Miscellaneous Subjects

This chapter discusses combinatorics in terms of permutations, combinations and the gamma function. These subjects enable counting possibilities in statistics. The chapter describes the power functions and asymptotic behaviour by using Taylor and Maclaurin series, polynomial fitting, and power function fitting. The power function fitting is used extensively for bias and variance description. The chapter elaborates the unweighted and the weighted least‐squares techniques together with error analysis and regression‐based confidence limits. It discusses systematic sampling, numerical integration and expected values, ranked samples with confidence limits, Monte Carlo experiments, and random number generators to illustrate the meaning of beta distribution‐based and regression‐based confidence limits. The chapter describes hypothesis testing by using null hypothesis and alternative hypothesis together with Type I and Type II errors. Approximations for the normal distribution using Taylor series and the power function fitting are also discussed.