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Carlo Beenakker
Carlo Beenakker
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For small $n$ Monte Carlo integration is not needed, so for example,. For $n$ up to 100 see Kolmogorov-Smirnov Tests when Parameters are Estimated with Applications to Tests of Exponentiality and Tests on Spacings by J. Durbin for $n$ up to 100 (table 3).

These exact results were used to construct the Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions. There are also analytical approximations, see An Analytic Approximation to the Distribution of Lilliefors’s Test Statistic for Normality.

For small $n$ Monte Carlo integration is not needed, so for example, Kolmogorov-Smirnov Tests when Parameters are Estimated with Applications to Tests of Exponentiality and Tests on Spacings by J. Durbin for $n$ up to 100 (table 3).

These exact results were used to construct the Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions. There are also analytical approximations, see An Analytic Approximation to the Distribution of Lilliefors’s Test Statistic for Normality.

For small $n$ Monte Carlo integration is not needed. For $n$ up to 100 see Kolmogorov-Smirnov Tests when Parameters are Estimated with Applications to Tests of Exponentiality and Tests on Spacings (table 3).

These exact results were used to construct the Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions. There are also analytical approximations, see An Analytic Approximation to the Distribution of Lilliefors’s Test Statistic for Normality.

Source Link
Carlo Beenakker
Carlo Beenakker
  • 188.1k
  • 18
  • 448
  • 651

For small $n$ Monte Carlo integration is not needed, so for example, Kolmogorov-Smirnov Tests when Parameters are Estimated with Applications to Tests of Exponentiality and Tests on Spacings by J. Durbin for $n$ up to 100 (table 3).

These exact results were used to construct the Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions. There are also analytical approximations, see An Analytic Approximation to the Distribution of Lilliefors’s Test Statistic for Normality.