Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Theodoropoulou Vasiliki
Supervisors info:
Παπαδάτος Νικόλαος Αναπληρωτής Καθηγητής Ε.Κ.Π.Α
Οικονόμου Αντώνιος Καθηγητής Ε.Κ.Π.Α
Τρέβεζας Σάμης Λέκτορας Ε.Κ.Π.Α
Original Title:
Εκτιμήσεις της Απόστασης Ολικής Κύμανσης και Εφαρμογές
Translated title:
Estimations of the Total Variation Distance and Applications
Summary:
In this postgraduate thesis we study the total variation distance between two probability distributions.
In the first chapter we mention some general properties and basic theorems.
In the second chapter we give an application of the total variation distance to the matching problem. Also, we study a new distance which is called ¨Factorial Moment Distance¨.
Ιn the third chapter we refer to the Poisson approach, which is one of the most important areas of Applies Probabilities and many researchers have studied it systematically. This is possible with an alternative method based on the meaning of w-functions. Finding appropriate upper bounds (near to 0) of the total variation distance between two distributions is a way of calculating the error which is derived from the approach.
In the fourth chapter is proved a convolution inequality for the standardized sum of independent absolutely continuous random variables.
Based on the inequality, provided that the support of the random variables is an interval, is proved the rate of convergence in total variation of the standardized sums of independent and identically distributed random variables to the standard normal Z. Also, we give applications in random sums.
In the fifth chapter we mention that there exists a new random variable which can be viewed as a transformation of X with a unimodal density, satisfying the covariance identity. We mention the properties of the random variable and an application to variance bounds.
In the sixth chapter upper bounds for the total variation distance between two
absolutely continuous random variables X and Y are obtained. Also, we give a proof of the local limit theorem.
Main subject category:
Science
Keywords:
total variation distance, factorial moment distance, transformation of random variable, matching problem, Poisson approach, covariance identity, w-function
