Statistical interpretation of data Estimation and hypothesis test of parameter in Poisson distribution

This standard is integrated on the basis of GB/T 4087.1-1983 "Point estimation of binomial distribution parameters for statistical processing and interpretation of data", GB/T 4087.2-1983 "Interval estimation of binomial distribution parameters for statistical processing and interpretation of data" and GB/T 4088-1983 "Testing of binomial distribution parameters for statistical processing and interpretation of data". This standard is based on the Poisson distribution population and specifies the methods of point estimation, interval estimation and testing of parameters. This standard can be used when there is sufficient reason to believe that the population obeys the Poisson distribution. This standard replaces GB/T 4087.1-1983, GB/T 4087.2-1983 and GB/T 4088-1983. Compared with GB/T4087.1-1983, GB/T4087.2-1983 and GB/T4088-1983, the changes in the technical content of this standard mainly include: --- The standard format has been modified according to the requirements of GB/T1.1-2000 "Guidelines for Standardization Part 1: Structure and Writing Rules of Standards"; --- Added P value test. GB/T 4089-2008 Statistical processing and interpretation of data Estimation and test of Poisson distribution parameters GB/T4089-2008 standard download decompression password: www.bzxz.net
This standard is based on the Poisson distribution population and specifies the methods of point estimation, interval estimation and test of parameters. This standard can be used when there is sufficient reason to believe that the population obeys the Poisson distribution.
This standard is integrated on the basis of GB/T4089-1983 "Statistical processing and interpretation of data - Estimation of Poisson distribution parameters" and GB/T4090-1983 "Statistical processing and interpretation of data - Test of Poisson distribution parameters". This standard replaces GB/T4089-1983 and GB/T4090-1983. Compared with GB/T4089-1983 and GB/T4090-1983, the changes in technical contents of this standard mainly include:
--- Added terms, symbols and definitions;
--- Added P value test in Appendix C.
Appendix A of this standard is a normative appendix, and Appendix B and Appendix C are both informative appendices.
This standard is proposed by China National Institute of Standardization.
This standard is under the jurisdiction of the National Technical Committee for the Application of Statistical Methods.
The drafting organizations of this standard are: China National Institute of Standardization, Guangzhou Product Quality Supervision and Inspection Institute, Peking University, Wuxi Product Quality Supervision and Inspection Institute, Fuzhou Chunlun Tea Co., Ltd. The
main drafters of this standard are: Yu Zhenfan, Ding Wenxing, Deng Suixing, Fang Xiangzhong, Chen Huaying, Chen Yuzhong, Fu Tianlong.
The previous versions of the standards replaced by this standard are:
---GB/T4089-1983;
---GB/T4090-1983.
The clauses in the following documents become the clauses of this standard through reference in this standard. For all dated referenced documents, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, the parties to the agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For all undated referenced documents, the latest versions are applicable to this standard.
GB/T4086.1 Numerical table of statistical distribution Normal distribution
GB/T4086.2 Numerical table of statistical distribution χ2 distribution
ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability
ISO3534-2:2006 Statistical vocabulary and symbols Part 2: Applied statistics
Foreword III
Introduction IV
1 Scope 1
2 Normative references 1
3 Terms, definitions and symbols 1
3.1 Terms and definitions 1
3.2 Symbols 1
4 Parameter estimation 2
4.1 Point estimation 2
4.2 Interval estimation 2
5 Tests on the parameters of the Poisson distribution 5
5.1 Null hypothesis and alternative hypothesis 5
5.2 Two-sided test H0:λ=λ0 H1:λ≠λ0 5
5.3 One-sided test H0:λ≤λ0 H1:λ>λ0 6
5.4 One-sided test H0:λ≥λ0 H1:λ<λ0 7
Appendix A (Normative) Two types of errors in significance tests 8
Appendix B (Informative) Bayesian estimation method for interval estimation 12
Appendix C (Informative) Equivalent test method 13

ICS 03.120.30
National Standard of the People's Republic of China
GB/T 40892008
Replaces GB/14089—1983, GB/T40901983Statistical interpretation of data--Estimation and hypothesis test of parameter in poisson distributionPublished on 16 July 2008
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of ChinaAdministration of Standardization of the People's Republic of China
Implementation on 1 January 2009
1 Scope
Normative references
3 Terms, definitions and symbols·
3. 1 Terms and definitions
3.2 Symbols
4 Parameter estimation
4.1 Point estimation...
4.2 Interval estimation
5 Tests on parameters of Poisson distributionwwW.bzxz.Net
5.1 Null hypothesis and alternative hypothesis
5.2 Two-sided test H:^a
5.3 One-sided test
5.4 One-sided test H:>a
Appendix A (Normative Appendix)
Appendix B (Informative Appendix)
Appendix C (Informative Appendix)
Two types of errors in significance tests
Bessie estimation method for interval estimation
Equivalent test methods
GB/T 4089-2008
GB/T 4089--2008
This standard is integrated on the basis of GB/T4089-1983 "Statistical processing and interpretation of data - Estimation of Poisson distribution parameters" and GB/T1090-1983 "Statistical processing and interpretation of data - Test of Poisson distribution parameters". This standard replaces GB/T4089-1983 and GB/T4090-1983. Compared with GB/T4089-1983 and GB/T4090-1983, the changes in technical content of this standard mainly include:
- Added terms, symbols and definitions;
- Added P value test in Appendix C.
