Abstract
Several prediction problems for progressively Type-II censored data are considered. This includes prediction of progressively censored lifetime as well as prediction of future observations. After introducing several concepts of point prediction, applications to exponential, extreme value, normal, and Pareto distributions are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdel-Aty Y, Franz J, Mahmoud MAW (2007) Bayesian prediction based on generalized order statistics using multiply type-II censoring. Statistics 41:495–504
Ahmadi J, MirMostafaee SM, Balakrishnan N (2012) Bayesian prediction of k-record values based on progressively censored data from exponential distribution. J Stat Comput Simul 82:51–62
AL-Hussaini EK, Ahmad AEBA (2003) On Bayesian predictive distributions of generalized order statistics. Metrika 57:165–176
Alam K (1972) Unimodality of the distribution of an order statistic. Ann Math Stat 43: 2041–2044
Ali Mousa MAM (2001) Inference and prediction for Pareto progressively censored data. J Stat Comput Simul 71:163–181
Ali Mousa MAM, Al-Sagheer S (2005) Bayesian prediction for progressively type-II censored data from the Rayleigh model. Comm Stat Theory Meth 34:2353–2361
Ali Mousa MAM, Jaheen ZF (2002a) Bayesian prediction for progressively censored data from the Burr model. Stat Papers 43:587–593
Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Birkhäuser, Boston
Balakrishnan N, Rao CR (1997) Large-sample approximations to the best linear unbiased estimation and best linear unbiased prediction based on progressively censored samples and some applications. In: Panchapakesan S, Balakrishnan N (eds) Advances in statistical decision theory and applications. Birkhäuser, Boston, pp 431–444
Balakrishnan N, Burkschat M, Cramer E (2008a) Best linear equivariant estimation and prediction in location-scale families. Sankhyā Ser B 70:229–247
Barlow RE, Proschan F (1966) Inequalities for linear combinations of order statistics from restricted families. Ann Math Stat 37:1574–1592
Basak I, Balakrishnan N (2009) Predictors of failure times of censored units in progressively censored samples from normal distribution. Sankhyā 71-B:222–247
Basak I, Basak P, Balakrishnan N (2006) On some predictors of times to failure of censored items in progressively censored samples. Comput Stat Data Anal 50:1313–1337
Burkschat M (2010) Linear estimators and predictors based on generalized order statistics from generalized Pareto distributions. Comm Stat Theory Meth 39:311–326
Christensen R (2011) Plane answers to complex questions: the theory of linear models, 4th edn. Springer, New York
Cohen AC (1951) Estimating parameters of logarithmic-normal distributions by maximum likelihood. J Am Stat Assoc 46:206–212
Cohen AC, Whitten BJ (1988) Parameter estimation in reliability and life span models. Marcel Dekker, New York
Cramer E (2004) Logconcavity and unimodality of progressively censored order statistics. Stat Probab Lett 68:83–90
Cramer E, Kamps U (2001a) Estimation with sequential order statistics from exponential distributions. Ann Inst Stat Math 53:307–324
Dharmadhikari S, Joag-dev K (1988) Unimodality, convexity, and applications. Academic, Boston
Doganaksoy N, Balakrishnan N (1997) A useful property of best linear unbiased predictors with applications to life-testing. Am Stat 51:22–28
Fernández AJ (2004b) One- and two-sample prediction based on doubly censored exponential data and prior information. TEST 13:403–416
Fernández AJ (2009) Bayesian estimation and prediction based on Rayleigh sample quantiles. Qual Quant 44:1–10
Goldberger AS (1962) Best linear unbiased prediction in the generalized linear regression model. J Am Stat Assoc 57:369–375
Huang JS, Ghosh M (1982) A note on strong unimodality of order statistics. J Am Stat Assoc 77:929–930
Huang JS, Ghosh M (1983) Corrigenda: “a note on strong unimodality of order statistics” [J Am Stat Assoc (1982) 77(380):929–930]. J Am Stat Assoc 78:1008
Ishii G (1978) Tokeiteki Yosoku (statistical prediction). In: Basic Sugaku, vol 7. Gendai-Sugakusha, Tokyo (in japanese)
Kambo N (1978) Maximum likelihood estimators of the location and scale parameters of the exponential distribution from a censored sample. Comm Stat Theory Meth 7:1129–1132
Kaminsky KS, Nelson PI (1975) Best linear unbiased prediction of order statistics in location and scale families. J Am Stat Assoc 70:145–150
Kaminsky KS, Rhodin L (1985) Maximum likelihood prediction. Ann Inst Stat Math 37:507–517
Kamps U, Cramer E (2001) On distributions of generalized order statistics. Statistics 35:269–280
Kim C, Han K (2009) Estimation of the scale parameter of the Rayleigh distribution under general progressive censoring. J Korean Stat Soc 38:239–246
Lawless JF (1971) A prediction problem concerning samples from the exponential distribution, with application in life testing. Technometrics 13:725–730
Madi MT, Raqab MZ (2009) Bayesian inference for the generalized exponential distribution based on progressively censored data. Comm Stat Theory Meth 38:2016–2029
Mahalanobis PC, Bose SS, Ray PR, Banerji SK (1934) Tables of random samples from a normal population. Sankhyā 1:289–328
Mohie El-Din MM, Shafay AR (2013) One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data. Stat Papers 54:287–307
Pradhan B, Kundu D (2009) On progressively censored generalized exponential distribution. TEST 18:497–515
Raqab MZ, Asgharzadeh A, Valiollahi R (2010) Prediction for Pareto distribution based on progressively Type-II censored samples. Comput Stat Data Anal 54:1732–1743
Schenk N, Burkschat M, Cramer E, Kamps U (2011) Bayesian estimation and prediction with multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions. J Stat Plan Infer 141:1575–1587
Takada Y (1981) Relation of the best invariant predictor and the best unbiased predictor in location and scale families. Ann Stat 9:917–921
Takada Y (1991) Median unbiasedness in an invariant prediction problem. Stat Probab Lett 12:281–283
Thomas DR, Wilson WM (1972) Linear order statistic estimation for the two-parameter Weibull and extreme value distribution from Type-II progressively censored samples. Technometrics 14:679–691
Tietjen GL, Kahaner DK, Beckman RJ (1977) Variances and covariances of the normal order statistics for sample sizes 2 to 50. In: Selected tables in mathematical statistics, vol 5. American Mathematical Society, Providence, pp 1–73
Wu SJ, Chen DH, Chen ST (2006a) Bayesian inference for Rayleigh distribution under progressive censored sample. Appl Stoch Models Bus Ind 22:269–279
Zacks S (1971) The theory of statistical inference. Wiley, New York
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Balakrishnan, N., Cramer, E. (2014). Point Prediction from Progressively Type-II Censored Samples. In: The Art of Progressive Censoring. Statistics for Industry and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4807-7_16
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4807-7_16
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-0-8176-4806-0
Online ISBN: 978-0-8176-4807-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)