NF ISO 16269-8
Statistical interpretation of data - Part 8 : determination of prediction interval
ISO 16269-8:2004 specifies methods of determining prediction intervals for a single continuously distributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence. Three different types of population are considered, namely normally distributed with unknown standard deviation, normally distributed with known standard deviation, and continuous but of unknown form. For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided prediction intervals. In all cases, there is a choice from among six confidence levels. The methods presented for types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation may also be used for non-normally distributed populations that can be transformed to normality. For types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation, the tables presented in ISO 16269-8:2004 are restricted to prediction intervals containing all the further m sampled values of the variable. For types of population that are continuous but of unknown form, the tables relate to prediction intervals that contain at least m - r of the next m values, where r takes values from 0 to 10 or 0 to m - 1, whichever range is smaller. For normally distributed populations, a procedure is also provided for calculating prediction intervals for the mean of m further observations.
ISO 16269-8:2004 specifies methods of determining prediction intervals for a single continuously distributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence.
Three different types of population are considered, namely normally distributed with unknown standard deviation, normally distributed with known standard deviation, and continuous but of unknown form.
For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided prediction intervals. In all cases, there is a choice from among six confidence levels.
The methods presented for types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation may also be used for non-normally distributed populations that can be transformed to normality.
For types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation, the tables presented in ISO 16269-8:2004 are restricted to prediction intervals containing all the further m sampled values of the variable. For types of population that are continuous but of unknown form, the tables relate to prediction intervals that contain at least m - r of the next m values, where r takes values from 0 to 10 or 0 to m - 1, whichever range is smaller.
For normally distributed populations, a procedure is also provided for calculating prediction intervals for the mean of m further observations.
- Avant-proposv
- Introductionvi
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1 Domaine d'application1
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2 Références normatives1
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3 Termes, définitions et symboles2
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3.1 Termes et définitions2
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3.2 Symboles2
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4 Intervalles de prédiction3
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4.1 Généralités3
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4.2 Comparaison avec d'autres types d'intervalles statistiques4
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5 Intervalles de prédiction relatifs à toutes les observations d'un nouvel échantillon d'une population de distribution normale dont l'écart-type est inconnu5
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5.1 Intervalles unilatéraux5
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5.2 Intervalles bilatéraux symétriques5
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5.3 Intervalles de prédiction relatifs à des populations non normales qui peuvent être transformées à la normalité5
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5.4 Détermination d'un effectif approprié, n, de l'échantillon initial, pour une valeur maximale donnée du coefficient d'intervalle de prédiction, k6
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5.5 Détermination de l'intervalle de confiance correspondant à un intervalle de prédiction donné6
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6 Intervalles de prédiction pour toutes les observations d'un nouvel échantillon d'une population de distribution normale dont l'écart-type est connu7
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6.1 Intervalles unilatéraux7
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6.2 Intervalles bilatéraux symétriques7
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6.3 Intervalles de prédiction pour des populations non normales qui peuvent être transformées à la normalité7
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6.4 Détermination d'un effectif approprié, n, de l'échantillon initial pour une valeur donnée de k8
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6.5 Détermination du niveau de confiance correspondant à un intervalle de prédiction donné8
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7 Intervalles de prédiction relatifs à la moyenne d'un nouvel échantillon d'une population de distribution normale8
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8 Intervalles de prédiction non paramétriques8
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8.1 Généralités8
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8.2 Intervalles unilatéraux9
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8.3 Intervalles bilatéraux9
- Annexe A (normative) Tableaux des coefficients d'intervalles de prédiction unilatéraux, k, pour un écart-type inconnu de la population13
- Annexe B (normative) Tableaux des coefficients d'intervalles de prédiction bilatéraux, k, pour un écart-type inconnu de la population31
- Annexe C (normative) Tableaux de coefficients d'intervalles de prédiction unilatéraux, k, pour un écart-type connu de la population49
- Annexe D (normative) Tableaux de coefficients d'intervalles de prédiction bilatéraux, k, pour un écart-type connu de la population67
- Annexe E (normative) Tableaux d'effectifs d'échantillon pour les intervalles de prédiction non paramétriques unilatéraux85
- Annexe F (normative) Tableaux d'effectifs d'échantillon pour les intervalles de prédiction non paramétriques bilatéraux91
- Annexe G (normative) Interpolation dans les tableaux97
- Annexe H (informative) Théorie statistique sous-jacente aux tableaux101
- Bibliographie108
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