Mathematical Statistics for Beginners

Abstract

At present a large inventory of discrete as well as continuous probability distributions are available. Mean, variance, skewness, and kurtosis are a set of constants of a probability distribution, which are useful for describing its properties and under certain circumstances for specifying it. These constants depend on the distribution of the random variable. Extensive knowledge on integration, differentiation and summation are required to find mean, variance, skewness and kurtosis of any probability distribution. It is difficult to explain these to students with limited knowledge in mathematics. This book derived and applied general formulae to directly find mean, variance, skewness and kurtosis, instead of using integration or differentiation or summation methods. General formulae for the determination of characteristic function, Laplace transform and moments of various distributions belonging to the transformed Chi-square family, generalized gamma family, generalized family of discrete distributions and log type distributions are derived and applied. This book also derives general formulae for finding point and interval estimators of function of parameters, identification of best population in the transformed Chi-square family including probability of correct identification. This book introduced and applied an easy method for selecting null and alternative hypotheses, finding p-values and taking decisions.