Reza Habibi

A Note on Approximating Continuous Distribution Functions

Abtsrcat This paper deals with the approximation of distribution func- tions of complicated statistics using Beta distribution. The problem is motivated and the performance of our method is evaluated by several examples. Two methods are suggested to estimate the parameters of Beta distribution. We approximate distributions of cusum statistic and Hsus G test statistic by this method. Error analysis is given. Fitting the mixture of Beta distributions are examined. Finally, a discussion Section is given.

Sensor fault detection and isolation: a game theoretic approach

ABSTRACT This paper studies sensor fault detection using a game theoretic approach. Sensor fault detection is considered as change point analysis in the coefficients of a regression model. A new method for detecting faults, referred to as two-way fault detection, is introduced which defines a game between two players, i.e. the fault detectors. In this new strategic environment, assuming that the independent states of the regression model are known, the test statistics are derived and their finite sample distributions under the null hypothesis of no change are derived. These test statistics are useful for testing the fault existence, as well as, the pure and mixed Nash equilibriums are derived for at-most-one-change and epidemic change models. A differential game is also proposed and solved using the Pontryagin maximum principle. This solution is useful for studying the fault detection problem in unknown state cases. Kalman filter and linear matrix inequality methods are used in finding the Nash equilibrium for the case of unknown states. Illustrative examples are presented to show the existence of the Nash equilibriums. Also, the proposed fault detection scheme is numerically evaluated via its application on a practical system and its performance is compared with the cumulative sum method.

Change Points with Linear Trend in Exponential Family Distribution

This paper considers the change point problem with linear trend in independent exponential family distributed random variables. It is interested to test if all random variables are identically distributed against there is a linear trend change at an unknown period of time among parameters of distribution of random variables. Testing procedures, which are considered, are two likelihood ratio-type approaches and the usual likelihood ratio approach. The test statistics are derived and their asymptotic behaviors are studied. Next, the power of three tests are compared and the conclusions are given . Testing procedures are studied in well-known distributions of exponential family. A real data example is also considered. This paper extends the Gupta and Ramanayake (2001) work in exponential distribution to the exponential family distribution.