On Calculation of Failure Probability for Structures Designed Based on Magnitudes of Historical Event

During their operational life, structures may be subject to various types of live load caused by events such as earthquakes, high speed winds, etc. Given the design life of a structure, the probability for a specific live load to cause a failure depends on the magnitude of the load structure it is designed to withstand (designed load). In this article, methods are developed for calculation of the failure probability for structures designed to withstand loads comparable to historical loads at the site of interest

Survival Analysis of the Men’s 100 Meter Dash Record

In the 2012 Summer Olympics in London seven out of eight finalists in the men’s 100 meter dash crossed the finish line in under 10 seconds. This result and other recent performances of exceptional sprinters such as Bolt have made experts wonder, not whether a new record will be set, but when and how much it will lower the present record. Seeking an answer, some researchers have tried to model the available data with the goal of using them to predict future records. This article presents a different approach based on theory of records for independent and identically distributed observations. It modifies the number of attempts to break a record to make the results of the theory of records applicable to this situation. The modification is necessary because many sports records have been broken more frequently than what this theory predicts. Two modifications of the number of attempts are considered, fixed rate via a geometric increase, and random rate via a non-homogeneous Poisson process

Mathematical Modeling, a Small Step in a Right Direction

Models developed by mathematicians/statisticians based on criterion such as goodness of fit often leads to a “best” model only for the data utilized. Moreover the parameters in such models often do not have physical interpretations and as such their validity cannot be checked by other means. This article makes argument against modeling processes that do not incorporate information from discipline related to the origin of data and presents an example to demonstrate benefits of doing so

On survival times of sport records

AbstractSurvival of sport records is investigated assuming that the number of attempts to break a record is governed by a non-homogeneous Poisson process. Explicit formulae for two practical cases are derived, and their applications are demonstrated using an example

Probabilistic Analysis of a Table Tennis Game

A game of table tennis is analyzed using elementary concepts of calculus, probability, and linear algebra. The analysis includes modeling using different approaches and a comparison of the results obtained under the new and the old rules for the game. The analysis demonstrates the steps of a mathematic modeling and illustrates the possible expansion of it.

A Procedure for Prediction of Sports Records

Sports records are of great interest to physiologists, sport fans, and the public. Records set in different sports sheds light on human strengths and limitations and provides data for scientific investigations. This article presents a simple procedure for prediction of the future records. It is based on some results of theory of records for independent and identically distributed sequences. Adjustments are made to the data to insure the relevance of calculations and appropriateness of results. A procedure for estimation of ultimate records is also included.

A statistical conversion technique: Objective and perceptive financial measures of the performance construct

This study develops a statistical technique that allows comparison of objective and perceptive financial measures of the performance construct. The proposed technique provides a simple and statistically meaningful method for conversion of objective or archival financial data into scales that can be used for testing the convergent validity with corresponding perceptive measures of performance. Use of the proposed technique can enhance flexibility in application of data collected from different sources and strengthen the generalizability of the findings across studies in the strategic management literature. Empirical data of performance measures are used to demonstrate the use of the technique. © 2005 Sage Publications

Rule of Tangent for Win-By-Two Games

Our study of win-by-two tie games is motivated by a famous 2010 Wimbledon tennis match whose final set was decided by the improbable score of 70-68. We introduce a trigonometric interpretation of the odds of winning points and games in tennis when serving from deuce. We place this result in the more general setting of a gamblers ruin problem and also propose a performance measure to quantify the serving and receiving skill of one player relative to another. Then we extend the analysis to table tennis and volleyball. These latter games are similar to tennis in that the winner must obtain a certain minimum score while leading by two points, but they differ in their determination of which player serves a given rally and in whether a point is awarded to the receiver for winning a rally. We quantify the impact of these differences on the outcomes of games, assuming that the probability for a player to win a single point does not change during a game. We also apply a Markov chain analysis to arrive at our earlier results for tennis and to calculate the expected length of a game after reaching deuce. Finally, we develop the idea of equivalent games so that the analysis can be carried out using only the probability of winning a point (that is, without regard for the question of which player is serving).