Appendix A of this standard is a normative appendix, and Appendix B and Appendix C are both informative appendices. This standard is proposed by the China National Institute of Standardization. This standard is under the jurisdiction of the National Technical Committee for the Application of Statistical Methods. The drafting units of this standard are: China National Institute of Standardization and Chemical Technology, Guangzhou Product Quality Supervision and Inspection Institute, Peking University, Wushi Product Quality Supervision and Inspection Institute, Fuzhou Chunlun Tea Co., Ltd. The main drafters of this standard are Yu Zhenfan, Ding Wenxing, Deng Suixing, Fang Xiangzhong, Chen Huaying, Chen Yuzhong, and Fu Tianlong. The previous versions of the standards replaced by this standard are: GB/T 4089---1983;
GB/T 4090—1983,
Hepinchengban.com
GB/T 4089—2008
Scientific research, industrial and agricultural manufacturing, and management work are inseparable from data, and the organization, analysis, and interpretation of these data are inseparable from statistical methods. Statistics is a discipline that studies the organization, analysis, and correct interpretation of digital data. People obtain various digital data from different sources. These digital data are usually disorganized and must be sorted and simplified before they can be used. Using perfect statistical methods, data can be sorted and arranged in an orderly manner. Using graphics or a few important parameters, the characteristics of a large amount of data can be expressed. This can avoid incorrect interpretations and reduce the cost of obtaining satisfactory data to a minimum, thereby improving economic benefits. The national standard "Statistical Processing and Interpretation of Data" includes the following items: Determination of statistical error range (GB/T3359) Estimation and confidence interval of the mean (GB/T3360) Comparison of two means in the case of paired observations (GB/T33G1) Estimation and test of a distribution parameter (GB/T 4088) Estimation and test of Poisson distribution parameters (GB/T4089) Normality test (GB/T4882)
- Normal sample outlier judgment and treatment (GB/T4883) Estimation and test of normal distribution mean and variance (GB/T4889) Power of normal distribution mean and variance test (GB/T4890) [Extreme value distribution Xiangben outlier judgment and treatment (GR/T6380) Gamma distribution (Pearson III Parameter estimation of exponential distribution (GB/T8055) Judgment and processing of sample outliers of exponential distribution (GB/T8056) "Statistical processing and interpretation of data Estimation and test of Poisson distribution parameters" There is no corresponding international standard. Partner Network
1 Scope
Statistical processing and interpretation of data
Estimation and test of Poisson distribution parameters
This standard is based on the Poisson distribution population, and the probability mass function of the distribution is: P(X = 2/) =
x-0.1.2...
Where>0 is the distribution parameter. This standard is based on independent random samples from the white population1, GB/T 4089-2008
., 2 specifies the methods of point estimation, interval estimation and test of parameters. This standard can be used when there is sufficient reason to believe that the population obeys Poisson distribution. 2 Normative references
The clauses in the following documents become clauses of this standard through reference in this standard. For any dated referenced document, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, parties to an agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this standard. GB/T4086.1 Statistical distribution numerical table Normal distribution GB/I4086.2 Statistical distribution numerical table 2 Distribution ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO3534-2:2006 Statistical vocabulary and symbols Part 2: Applied statistics 3 Terms, definitions and symbols
The terms, definitions and symbols determined by IS03534-1:2006 and IS03534-2:2006 and the following terms, definitions and symbols apply to this standard. For ease of reference, some terms and symbols are directly quoted from the above standards. 3.1 Terms and Definitions
The terms and definitions given in ISO 3534-1:2006 and TSO 3534-2:2006 apply to this standard. 3.2 Symbols
Sample size
Parameter of the sedative distribution
Lower confidence limit for the value in an interval estimate
Upper confidence limit for the value in an interval estimate
Significance level
Specified value for the probability of a type II error
Significance testProbability of a type I error, the probability of rejecting the null hypothesis when it is trueProbability of a type II error, the probability of not rejecting the null hypothesis when it is false<Significance test>Null hypothesis
Significance test>Alternative hypothesis
Probability of event A
Sample observations1,. . The sum of , T
<Interval estimation> Confidence level
GB/T 4089--2008
4 Parameter estimation
4.1 Point estimation
The estimate of is recorded as,
4.2 Interval estimation
4.2.1 Three forms of confidence intervals
There are three commonly used forms of confidence intervals entered: a) Two-sided confidence interval (,u), where 0Aru≤+αx b) One-sided confidence interval with only lower confidence limit (,+α), where,≥0. ) One-sided confidence interval with only upper confidence limit (0,), this ≥>0 Which type of confidence interval to choose should be determined according to the needs of the problem being studied. (1)
A, where input u is a function of the observed value. The confidence interval used in this standard satisfies the following conditions: the frequency of the event that the obtained confidence interval contains the true input value is approximately equal to the confidence level 1--α. Specifically, the two-sided interval should satisfy: P(>,<)<,1-α The one-sided confidence interval should satisfy:
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