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Sequential Analysis
Design Methods and Applications
Volume 37, 2018 - Issue 1
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Original Articles

Two-stage procedures for the bounded risk point estimation of the parameter and hazard rate in two families of distributions

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Pages 69-89 | Received 22 Apr 2017, Accepted 18 Dec 2017, Published online: 08 Mar 2018

References

  • Ahsanullah, M. (1980). Linear Prediction of Record Values for the Two Parameter Exponential Distribution, Annals of Institute of Statistical Mathematics 32: 363–368.
  • Burr, I. W. (1942). Cumulative Frequency Functions, Annals of Mathematical Statistics 13: 215–232.
  • Chaturvedi, A. and Alam, Md. W. (2010). UMVUE and MLE in a Family of Lifetime Distributions, Journal of Indian Statistical Association 48: 189–213.
  • Chen, Z. (2000). A New Two-Parameter Lifetime Distribution with Bathtub Shape or Increasing Failure Rate Function, Statistics & Probability Letters 49: 155–161.
  • Cislak, P. J. and Burr, I. W. (1968). On a General System of Distributions; I. Its Curve-Shape Characteristics; II. The Sample Median, Journal of American Statistical Association 63: 627–635.
  • Davis, D. J. (1952). The Analysis of Some Failure Data, Journal of American Statistical Association 47: 113–150.
  • Gurvich, A. T., Dibenedetto, A. T., and Rande, S. V. (1997). A New Statistical Distribution for Characterizing the Random Strength of Brittle Materials, Journal of Materials Sciences 32: 2559–2564.
  • Isogai, E. and Uno, C. (1994). Sequential Estimation of a Parameter of an Exponential Distribution, Annals of Institute of Statistical Mathematics 46: 77–82.
  • Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions—I, New York: Wiley.
  • Khan, R. U. and Zia, B. (2009). Recurrence Relations for Single and Product Moments of Record Values from Gompertz Distribution and a Characterization, World Applied Sciences Journal 7: 1331–1334.
  • Kleiber, C. (2004). Lorenz Ordering of Order Statistics from Log-Logistic and Related Distributions, Journal of Statistical Planning and Inference 120: 13–19.
  • Lai, C. D., Xie, M., and Murthy, D. N. P. (2003). Modified Weibull Model, IEEE Transactions Reliability 52: 33–37.
  • Ljubo, M. (1965). Curves and Concentration Indices for Certain Generalized Pareto Distributions, Statistical Review 15: 257–260.
  • Lomax, K. S. (1954). Business Failures. Another Example of the Analysis of Failure Data, Journal of American Statistical Association 49: 847–852.
  • Mahmoud, M. A. W. and Al-Nagar, H.Sh. (2009). On Generalized Order Statistics from Linear Exponential Distribution and Its Characterization, Statistical Papers 50: 407–418.
  • Mahmoudi, E. and Lalehzari, R. (2017). Bounded Risk Estimation of the Hazard Rate Function of the Exponential Distribution: Two-Stage Procedure, Sequential Analysis 36: 38–54.
  • Mahmoudi, E. and Roughani, G. (2015). Bounded Risk Estimation of the Scale Parameter of a Gamma Distribution in a Two-Stage Sampling Procedure, Sequential Analysis 34: 25–38.
  • Moore, A. H. and Bilikam, J. E. (1978). Bayesian Estimation of Parameters of Life Distributions and Reliability from Type II Censored Samples, IEEE Transactions Reliability 27: 64–67.
  • Mukhopadhyay, N. (1980). A Consistent and Asymptotically Efficient Two-Stage Procedure to Construct Fixed-Width Confidence Interval for the Mean, Metrika 27: 281–284.
  • Mukhopadhyay, N. (1994). Improved Sequential Estimation of Means of Exponential Distributions, Annals of Institute of Statistical Mathematics 46: 509–519.
  • Mukhopadhyay, N. and Datta, S. (1995). On Fine-Tuned Bounded Risk Sequential Point Estimation of the Mean of an Exponential Distribution, South African Statistical Journal 29: 9–27.
