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The computation of standard normal distribution integral in any required precision based on reliability method

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  • Yuge Dong
  • Haimeng Zhang
  • Liangguo He
  • Can Wang
  • Minghui Wang

Abstract

Based on reliability theory, the value of the standard normal distribution integral can be obtained by calculating the probability of the failure domain of the linear performance function. After the sample space is divided into some sub-sample spaces, a number of sub-failure domains are obtained. In the paper, the methods of computing the probabilities of sub-failure domains are discussed. All the formulae and the steps of computing the standard normal distribution integral which meet any required precision are given in the paper. Examples show that it is easy for the method to compute the standard normal distribution integral.

Suggested Citation

  • Yuge Dong & Haimeng Zhang & Liangguo He & Can Wang & Minghui Wang, 2019. "The computation of standard normal distribution integral in any required precision based on reliability method," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(6), pages 1517-1528, March.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:6:p:1517-1528
    DOI: 10.1080/03610926.2018.1433855
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    Cited by:

    1. Yuge Dong & Qingtong Xie & Shuguang Ding & Liangguo He & Hu Wang, 2022. "The evaluation of bivariate normal probabilities for failure of parallel systems," Statistical Papers, Springer, vol. 63(5), pages 1585-1614, October.

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