Descriptive measures for nominal categorical variables

Descriptive measures/statistics are tools to understand the features of a probability/frequency distribution. Not many descriptive measures/statistics have been attempted for nominal categorical data. The present paper is motivated to provide some sensible descriptive statistics, analogous to the variance, skewness, and kurtosis, for univariate nominal categorical data. The measures are illustrated by some real data. Some intuitive test procedures are also described in this context.