Statistical interpretation of data Parameter estimation for gamma distribution (Pearson 3 distribution)

This standard applies to various random variables that obey r distribution. This standard specifies the method for estimating the parameters of r distribution based on sample values. GB 8055-1987 Statistical processing and interpretation of data Parameter estimation of Pearson distribution GB8055-1987 Standard download decompression password: www.bzxz.net
This standard applies to various random variables that obey r distribution. This standard specifies the method for estimating the parameters of r distribution based on sample values.

1 Introduction
National Standard of the People's Republic of China
Statistical interpretation of dataParameter estimation for gamma distribution(Pearson I distribution)
1.1 Scope and purpose
UDC 519. 28
GB8055-87
This standard is applicable to various random variables that obey the distribution of gamma. This standard specifies the method of estimating the parameters of the distribution based on sample values. 1.2 Application conditions
The data obtained from measurement, experiment and investigation shall be subjected to theoretical analysis, empirical judgment or statistical test. If they obey the distribution of gamma, the point estimate and interval estimate of their parameters can be determined according to this standard. Terminology
The statistical terminology used in this standard can be found in GB3358--·82 "Statistical Terminology and Symbols". In addition, the terminology is also specified as follows:
2.1 Coefficient of skewness coefficient of Skewness The ratio of the third central moment of the population to the cube of the standard deviation. C, - E(X -- E(X))/(VE(X = E(X)))3Geometric mean of sample
2.2Geometric mean of sample
》The first power of the product of sampling units.
2.3Function
f--functiont
The ratio of the derivative of the function to the function.
tdr(m)/r(m）
W(m) = r(m)/l(m) (or
3 Symbols and their meanings
For ease of use, the symbols used in this standard and their meanings are listed in Appendix A (Supplement). 4 Point estimate of r distribution parameters
4.1 Point estimate of two-parameter T distribution
The density function of the two-parameter distribution is:
Approved by the National Bureau of Standards on September 2, 1987
Marked thin and slow figure
Water standard supply
The most important material sound special under the paragraph
1988-04-01
f(t; n,U) ?
GB 8055 --87
Jb1(m)(b
Where, m0 is the shape parameter: 0 is the scale parameter When, α, is the sample observation value, this section gives the point estimate of the parameter m. 4.1.1 Moment Estimation (n>10)
When the accuracy requirement is not high, this method can be used. Implementation steps:
Calculate the sample mean
Calculate the sample variance
Calculate the moment estimate of mbzxz.net
d. Calculate the moment estimate of the force
4.1.2 Maximum Likelihood Estimation (n≥[0)
·（2）
There are two methods for seeking maximum likelihood estimation, the approximate formula method and the Newton iteration method. The maximum likelihood estimation calculation error given by the approximate formula method can reach 10, and the Newton iteration method can give a higher calculation accuracy. In actual work, one of them can be selected according to needs. 4.1.2.1 Approximate formula method
Implementation steps:
Calculate the statistic
I -- Int -- Int
where a is the geometric mean of the sample.
b Calculate the maximum likelihood estimate of m
When 0
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