The purpose of this book is to postulate some theories and test them numerically.
Estimation is often a difficult task and it has wide application in social sciences and
financial market. In order to obtain the optimum efficiency for some classes of
estimators, we have devoted this book into three specialized sections.
This paper considers the problem of estimating the population mean using
information on auxiliary variable in presence of non response. Exponential ratio and
exponential product type estimators have been suggested and their properties are studied. An
empirical study is carried out to support the theoretical results.
Authors: David D. Tung
Comments: 27 Pages.
In this paper, we will investigate the problem of obtaining
confidence intervals for a baseball team's Pythagorean expectation, i.e.
their expected winning percentage and expected games won. We study
this problem from two different perspectives. First, in the framework
of regression models, we obtain confidence intervals for prediction, i.e.
more formally, prediction intervals for a new observation, on the basis
of historical binomial data for Major League Baseball teams from the
1901 through 2009 seasons, and apply this to the 2009 MLB regular
season. We also obtain a Scheffé-type simultaneous prediction band
and use it to tabulate predicted winning percentages and their
prediction intervals, corresponding to a range of values for log(RS=RA).
Second, parametric bootstrap simulation is introduced as a data-driven,
computer-intensive approach to numerically computing confidence
intervals for a team's expected winning percentage. Under the
assumption that runs scored per game and runs allowed per game are
random variables following independent Weibull distributions, we
numerically calculate confidence intervals for the Pythagorean expectation
via parametric bootstrap simulation on the basis of each team's runs
scored per game and runs allowed per game from the 2009 MLB
regular season. The interval estimates, from either framework, allow us to
infer with better certainty as to which teams are performing above or
below expectations. It is seen that the bootstrap confidence intervals
appear to be better at detecting which teams are performing above
or below expectations than the prediction intervals obtained in the
In this book, for the first time we introduce the notions of Ngroups,
N-semigroups, N-loops and N-groupoids. We also
define a mixed N-algebraic structure. We expect the reader to be
well versed in group theory and have at least basic knowledge
about Smarandache groupoids, Smarandache loops,
Smarandache semigroups and bialgebraic structures and
Smarandache bialgebraic structures.