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GB/T 8055-2009 English PDF

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GB/T 8055-2009: Statistical interpretation of data -- Parameter estimation for gamma distribution (Pearson Ⅲ distribution)
Status: Valid

GB/T 8055: Evolution and historical versions

Standard IDContents [version]USDSTEP2[PDF] delivered inStandard Title (Description)StatusPDF
GB/T 8055-2009English349 Add to Cart 3 days [Need to translate] Statistical interpretation of data -- Parameter estimation for gamma distribution (Pearson Ⅲ distribution) Valid GB/T 8055-2009
GB/T 8055-1987EnglishRFQ ASK 9 days [Need to translate] Statistical interpretation of data Parameter estimation for gamma distribution (Pearson 3 distribution) Obsolete GB/T 8055-1987

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Basic data

Standard ID GB/T 8055-2009 (GB/T8055-2009)
Description (Translated English) Statistical interpretation of data -- Parameter estimation for gamma distribution (Pearson �� distribution)
Sector / Industry National Standard (Recommended)
Classification of Chinese Standard A41
Classification of International Standard 03.120.30
Word Count Estimation 15,128
Date of Issue 2009-10-15
Date of Implementation 2009-12-01
Older Standard (superseded by this standard) GB/T 8055-1987
Quoted Standard GB/T 3358.1; GB/T 3358.2; GB/T 4086.1; GB/T 4086.2
Regulation (derived from) Announcement of Newly Approved National Standards No. 11 of 2009 (No. 151 overall)
Issuing agency(ies) General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China, Standardization Administration of the People's Republic of China
Summary This standard specifies the distribution according to the observed value estimates �� parameters. This standard applies to �� distributed population parameter estimation, measurement, testing, survey data, if by theoretical analysis, experience, judgment or statistical tests, it can reasonably be considered its overall distribution from ��, �� be determined according to the standard distribution parameters point estimates and confidence intervals.

GB/T 8055-2009: Statistical interpretation of data -- Parameter estimation for gamma distribution (Pearson Ⅲ distribution)


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Statistical interpretation of data. Parameter estimation for gamma distribution (Pearson Ⅲ distribution) ICS 03.120.30 A41 National Standards of People's Republic of China Replacing GB/T 8055-1987 Statistical processing and interpretation of data Γ distribution (Pearson Ⅲ distribution) Parameter Estimation Posted 2009-10-15 2009-12-01 implementation Administration of Quality Supervision, Inspection and Quarantine of People's Republic of China Standardization Administration of China released

Table of Contents

Preface Ⅰ Introduction Ⅱ 1 Scope 1 2 Normative references 1 3 Terms, definitions and symbols 1 3.1 Terms and definitions 3.2 Symbols 2 Point 4 Γ Distribution Parameter Estimation 2 4.1 point two-parameter Γ Distribution Parameter Estimation 2 Point 4.2 three-parameter Γ distribution parameter estimation 3 Section 5 two-parameter Γ distribution parameter estimation 4 5.1 m1 parameter confidence interval (m1 > 1) 4 5.2 Parameter Chou confidence interval 4 Appendix A (normative) density function 6

Foreword

"Data processing and interpretation of the statistics" includes the following national standards. Statistical processing and interpretation --- GB/T 3359 statistical data to determine the tolerance interval Statistical interpretation of comparison in the case of two paired observations mean --- GB/T 3361 data Statistical interpretation of Binomial Distribution Reliability sided lower confidence limit --- GB/T 4087 data --- Statistical processing and interpretation binomial distribution parameters GB/T 4088 Estimation and Test Data --- Statistical processing and interpretation of the Poisson distribution parameters GB/T 4089 Estimation and test data --- GB/T 4882 Statistical interpretation of data normality test --- Analyzing and processing GB /statistical processing and interpretation of normal sample outliers T 4883 data --- GB/T 4885 Normal distribution complete reliability lower confidence limit --- GB /statistical processing and interpretation of the mean and variance of normal distribution of data T 4889 Estimation and Testing --- GB Statistical interpretation of normal distribution mean and variance test the efficacy/T 4890 data --- GB /Statistical interpretation Γ distribution (Pearson Ⅲ distribution) parameters T 8055 data estimates --- GB /statistical processing and interpretation of data distribution index T 8056 judgment and sample handling outliers Analyzing and Processing --- GB /statistical processing and interpretation of Type Ⅰ extreme value distribution of the sample outliers T 6380 data --- GB /statistical processing and interpretation of test results of multiple comparisons of data T 10092 --- GB/T 10094 quantile normal confidence limits and coefficient of variation This standard replaces GB/T 8055-1987 "Statistical interpretation Г distribution (Pearson Ⅲ distribution) parameter data estimation." This standard and GB/T 8055-1987 compared to the main changes are as follows. --- According to GB/T 1.1-2000 "Standardization Guide Part 1. Standard structure and write rules," the requirements of the standard format It has been revised; --- In the new revised standard procedure to remove the B block diagram with the original standard appendix; --- In the new revised standard to remove the original standard three-parameter Γ Appendix C Distribution incomplete sample point estimate (fitting method); --- In the new revised standard to remove the original standard Appendix D Application. Appendix A of this standard is a normative appendix. Application of this standard by the National Standardization Technical Committee on statistical methods (SAC/TC21) and focal points. This standard was drafted. Beijing University of Technology, China National Institute of Standardization, Beijing University. The main drafters of this standard. Xue stay root, Ding Wenxing, YU Zhen Fan, Ma Yue-hong, Xie law, Zhong Xiang room. This standard replaces the standards previously issued as follows. --- GB/T 8055-1987.

