ADTestStat function

Plots cumulative density for AD test and computes confidence interval for AD test stat.

Anderson-Darling(AD) test can be used to carry out distribution equality test and is similar to Kolmogorov-Smirnov test. AD test statistic is defined as: [REMOVE_ME]$A^2=n\int_{-\infty}^{\infty}\frac{[\hat{F}(x)-F(x)]^2}{F(x)[1-F(x)]}dF(x) [REMOVE_ME_2]$

which is equivalent to [REMOVE_ME]$=-n-\frac{1}{n}\sum_{i=1}^n(2i-1)[\ln F(X_i)+\ln(1-F(X_{n+1-i}))] [REMOVE_ME_2]$

ADTestStat(number.trials, sample.size, confidence.interval)

Arguments

• number.trials: Number of trials
• sample.size: Sample size
• confidence.interval: Confidence Interval

Returns

Confidence Interval for AD test statistic

Description

Anderson-Darling(AD) test can be used to carry out distribution equality test and is similar to Kolmogorov-Smirnov test. AD test statistic is defined as:

which is equivalent to

Examples

# Probability that the VaR model is correct for 3 failures, 100 number
   # observations and  95% confidence level
   ADTestStat(1000, 100, 0.95)

Author(s)

Dinesh Acharya

References

Dowd, K. Measuring Market Risk, Wiley, 2007.

Anderson, T.W. and Darling, D.A. Asymptotic Theory of Certain Goodness of Fit Criteria Based on Stochastic Processes, The Annals of Mathematical Statistics, 23(2), 1952, p. 193-212.

Kvam, P.H. and Vidakovic, B. Nonparametric Statistics with Applications to Science and Engineering, Wiley, 2007.