Edited by

Dr. M. Shafiqur Rahman
Department of Operations Management and Business Statistics College of Economics and Political Science Sultan Qaboos University Muscat, Sultanate of Oman.

ISBN 978-93-91882-17-4 (Print)
ISBN 978-93-91882-18-1 (eBook)
DOI: 10.9734/bpi/mono/978-93-91882-17-4

Social science, commerce and business students usually have limited knowledge in mathematics, especially in algebra and calculus. Mathematical Statistics deals with probability distributions of random variables, their properties, estimation and test of hypothesis regarding the parameters of probability distributions. Currently many discrete and 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. Conventional methods for finding these constants are difficult, lengthy and time consuming. These methods require extensive knowledge on integration, differentiation and summation. It is difficult to explain these to students with limited knowledge in mathematics.

This book derives general formulae for finding mean, variance, skewness, kurtosis, moments, cumulants of any probability distribution belonging to some family of discrete as well as continuous probability distributions such as generalized family of discrete distributions (GFDD), Class of log-type distributions (CLD), Generalized gamma (GG), Transformed Chi-square family (TCF), etc. This book also derives general formulae for finding point and interval estimators of function of parameters, identification of best population in the TCF including probability of correct identification. Just by looking at the probability density function of a probability distribution one can easily apply these formulae without using integration, differentiation or summation rules. The purpose of this book is to offer a time-saving device for students with limited mathematical knowledge.

This book is based on the important contributions in Mathematical Statistics by Dr. M. S. Rahman and his co-authors named Professor R.P. Gupta (Former Professor, Department of Mathematics, Statistics and Computer Science, Dalhousie University, Canada), Professor M. A. Karim (Department of Statistics, Chittagong University, Bangladesh), Mrs. Syfun Nahar (Adjunct Lecturer, Department of OMBS, CEPS, SQU, Oman), and Mr. Rock Abulaka (Lecturer, Department of Mathematics, Statistics and Computer Science, UPNG). Mr. Rock Abulaka is a student of Dr. M. S. Rahman. I express my deepest sense of gratitude to Professor R.P. Gupta for his guidance and encouragement. It was a privilege and a pleasure to work with him. I am deeply indebted to my co-authors. It is impossible to acknowledge the cooperation of many people and friends whose direct and indirect influence has increased the quality of this book. Valuable comments from the reviewers are highly acknowledged. I would like to thank Sultan Qaboos University authority for giving me faculty position and office where I have worked afterhours and used University facilities to complete this book. Deepest appreciation and many thanks are due to my family members for their love, inspiration, and sacrifice during the research period.

I expect this book will be useful for all Statistics students and researchers to understand Mathematical Statistics having limited knowledge in Mathematics.

Media Promotion

### Content

##### Mathematical Statistics for Beginners

M. Shafiqur Rahman

Mathematical Statistics for Beginners, 30 August 2021, Page 1-100
https://doi.org/10.9734/bpi/mono/978-93-91882-17-4

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.