Skip to main content
SpringerLink
Log in

Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples

  • Regular Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

This paper deals with the preliminary test estimation (PTE) of the parameters of the exponential and Pareto distributions in censored samples. The biases, risk functions, efficiency tables and the graphs for the relative efficiency for the proposed estimators for the parameters of the exponential and Pareto distributions are given. We find that the proposed estimators dominate the corresponding unrestricted (usual) estimators in the neighborhood of null hypothesis. The range of the parameters for which the proposed estimators dominate the corresponding usual estimators for different sample sizes and level of significance are given. The findings of the paper will be useful for the practitioners who are dealing with the censored samples in life testing experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balakrishnan N (1990) On the maximum likelihood estimation of the location and scale parameters of exponential distribution based on multiply Type II censored samples. J Appl Stat 17: 55–61

    Article  Google Scholar 

  • Bancroft TA (1944) On biases in estimation due to use of preliminary tests of significance. Ann Math Stat 15: 190–204

    Article  MATH  MathSciNet  Google Scholar 

  • Bancroft TA (1964) Analysis and inference for incompletely specified models involving the use of preliminary test(s) of significance. Biometrics 20: 427–442

    Article  MATH  MathSciNet  Google Scholar 

  • Benda N (1996) Pre-test estimation and design in the linear model. J Stat Plan Inference 52: 225–240

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen AC, Whitten BJ (1988) Parameter estimation for reliability and life span models. Marcel Dekker, New York

    Google Scholar 

  • Chiou P, Han C-P (1999) Conditional interval estimation of the ratio of various components following rejection of a pre-test. J Stat Comput Simul 63: 105–119

    Article  MATH  MathSciNet  Google Scholar 

  • Davis DJ (1952) The analysis of some failure data. J Am Stat Assoc 47: 113–150

    Article  Google Scholar 

  • Giles JA, Gilies DEA (1993) Pre-test estimation in econometrics: recent developments. J Econ Surv 7: 145–197

    Article  Google Scholar 

  • Han C-P (2002) Influential observations in a preliminary test estimation of the mean. Pak J Stat 18: 321–333

    MATH  Google Scholar 

  • Han C-P, Bancroft TA (1968) On pooling means when variance is unknown. J Am Stat Assoc 63: 1333–1342

    Article  MathSciNet  Google Scholar 

  • Han C-P, Rao CV, Ravichandran J (1977) Inference based on conditional specification: a second bibliography. Commun Stat Theory Methods 17: 1945–1964

    MathSciNet  Google Scholar 

  • Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Judge GG, Bock ME (1978) The statistical implications of pre-test and stein-rule estimators in econometrics. North-Holland, Amsterdam

    MATH  Google Scholar 

  • Kibria BMG, Saleh AKMdE (1993) Performance of shrinkage preliminary test estimator in regression analysis. Jahangirnagar Rev A17: 133–148

    Google Scholar 

  • Kibria BMG, Saleh AKMdE (2005) Comparison between Han-Bancroft and Brook methods to determine the optimal significance level for pre-test estimator. J Probab Stat Sci 3: 293–303

    Google Scholar 

  • Kibria BMG, Saleh AKMdE (2006) Optimum critical value for the pre-test estimators. Commun Stat Theory Methods 35(2): 309–320

    Article  MATH  MathSciNet  Google Scholar 

  • Kulldroff G (1963) Estimation of one or two parameters of the exponential distribution on the basis of suitably chosen order statistics, vol 34. Ann Math Stat 1419–1431

  • Kulldorf G, Vannman K (1973) Estimation of the location and scale parameters of a Pareto distribution by linear functions of order statistics. J Am Stat Assoc 68: 218–227

    Article  Google Scholar 

  • Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New York

    MATH  Google Scholar 

  • Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

    MATH  Google Scholar 

  • Pareto V (1897) Cours d’Economic politique, vol 2 Lausanne: F. Rouqe and Paris: F. Pichon

  • Piegorsch WW (1987) Performance of likelihood based internal estimates for two-parameter exponential samples subject to type 1 censoring. Technometrics 29: 41–49

    Article  MATH  MathSciNet  Google Scholar 

  • Rohatgi VK, Saleh AKMdE (1987) Estimation of the common scale parameter of the two Pareto distributions in censored samples. Naval Res Logistics 34: 235–238

    MATH  MathSciNet  Google Scholar 

  • Saleh AKMdE (1966) Estimation of the parameters of the exponential distribution based on optimum statistics in censored samples. Ann Math Stat 37: 1717–1735

    Article  MathSciNet  Google Scholar 

  • Saleh AKMd (2006) Theory of preliminary test and stein-type estimations with applications. Wiley, New York

    Book  Google Scholar 

  • Saleh AKMd, Kibria BMG (1993) Performances of some new preliminary test ridge regression estimators and their properties. Commun Stat Theory Methods 22: 2747–2764

    Article  MATH  MathSciNet  Google Scholar 

  • Vannman K (1976) Estimators based on order statistics from a Pareto distribution. J Am Stat Assoc 71: 704–708

    Article  MathSciNet  Google Scholar 

  • Williams SL, Ferrigno L, Mora P, Rosmini F, Maraini G (2002) Baseline cataract type and 10-year mortality in the Italian-American case-control study of age-related cataract. Am J Epidemiol 156(2): 127–131

    Article  Google Scholar 

  • Wright FT, Engelhardt M, Bain LJ (1978) Inferences for the two-parameter exponential distribution under type I censored sampling. J Am Stat Assoc 73: 650–655

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Florida International University, Miami, FL, 33199, USA

    B. M. Golam Kibria

  2. Department of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    A. K. Md. E. Saleh

Authors
  1. B. M. Golam Kibria
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Md. E. Saleh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. M. Golam Kibria.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kibria, B.M.G., Saleh, A.K.M.E. Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples. Stat Papers 51, 757–773 (2010). https://doi.org/10.1007/s00362-008-0163-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-008-0163-y

Keywords

Search

Navigation