standard normal random variableとは 意味・読み方・使い方

名詞

standard normal random variable (複数形 standard normal random variables)

1. (probability theory, statistics) A random variable whose probability distribution is a standard normal distribution.
   • 2000, George E. Monahan, Management Decision Making: Spreadsheet modeling, analysis, and applications, Volume 1, Cambridge University Press, page 405,

     Suppose ${\displaystyle X\sim N(\mu ,\sigma )}$. Then

     ${\displaystyle Z={\frac {x-\mu }{\sigma }}}$

     is a standard normal random variable. In other words, any normal random variable can be standardized by subtracting the mean from the variable and dividing the difference by the standard deviation.

   • 2010, Todd C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Taylor & Francis (CRC Press), page 1,

     This technique is based on a polynomial transformation that proceeds by taking the sum of a linear combination of a standard normal random variable, its square, and its cube.

   • 2016, Maria Dolores Ugarte, Ana F. Militino, Alan T. Arnholt, Probability and Statistics with R, 2nd Edition, Taylor & Francis (CRC Press), page 297,

     A normal random variable with μ = 0 and σ = 1, often denoted Z, is called a standard normal random variable. […] Further, any normal random variable can be converted to a standard normal random variable using (4.25).