Abstract
In this paper we develop procedures for obtaining confidence intervals for the location and scale parameters of a Pareto distribution as well as upper and lower γ probability tolerance intervals for a proportion β when the observed samples are progressively censored. The intervals are exact, and are obtained by conditioning on the observed values of the ancillary statistics. Since the procedures assume that the shape parameter ν is known, a sensitivity analysis is also carried out to see how the procedures are affected by changes in ν.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggarwala, R. and Balakrishnan, N. (1999). Progressive Censored Samples: Theory and Application, New York: Birkhäuser (to appear).
Aggarwala, R. and Balakrishnan, N. (1998). Some properties of progressive censored order statistics from arbitrary and uniform distributions, with applications to inference and simulation, Journal of Statistical Planning and Inference, 70 35–49.
Aggarwala, R. and Balakrishnan, N. (1997). Some properties of progressive censored order statistics from the Pareto distribution with applications to inference, Statistics and Probability Letters, submitted for publication.
Arnold, B.C. (1983). Pareto Distributions, Fairland, MD: International Cooperative Publishing House.
Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N. (1992). A First Course in Order Statistics, New York: John Wiley & Sons.
. Balakrishnan, N. and Sandhu, R. A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples, Sankhyá, Series B, 58, 1–9.
Childs, A. and Balakrishnan, N. (1997). Conditional inference procedures for the Pareto distribution based on Type-II right censored samples, submitted for publication.
David, H. A. (1981). Order Statistics, second edition, New York: John Wiley & Sons.
Johnson N. L., Kotz S., and Balakrishnan N. (1994). Continuous Univariate Distributions, Vol. 1, second edition, New York: John Wiley & Sons.
Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data, New York: John Wiley & Sons.
Mann, N. R. (1969). Exact three-order-statistic confidence bounds on reliable life for a Weibull model with progressive censoring, Journal of the American Statistical Association, 64 306–315.
Montanari, G. C. and Cacciari, M. (1988). Progressively-censored aging tests on XLPE-insulated cable models, IEEE Transactions on Electrical Insulation, 23 365–372.
Thomas, D. R. and Wilson, W. M. (1972). Linear order statistic estimation for the two-parameter Weibull and Extreme-value distributions from Type-II progressively censored samples, Technometrics, 14 679–691.
Viveros, R. and Balakrishnan, N. (1994). Interval estimation of parameters of life characteristics from progressively censored data, Technometrics, 36 84–91.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Aggarwala, R., Childs, A. (2000). Conditional Inference for the Parameters of Pareto Distributions when Observed Samples are Progressively Censored. In: Balakrishnan, N., Melas, V.B., Ermakov, S. (eds) Advances in Stochastic Simulation Methods. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1318-5_17
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1318-5_17
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7091-1
Online ISBN: 978-1-4612-1318-5
eBook Packages: Springer Book Archive