Statistics

2407 Submissions

[2] viXra:2407.0015 [pdf] submitted on 2024-07-02 06:50:01

Introduction to the Probability Theory

Authors: Taha Sochi
Comments: 185 Pages.

This book is a collection of notes and solved problems about probability theory. The book also contains proposed exercises attached to the solved problems as well as computer codes (in C++ language) added to some of these problems for the purpose of calculation, test and simulation. Illustrations (such as figures and tables) are added when necessary or appropriate to enhance clarity and improve understanding. In most cases intuitive arguments and methods are used to make the notes and solutions natural and instinctive. Like my previous books, maximum clarity was one of the main objectives and criteria in determining the style of writing, presenting and structuring the book as well as selecting its contents.
Category: Statistics

[1] viXra:2407.0002 [pdf] submitted on 2024-07-01 14:25:14

Hybrid Approach of Hypothesis Testing to Test the Mean Difference Between Two Groups Utilising Gaussian Distribution and Confidence Interval

Authors: Kazi Sakib Hasan
Comments: 24 Pages.

This paper presents an easier and new robust method for hypothesis testing to conclude significant mean differences between two independent or paired samples using the concepts of location, variability, confidence intervals and Gaussian distribution. For hypothesis testing of two samples, t-test is widely used. Beside this, Wilcoxon signed-rank test and often permutation test is also conducted. Each of these methods have their own rigorousness and drawbacks for which general people and non-statistics students often find it hard to conduct experiments using these. To fix these issues, a new method of hypothesis testing is proposed in this paper that basically utilises the properties of normally distributed data and resampling, and is relatively easier to calculate using only pen and paper. The time complexity analysis of each program is also conducted to give a concise overview about which hypothesis testing algorithm is more efficient and faster to execute, since statisticians use a lot of software nowadays for their analytical tasks.
Category: Statistics