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This book discusses diverse concepts and notions - and their applications - concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In...

This book is devoted to the fundamentals of order and rank statistics. Primarily focusing on theoretical properties, it also discusses practical aspects, including interesting applications of step and impulse functions for the distribution of random variables, magnitudes, and signs. New concepts are introduced, such as independent and semi-identically distributed random vectors and probability density-mass functions. This book also presents an investigation of relative magnitudes in order statistics, and of correlation coefficients among signs, ranks, and magnitudes.

The basic...