  • Mukhopadhyay, N. and Pepe, W. (2006). Exact Bounded Risk Estimation When the Terminal Sample Size and Estimator Are Dependent: The Exponential Case, Sequential Analysis 25: 85–101.
  • Nakagami, M. (1960). The m-Distribution - A General Formulation of Intensity Distribution of Rapid Fading, in Statistical Method in Radio Wave Propagation, W. C. Hoffman, ed., pp. 3–36, Oxford: Pergamon Press.
  • Nikulin, M. and Haghighi, F. (2006). A Chi-Squared Test for the Generalized Power Weibull Family for the Head-and-Neck Cancer Censored Data, Journal of Mathematical Sciences 133: 1333–1341.
  • Patel, J. K., Kapadia, C. H., and Owen, D. B. (1976). Handbook of Statistical Distributions, New York: Dekker.
  • Rohtagi, V. K. and Saleh, A. K. Md. E. (2012). An Introduction to Probability and Statistics, second edition, New York: Wiley.
  • Roughani, G. and Mahmoudi, E. (2015). Exact Risk Evaluation of the Two-Stage Estimation of the Gamma Scale Parameter under Bounded Risk Constraint, Sequential Analysis 34: 387–405.
  • Sinha, S. K. (1986). Reliability and Life Testing, New Delhi: Wiley Eastern.
  • Starr, N. and Woodroofe, M. (1972). Further Remarks on Sequential Estimation: The Exponential Case, Annals of Mathematical Statistics 43: 1147–1154.
  • Stein, C. (1945). A Two Sample Test for a Linear Hypothesis Whose Power Is Independent of the Variance, Annals of Mathematical Statistics 16: 243–258.
  • Stein, C. (1949). Some Problems in Sequential Estimation (abstract), Econometrica 17: 77–78.
  • Stoner, E. G., Edie, D. D., and Durham, S. D. (1994). An End-Effect Model for the Single-Filament Tensile Test, Journal of Materials Sciences 29: 6561–6574.
  • Tadikamalla, P. R. (1980). A Look at the Burr and Related Distributions, International Statistical Review 48: 337–344.
  • Takada, Y. (1986). Non-Existence of Fixed Sample Size Procedures for Scale Families, Sequential Analysis 5: 93–101.
  • Takada, Y. and Nagata, Y. (1992). Fixed-Width Sequential Confidence Interval for the Mean of a Gamma Distribution, Journal of Statistical Planning and Inference 44: 277–289.
  • Tyagi, R. K. and Bhattacharya, S. K. (1989). A Note on the MVU Estimation of Reliability for the Maxwell Failure Distribution, Estadistica 41: 73–79.
  • Uno, C., Isogai, E., and Lim, D. L. (2004). Sequential Point Estimation of a Function of the Exponential Scale Parameter, Austrian Journal of Statistics 33: 281–291.
  • Voda, V. G. (1978). Concerning an Application of the Weibull Distribution to Reliability Aspects in Metrology, Metrologia Aplicată 25: 123–124.
  • Woodroofe, M. (1977). Second-Order Approximations for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.
  • Xie, M. and Lai, C. D. (1995). Reliability Analysis Using an Additive Weibull Model with Bathtub-Shaped Failure Rate Function, Reliability Engineering and System Safety 52: 87–93.
  • Xie, M., Tang, Y., and Goh, T. N. (2002). A Modified Weibull Extension with Bathtub-Shaped Failure Rate Function, Reliability Engineering and System Safety 76: 279–285.
  • Zacks, S. (2009a). The Exact Distributions of the Stopping Times and Their Functionals in Two-Stage and Sequential Fixed-Width Confidence Intervals of the Exponential Parameter, Sequential Analysis 28: 69–81.
  • Zacks, S. (2009b). Stage-Wise Adaptive Designs, New York: Wiley.
  • Zacks, S. (2017). Sample Path Analysis and Distributions of Boundary Crossing Times, New York: Wiley.
  • Zacks, S. and Khan, A. (2011). Two-Stage and Sequential Estimation of the Scale Parameter of a Gamma Distribution with Fixed-Width Intervals, Sequential Analysis 30: 297–307.
  • Zacks, S. and Mukhopadhyay, N. (2006a). Bounded Risk Estimation of the Exponential Parameter in a Two-Stage Sampling, Sequential Analysis 25: 437–452.
  • Zacks, S. and Mukhopadhyay, N. (2006b). Exact Risks of Sequential Point Estimators of the Exponential Parameter, Sequential Analysis 25: 203–220.

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