Introduction

0.1 standard is applicable to the case Γ distribution in compliance observation. Before using this standard, you need to determine or verify whether the observations obey Γ distributed. The traditional method is empirical judgment histogram method; commonly used statistical tests is χ 2 goodness of fit test. Both methods can be Mathematical Statistics Textbooks found. 0.2 standard specifies the method Γ distribution parameter estimation based on observations. Estimating of the point estimates for two-parameter Γ distribution, using There are moments estimation method and maximum likelihood estimation method. Moment estimation method is commonly used method of Parametric point estimation. Because the method is simple, and We have a good estimate of small and large-sample properties, so use common. Maximum likelihood estimation is another common method of Parametric point estimation, It can make full use of information distribution, a more accurate estimate. This standard gives the maximum likelihood estimators Two Algorithms. Approximate Formula Method And Newton iteration method. 0.3 pairs of three-parameter Γ distribution fitting method used in this standard given point parameters estimates. 0.4 In order to obtain the accuracy of estimation parameters, people often need to calculate confidence intervals for parameters. This standard gives the two-parameter distribution Γ Confidence interval of parameters. Statistical processing and interpretation of data Γ distribution (Pearson Ⅲ distribution) Parameter Estimation

1 Scope

This standard specifies the method Γ distribution parameter estimation based on observations. This standard applies to Γ overall distribution parameter estimation; measurement, testing, survey data obtained, if by theoretical analysis, judgment or experience After statistical tests, could reasonably be considered to come from the overall distribution of Γ, is available according to the criteria to determine the point Γ distribution parameters and interval estimation.

2 Normative references

The following documents contain provisions which, through reference in this standard and become the standard terms. For dated references, subsequent Amendments (not including errata content) or revisions do not apply to this standard, however, encourage the parties to the agreement are based on research Whether the latest versions of these documents. For undated reference documents, the latest versions apply to this standard. GB/T 3358.1 Statistics Vocabulary and symbols - Part 1. General statistical terms and terms (GB/T 3358.1- for Probability 2009, ISO 3534-1.2006, IDT) GB/T 3358.2 Statistics Vocabulary and symbols - Part 2. Applied Statistics (GB/T 3358.2-2009, ISO 3534-2.2006, IDT) GB/T 4086.1 Tables for statistical distributions normal GB/T 4086.2 Tables for statistical distributions χ

2 Distribution

3 Terms, definitions and symbols 3.1 Terms and Definitions GB/T 3358.1 and GB/T 3358.2 and established the following terms and definitions apply to this standard. 3.1.1 Third-order central moments cubic ratio of the standard deviation of the population. CS = EX- () [] EX 3/EX- () [] EX Sang () 2 3.1.2 Like observations of a like product Power. Su x0 = Π 3.1.3 And the ratio of the derivative of the function Γ Γ function. Ψ () m1 = Γ () 'm1/Γ () or m1 dΓ () m1 d m1 / Γ () () m1 3.1.4 Interval estimation of parameters [theta] (T0, T1), wherein a statistic limit interval T0, T1, satisfies P [T0 < θ < T1] ≥1-α. Note 1. The degree of confidence reflects the proportion of the long sequence is repeated under the same conditions of random sampling, the confidence interval contains the true value of the parameter. Confidence interval does not reflect the concept of

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