# On the outstanding elements and record values in the exponential and gamma populations.

• Volume: 32, Issue: 2, page 116-130
• ISSN: 0041-0241

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## Abstract

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Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution of the sum of record values as well as that of a linear combination of record values are obtained for the exponential case. Probability integrals of the sum of record values and the probability integral of the sum of outstanding elements are suggested for all values. Then, the distribution of the n-th record values in a gamma population is put in a closed form. Further, the distribution of the linear combination of the spacings of outstanding elements as well as that of the linear combination of the outstanding elements themselves are obtained. Finally the distribution of a ratio of two record values is obtained.

## How to cite

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Lingappaiah, G. S.. "On the outstanding elements and record values in the exponential and gamma populations.." Trabajos de Estadística e Investigación Operativa 32.2 (1981): 116-130. <http://eudml.org/doc/40663>.

@article{Lingappaiah1981,
abstract = {Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution of the sum of record values as well as that of a linear combination of record values are obtained for the exponential case. Probability integrals of the sum of record values and the probability integral of the sum of outstanding elements are suggested for all values. Then, the distribution of the n-th record values in a gamma population is put in a closed form. Further, the distribution of the linear combination of the spacings of outstanding elements as well as that of the linear combination of the outstanding elements themselves are obtained. Finally the distribution of a ratio of two record values is obtained.},
author = {Lingappaiah, G. S.},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Inferencia bayesiana; Predicción; outstanding elements; gamma populations; exponential distribution; predictive distribution; linear combination of record values; probability integrals; linear combination of spacings of outstanding elements; distribution of ratio of record values; prediction},
language = {eng},
number = {2},
pages = {116-130},
title = {On the outstanding elements and record values in the exponential and gamma populations.},
url = {http://eudml.org/doc/40663},
volume = {32},
year = {1981},
}

TY - JOUR
AU - Lingappaiah, G. S.
TI - On the outstanding elements and record values in the exponential and gamma populations.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1981
VL - 32
IS - 2
SP - 116
EP - 130
AB - Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution of the sum of record values as well as that of a linear combination of record values are obtained for the exponential case. Probability integrals of the sum of record values and the probability integral of the sum of outstanding elements are suggested for all values. Then, the distribution of the n-th record values in a gamma population is put in a closed form. Further, the distribution of the linear combination of the spacings of outstanding elements as well as that of the linear combination of the outstanding elements themselves are obtained. Finally the distribution of a ratio of two record values is obtained.
LA - eng
KW - Inferencia bayesiana; Predicción; outstanding elements; gamma populations; exponential distribution; predictive distribution; linear combination of record values; probability integrals; linear combination of spacings of outstanding elements; distribution of ratio of record values; prediction
UR - http://eudml.org/doc/40663
ER -

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