” . The American Statistician , 26 : 31 – 34 .
   Web of Science ®Google Scholar
• Gupta , S. S. 1960 . “Order Statistics From the Gamma Distribution” . Technometrics , 2 : 243 – 262 .
   Google Scholar
• Gupta , S. S. and Groll , P. A. 1961 . “Gamma Distribution in Acceptance Sampling Based on Life Tests” . Journal of the American Statistical Association , 56 : 942 – 970 .
   Web of Science ®Google Scholar
• Hájek , J. and Šidák , Z. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Harter , H. L. 1969 . Order Statistics and Their Use in Testing and Estimation , Vol. 2 , Aerospace Research Laboratories, Office of Aerospace Research, U.S. Air Force .
   Google Scholar
• Harter , H. L. and Moore , A. H. 1965 . “Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations From Complete and From Censored Samples” . Technometrics , 7 : 639 – 643 .
   Web of Science ®Google Scholar
• Hildebrand , F. B. 1956 . Introduction to Numerical Analysis , New York : McGraw-Hill Book Co. International Mathematical . and Statistical Libraries (1977), “IMSL-Library 1,” Houston, Tex
   Google Scholar
• Lindley , D. V. , East , D. A. and Hamilton , P. A. 1960 . “Tables for Making Inference About the Variance of a Normal Distribution” . Biometrika , 47 : 433 – 437 .
   Web of Science ®Google Scholar
• Linhart , H. 1965 . “Approximate Confidence Limits for the Coefficient of Variation of Gamma Distributions” . Biometrics , 31 : 737
   Google Scholar
• Mann , N. R. and Grubbs , F. E. 1974 . “Chi-Square Approximations for Exponential Parameters, Prediction Intervals and Beta Percentiles” . Journal of the American Statistical Association , 69 : 654 – 661 .
   Web of Science ®Google Scholar
• Mann , N. R. , Grubbs , F. E. , Schafer , R. E. and Singpurwalla , N. D. 1974 . Methods for Statistical Analysis of Reliability and Life Data , New York : John Wiley & Sons .
   Google Scholar
• Pachares , J. 1961 . “Tables for Unbiased Tests on the Variance of a Normal Population” . Annals of Mathematical Statistics , 32 : 84 – 87 .
   Google Scholar
• Patnaik , P. B. 1949 . “The Non-Central x 2 F-Distributions and Their Applications” . Biometrika , 36 : 202 – 232 .
   PubMed Web of Science ®Google Scholar
• Rao , C. R. 1965 . Linear Statistical Inference and Its Applications , New York : John Wiley & Sons .
   Google Scholar
• Sarhan , A. E. and Greenberg , B. G. 1962 . Contributions to Order Statistics , New York : John Wiley & Sons .
   Google Scholar
• Shorack , G. R. 1972 . “The Best Test of Exponentiality Against Gamma Alternatives” . Journal of the American Statistical Association , 67 : 213 – 214 .
   Web of Science ®Google Scholar
• Tate , R. F. and Klett , G. W. 1959 . “Optimal Confidence Intervals for the Variance of a Normal Distribution” . Journal of the American Statistical Association , 54 : 674 – 682 .
   Web of Science ®Google Scholar
• Wilk , M. B. , Gnanadesikan , R. and Huyett , M. J. 1962 . “Estimamation of Parameters of the Gamma Distribution Using Order Statistics” . Biometrika , 49 : 525 – 535 .
   Web of Science ®Google Scholar