A Study on Runs and Related Random Variables

In the statistical theory, one of the major areas of studies is 'study of random variables'. where random variables are mapping from sample space to real line. Sample space is collection of all possible outcomes of the random experiment under consideration. Study of random variables includes the following. (1) Derivation of probability mass function/probability distribution function. (2) Evaluation of expression of raw moments,moment generating function,median,mode etc. (3) Its relation with other random variables. Generally one main thing associated with random variables is parameter. Inference aspect of the parameter is also main topic. Many times we are carrying out parametric inference but in a number of cases we have to deal with an- other major branch subject Statistics namely nonparametric inference. This subject of nonparametric inference is a well developed subject and a number of quality text books are available for students, teachers and researchers. Generally in nonparametric inference various tests such as Sign test, Run test, Median test, Wilcoxon test etc. are used. Run test is one of the major tools.