Maximum observed likelihood prediction of future record values

• Grigoriy Volovskiy ^[1] ; Udo Kamps ^[1]
  1. [1] Rheinisch-Westfälische Technische Hochschule Aachen University

     Rheinisch-Westfälische Technische Hochschule Aachen University

     Städteregion Aachen, Alemania

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 4, 2020, págs. 1072-1097
• Idioma: inglés
• DOI: 10.1007/s11749-020-00701-7
• Texto completo no disponible (Saber más ...)
• Resumen

  • Point prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

• Referencias bibliográficas
  • Ahmadi J, Doostparast M (2006) Bayesian estimation and prediction for some life distributions based on record values. Stat Pap 47(3):373–392
  • Ahsanullah M (1980) Linear prediction of record values for the two parameter exponential distribution. Ann Inst Stat Math 32(1):363–368
  • Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, Hoboken
  • Awad AM, Raqab MZ (2000) Prediction intervals for the future record values from exponential distribution: comparative study. J Stat Comput...
  • Balakrishnan N, Cramer E (2014) The art of progressive censoring. Springer, New York
  • Basak P, Balakrishnan N (2003) Maximum likelihood prediction of future record statistic. In: Lindqvist B, Doksum K (eds) Mathematical and...
  • Bayarri MJ, DeGroot MH (1988) Discussion: auxiliary parameters and simple likelihood functions. In: Berger JO, Wolpert RL (eds) The likelihood...
  • Bayarri MJ, DeGroot MH, Kadane JB (1987) What is the likelihood function? (with discussion). In: Gupta SS, Berger JO (eds) Statistical decision...
  • Berger JO, Wolpert RL (1988) The likelihood principle, 2nd edn. Institute of Mathematical Statistics, Hayward
  • Birnbaum A (1962) On the foundations of statistical inference. J Am Stat Assoc 57(298):269–306
  • Bjørnstad JF (1996) On the generalization of the likelihood function and the likelihood principle. J Am Stat Assoc 91(434):791–806
  • Burkschat M (2009) Linear estimators and predictors based on generalized order statistics from generalized Pareto distributions. Commun Stat...
  • Chandler KN (1952) The distribution and frequency of record values. J R Stat Soc Ser B Stat Methodol 14:220–228
  • Dunsmore IR (1983) The future occurrence of records. Ann Inst Stat Math 35(1):267–277
  • Dziubdziela W, Kopociński B (1976) Limiting properties of the k-th record values. Appl Math (Warsaw) 2(15):187–190
  • Groeneveld RA, Meeden G (1977) The mode, median, and mean inequality. Am Stat 31(3):120–121
  • Gupta RC, Kirmani SNUA (1988) Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probab Eng Inf Sci...
  • Kadri T, Smaili K (2014) The exact distribution of the ratio of two independent hypoexponential random variables. Br J Math Comput Sci 4(18):2665–2675
  • Kaminsky KS (1987) Prediction of ibnr claim counts by modelling the distribution of report lags. Insur Math Econ 6(2):151–159
  • Kaminsky KS, Rhodin LS (1985) Maximum likelihood prediction. Ann Inst Stat Math 37(3):507–517
  • Kamps U (1995) A concept of generalized order statistics. J Stat Plan Inference 48(1):1–23
  • Keseling C (1999) Charakterisierung von Wahrscheinlichkeitsverteilungen durch verallgemeinerte Ordnungsstatistiken. Ph.D. thesis, RWTH Aachen...
  • Madi MT, Raqab MZ (2004) Bayesian prediction of temperature records using the Pareto model. Environmetrics 15(7):701–710
  • Nadar M, Kızılaslan F (2015) Estimation and prediction of the Burr type XII distribution based on record values and inter-record times. J...
  • Nagaraja HN (1986) Comparison of estimators and predictors from two-parameter exponential distribution. Sankhyā Ser B 48(1):10–18
  • Nayak TK, Kundu S (2002) Some remarks on generalizations of the likelihood function and the likelihood principle. In: Balakrishnan N (ed)...
  • Nevzorov VB (2001) Records: mathematical theory. American Mathematical Society, Providence
  • Raqab MZ (2001) Optimal prediction intervals for the exponential distribution based on generalized order statistics. IEEE Trans Reliab 50(1):112–115
  • Raqab MZ (2007) Exponential distribution records: different methods of prediction. In: Ahsanullah M, Raqab MZ (eds) Recent developments in...
  • Raqab MZ, Ahmadi J, Doostparast M (2007) Statistical inference based on record data from Pareto model. Statistics 41(2):105–118
  • Razmkhah M, Ahmadi J (2013) Pitman closeness of current k-records to population quantiles. Stat Probab Lett 83(1):148–156
  • Ross SM (2014) Introduction to probability models. Academic Press, Oxford
  • Volovskiy G (2018) Likelihood-based prediction in models of ordered data. Ph.D. thesis, RWTH Aachen University