Prediction in Samples From the Gamma Distribution as Applied to Life Testing

Lingappaiah, G. S.

doi:10.1111/j.1467-842x.1974.tb00910.x

Cited by 16 publications

(10 citation statements)

References 3 publications

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“…This prediction of order statistics in a future sample has been extensively analysed by many authors. For example, Dunsmore [1] and Lingappaiah [9]- [11] deal with this problem from the Bayesian point of view while Faulkenberry [2], Kaminsky [4], Lawless [5] and Lingappaiah [6], [7] treat this problem in the classical sense. In all these works a single sample or a series of samples are considered, all from the same model.…”

Section: Introductionmentioning

confidence: 98%

A study of shifting models in life tests via bayesian approach using semi-or-used priors (SOUPS)

Lingappaiah

1985

Ann Inst Stat Math

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SummaryThis paper analyses the shift in parameter of a life test model. This analysis depends on the prediction of order statistics in future samples based on order statistics in a series of earlier samples in life tests having a general exponential model. While a series of k samples are being drawn, model itself undergoes a change. Firstly, a single shift is considered and the effect of this shift on the variance is discussed. Generalisation with s shifts (s~k) in k samples is also taken up and the semi-or-used priors (SOUPS) have been used to get predictive distributions. Finally, shift after i (i~_k) stages, from exponential to gamma model is considered and for this case effect of the shift on the variance as well as on the Bayesian prediction region (BPR) is analysed along with set of tables.

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Section: Introductionmentioning

confidence: 98%

A study of shifting models in life tests via bayesian approach using semi-or-used priors (SOUPS)

Lingappaiah

1985

Ann Inst Stat Math

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“…Lawless [16], [17] also predicts order statistics in the 391 case of exponential. Lingappaiah [22], [23] deals with this problem in exponential and gamma distributions. Kaminsky [13] gives rigorous bounds for the results of Lawless [16] and Lingappaiah [22].…”

Section: Introductionmentioning

confidence: 99%

Bayesian approach to prediction and the spacings in the exponential distribution

Lingappaiah

1979

Ann Inst Stat Math

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SummaryA series of independent samples are drawn from a general population with positive variation f(x, ~), x>0. Based on the Bayesian approach, a general predictive distribution is given, to predict a statistic in the future sample based on the statistics in the earlier samples (or stages). Few general classes of distributions of this type like KoopmanPitman family, power function family and Burr's class of distributions are considered to show how this procedure works in predicting order statistics in the future sample. Also, the sum of the spacings in the future samples from an exponential population is predicted in terms of similar sum of spacings in the earlier samples. Discussion on the variance of this predictive distribution is dealt with. Finally, an illustrative example with simulated samples from an exponential population gives actual prediction of an order statistic as well as the sum of spacings in the future sample.

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“…Obviously, if r = 0, (11) reduces to (10). Though it is slightly complex to find variance, in general, however if a = 1, k^ = 1, i = 1,...,s in (11), we have…”

Section: Introductionmentioning

confidence: 99%

“…One is .the classical approach based on the independence of statistics and their exact distributions. Such is the case in Lawless [9], Paulkenberry [8], Kaminsky, Luks and Nelson [7 J and also in Lingappaiah [10] , [i 1] . But, another method, is the Bayes approach with posterior distributions and suitable priors.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Approach to the Prediction Problem in Gamma Population

Lingappaiah¹

1978

Demonstratio Mathematica

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Prediction in Samples From the Gamma Distribution as Applied to Life Testing

Abstract: A prediction problem concerning ~emples h m the Te~lanomclti~, Technometrim, 2. 243-262. exponential disbribution with applications in life tasting." 13, 726-730.

Cited by 16 publications

References 3 publications

A study of shifting models in life tests via bayesian approach using semi-or-used priors (SOUPS)

A study of shifting models in life tests via bayesian approach using semi-or-used priors (SOUPS)

Bayesian approach to prediction and the spacings in the exponential distribution

Bayesian Approach to the Prediction Problem in Gamma Population

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