The confidence interval of quantile Xp for normal distribution

This standard specifies the method for determining the quantile x and confidence interval based on samples and given confidence levels when the product characteristic values ​​follow a normal distribution and the mean and standard deviation are unknown. This standard applies to situations where the product characteristic values ​​have been verified to follow a normal distribution. GB 10094-1988 Normal distribution quantile confidence interval GB10094-1988 standard download decompression password: www.bzxz.net
This standard specifies the method for determining the quantile x and confidence interval based on samples and given confidence levels when the product characteristic values ​​follow a normal distribution and the mean and standard deviation are unknown. This standard applies to situations where the product characteristic values ​​have been verified to follow a normal distribution.

National Standard of the People's Republic of China
The confidence interval of quantile xpfor normal distribution
1 Subject content and scope of application
UDC 519.2
GB10094:88
This standard specifies the method for determining the quantile and confidence interval based on the sample and given water when the product characteristic values ​​obey the normal distribution and the mean and standard deviation are unknown.
This standard applies to the situation where the product characteristic values ​​have been verified to follow the normal distribution. 2
Referenced standards
GB3187 Basic terms and definitions of reliability GB3358 Statistical terms and symbols
GB4885 Normal distribution study Full sample reliability One-sided trade credit lower limit GB1086.1～1086.6 Statistical distribution value table 3 Symbol
Sample size
Sample, individual characteristic value||t t||Sample mean
Sample variance
Confidence level
Quantile of probability distribution
, one-sided confidence upper limit of
, one-sided confidence lower limit of
One-sided statistical tolerance limit coefficient of normal distribution
『Function
Confidence limit calculation formula
4.1 One-sided confidence lower limit
State Administration of Technical Supervision 1988-12-10 published r
I(n + 1) n(n) and (
1989-10-01 implementation
GB10094-88
The confidence level of the normal distribution quantile is 1-α. The one-sided confidence lower limit is: when p≤0.50, SA
When p≥ 0. 50.C - r -f- sh.. Among them:, check the table of one-sided statistical tolerance limit coefficients of normal distribution with sample size n, R=1-,?=α; check the table of one-sided statistical tolerance limit coefficients of normal distribution with sample size n, R 1 -
normalized one-sided statistical tolerance limit coefficient table of normal distribution. 4.2 One-sided confidence upper limit
The one-sided confidence upper limit of the normal distribution quantile with a confidence level of 1-α is: when p≤0.50, Cu=-SKa;
When p>0.50.Cu=+SKl
Where: The method for checking the values ​​of person. and person. is the same as the method for checking K. and Ka in Article 4.1. 4.3 Bilateral confidence upper and lower limits
The normal distribution quantile, with a confidence level of 1-, has a bilateral confidence lower limit: when ≤0.50, 8K1
When p≥0.50, Ct=Yuan+SK
The bilateral confidence upper limit is:
When ≤0.50, Cu-SK
When p≥0.50.Cc= +8kl-
Where: The value is checked in the table of one-sided statistical allowable limit coefficients of normal distribution with sample size n, R=1—, small is n, R=p, y=
·（3）
·（4）
; K1-The value is checked in the table of one-sided statistical allowable limit coefficients of normal distribution with sample size large. 4.4 This standard gives p equal to 10-7, 10*10-5, 10-1, 10-\, 0. 0.1, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 0.95, 0.99, 0.999, 0.9999, 0.95, 0.9°, 0.9°, 0.9°, the one-sided lower confidence limit, one-sided upper confidence limit, two-sided upper and lower confidence limits of the normal distribution quantile z. 5 K coefficient table and its approximate formula
5.1 The exact value table of K coefficient used in this standard is given by the "one-sided statistical allowable limit coefficient table of normal distribution" in GB4885, where \ = 2(1)50(10)120.
5.2When n≥10, P≤0.15, the approximate formula of K coefficient is: Ka
af,-.(fa, fr)
PF-a(fi,J2)
where: ., is the 1-p quantile of the standard normal distribution; fh 2 ng;
·（5）
·（6)
GB10094--88
T(n/2)
·（8)
Since fi and f2 are not necessarily integers, Ft-a(Ji,f) can be linearly interpolated using the F distribution table, or using the Paulson-Takeuchi approximate formula: Let: F1-（J1J2）=9, then the equation
(+ 2()(+·( The larger of the two roots 312 in 0
is [F1-(f1, 2). When = 0.05, the absolute error at 1f:5 is 6×10-2, and the relative error at j1, f210 is no more than 10-3. 323
GB10094—88
Appendix A
(reference)
The rainfall data of a city measured by a meteorological station in 1972 are as follows: 1063.8
After inspection, the annual rainfall follows a normal distribution. Find the bilateral confidence limits of the 10% quantile T0.1 and the 90% quantile 0.gm when the confidence level is 0.90.
The sample mean and sample standard deviation calculated from the data are: z = 1154.782
S = 195. 162
From formula (3) and (4), when the confidence level is 0.90, the upper and lower confidence limits of 10.10 are: Ct = - SKo. 95
Cu — SK0.05
%0.9a's upper and lower confidence limits are: Cu=i+ SKo.D5.
Cu=i+SKo.95
When 72 and R0.90, the K coefficient table shows: Ko.05 = 1. 043
Therefore, the lower and upper confidence limits of 0.10 are: Ko.95 1. 577
Ct = 1154. 782 - 195. 162 X 1. 577 = 847. 012Cu = 1154.782 — 195. 162 X 1. 043 = 951. 228324
1o.90The lower and upper limits of the bilateral confidence interval are: GB10094-88
CL = 1154. 782 + 195. 162 X 1. 043 = 1358. 336Cu=1154.782+195.162×1.577=1462.552A2The life distribution of a certain high-temperature alloy steel is log-normal distribution. Twelve specimens were taken for life test at 660C temperature and 4kgf/mm2 stress, and the data were as follows: 935, 1025, 1081, 1180, 1197, 1234, 1328, 1521, 1621, 1621, 16941933h. Find the lower confidence limit of the reliable life t0.9g with a reliability of 0.99 and a confidence level of 0.90. Take the logarithm of the test value t., that is: 1nt, then, ratio 2,,, is a sample taken from a normal population, from which we can calculate: 1-7.1949
S = 0.2258
The reliable life t0.99 corresponds to the 1% quantile 0.01 of the normal distribution, and its confidence level is 0.90. The lower confidence limit is: Ct = -SKn.90
For n = 12, = 1 α = 0.90, R 1 = 0.99, we can check the coefficient table to get: Ko.90 3.371Www.bzxZ.net
So the confidence level of the reliable life to.99 is 0.90. The lower confidence limit is: (to.9g) -et = exp(7.1949 - 0.2258 × 3. 371)=622.47h
Additional remarks;
This standard was proposed by the National Technical Committee for Standardization of Statistical Methods Application. This standard was drafted by the Working Group of the Reliability Statistics Subcommittee of the National Technical Committee for Standardization of Statistical Methods Application. The main drafter of this standard was Wang Lingling.
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