Stein's method

<p>Stein's method is a general method in <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> to obtain bounds on the distance between two <a href="/facts/Probability_distributions/EpsKKVRu">probability distributions</a> with respect to a <a href="/facts/Probability_metric/u6kgN8Dc">probability metric</a>. It was introduced by <a href="/facts/Charles_Stein_(statistician)/zoz8RXWn">Charles Stein</a>, who first published it in 1972, to obtain a bound between the distribution of a sum of 
  
    
      
        m
      
    
    {\displaystyle m}
  
-dependent sequence of <a href="/facts/Random_variables/TwTBXnLT">random variables</a> and a <a href="/facts/Normal_distribution/UapjjPyQ">standard normal distribution</a> in the <a href="/facts/Uniform_norm/5yIkjNE3">Kolmogorov (uniform) metric</a> and hence to prove not only a <a href="/facts/Central_limit_theorem/0gc2L0Wd">central limit theorem</a>, but also bounds on the rates of <a href="/facts/Limit_of_a_sequence/Ktge2RwL">convergence</a> for the given metric.
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Stein's method open-in-new

Stein's method