This book aims to provide a thorough understanding of distribution theory and data analysis using statistical software to solve problems related to basic statistics, probability models, and simulation. The volume provides a detailed concept of different distributions used in statistics with their application in real-life situations. Covering the analytical aspects using the latest software, the volume discusses stochastic methods and other statistical methods. It provides statistical data analysis by taking multiple actual situations using the open-source software R version 4.0 and Python 3.0+. A detailed study of the statistical models is provided with examples related to health, agriculture, insurance, and other sectors. Each chapter will help you to increase your knowledge starting from basic statistics to advanced statistics. Key features: Discusses the importance of probability in the field of applied statistics and its importance in day-to-day life Discusses methods for graphical representations and summary statistics with the help of numerous examples related to actual situations Considers which distribution theories should be applied in different situations Shows how to handle real-life problems related to probability Introduces different ways of data handling using various software Topics include random variables, statistical properties and theorems, discrete probability models, Weibull distributions, sample generation, Pareto and Burr distributions, data analysis through the freely available statistical package Python, and more. Written clearly for both students and researchers, this volume will be a valuable resource on distribution theories and their applications.