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- 검색키워드
- 저자 : M. Doostparast (검색결과 3 건)
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Statistical Evidence Methodology for Model Acceptance Based on Record Values
M. Doostparast,M. Emadi 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.2
An important role of statistical analysis in science is interpreting ob-served ata as evidence, that is “what do the data say?”. Although standardstatistical methods (hypothesis testing, estimation, condence intervals) areroutinely used for this purpose, the theory behind those methods containsno dened concept of evidence and no answer to the basic question “whenis it correct to say that a given body of data represent evidence supportingone statistical hypothesis against another?” (Royall, 1997).In this article, we use likelihod ratios to measure evidence provided byrecord values in favor of a hypothesis and against an alternative. This hy-pothesis is concerned on mean of an exponential model and prediction offuture record values.AMS 2000 subject classications.Primary 62G10; Secondary 62G30.Keywords. Exponential model, hypothesis testing, likelihod ratio, prediction, recordvalues, statistical evidence.1. IntroductionLet {Xi,i ≥ 1} be a sequence of independent and identically distributedcontinuous random variables having the same distribution as the (population)random variable X. An observationXj will be called an upper record value if itsvalue exceeds that of all previous observations. ThusXj is an (upper) record valueifXj > X i for everyi < j . Let us assume thatXj is observed at timej. Thenthe (upper) record time{Tn,n≥1} sequence is dened in the following manner:T1 = 1 ,with probability 1 and, forn ≥2,Tn = min {j > T n1 :Xj > X Tn 1}.Received August 2005; accepted April 2006.1Corresponding author. Department of Statistics, Ferdowsi University of Mashhad, P. O.Box 91775-1159, Mashhad, Iran (e-mail: doostparast@wali.um.ac.ir)
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STATISTICAL EVIDENCE METHODOLOGY FOR MODEL ACCEPTANCE BASED ON RECORD VALUES
Doostparast M.,Emadi M. The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.2
An important role of statistical analysis in science is interpreting observed data as evidence, that is 'what do the data say?'. Although standard statistical methods (hypothesis testing, estimation, confidence intervals) are routinely used for this purpose, the theory behind those methods contains no defined concept of evidence and no answer to the basic question 'when is it correct to say that a given body of data represent evidence supporting one statistical hypothesis against another?' (Royall, 1997). In this article, we use likelihood ratios to measure evidence provided by record values in favor of a hypothesis and against an alternative. This hypothesis is concerned on mean of an exponential model and prediction of future record values.
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A random model for the scale parameter in the Fréchet populations
Baratnia M.,Doostparast M. 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.2
This paper deals with one-way classifcation analysis when the response variable follows the one-parameter Fréchet distribution and the factor efects are random. The stochastic properties of the response variable are studied in detail. Maximum like-lihood estimations of the model parameters are also given in explicit expressions. Under the square error loss function, the best predictions for the random-efects are derived. Three procedures for testing the hypothesis of population homogeneity are proposed and misspecifcation problem is investigated in a special case. Sev-eral illustrative examples are also given to assess the performances of the proposed model. Findings of this paper may be used in engineering, survival and, longitudinal studies.
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