Dowd (version 0.12)

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

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: $$A^2=n\int_{-\infty}^{\infty}\frac{[\hat{F}(x)-F(x)]^2}{F(x)[1-F(x)]}dF(x)$$ which is equivalent to $$=-n-\frac{1}{n}\sum_{i=1}^n(2i-1)[\ln F(X_i)+\ln(1-F(X_{n+1-i}))]$$

Usage

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

Arguments

number.trials

Number of trials

sample.size

Sample size

confidence.interval

Confidence Interval

Value

• Confidence Interval for AD test statistic

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.

Examples

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